Markov-modulated and feedback fluid queues

NARCIS (Netherlands)

Scheinhardt, Willem R.W.

1998-01-01

In the last twenty years the field of Markov-modulated fluid queues has received considerable attention. In these models a fluid reservoir receives and/or releases fluid at rates which depend on the actual state of a background Markov chain. In the first chapter of this thesis we give a short

Poisson processes

NARCIS (Netherlands)

Boxma, O.J.; Yechiali, U.; Ruggeri, F.; Kenett, R.S.; Faltin, F.W.

2007-01-01

The Poisson process is a stochastic counting process that arises naturally in a large variety of daily life situations. We present a few definitions of the Poisson process and discuss several properties as well as relations to some well-known probability distributions. We further briefly discuss the

Semi-Markov processes

CERN Document Server

Grabski

2014-01-01

Semi-Markov Processes: Applications in System Reliability and Maintenance is a modern view of discrete state space and continuous time semi-Markov processes and their applications in reliability and maintenance. The book explains how to construct semi-Markov models and discusses the different reliability parameters and characteristics that can be obtained from those models. The book is a useful resource for mathematicians, engineering practitioners, and PhD and MSc students who want to understand the basic concepts and results of semi-Markov process theory. Clearly defines the properties and

A relation between non-Markov and Markov processes

International Nuclear Information System (INIS)

Hara, H.

1980-01-01

With the aid of a transformation technique, it is shown that some memory effects in the non-Markov processes can be eliminated. In other words, some non-Markov processes are rewritten in a form obtained by the random walk process; the Markov process. To this end, two model processes which have some memory or correlation in the random walk process are introduced. An explanation of the memory in the processes is given. (orig.)

Poisson Processes in Free Probability

OpenAIRE

An, Guimei; Gao, Mingchu

2015-01-01

We prove a multidimensional Poisson limit theorem in free probability, and define joint free Poisson distributions in a non-commutative probability space. We define (compound) free Poisson process explicitly, similar to the definitions of (compound) Poisson processes in classical probability. We proved that the sum of finitely many freely independent compound free Poisson processes is a compound free Poisson processes. We give a step by step procedure for constructing a (compound) free Poisso...

Poisson branching point processes

International Nuclear Information System (INIS)

Matsuo, K.; Teich, M.C.; Saleh, B.E.A.

1984-01-01

We investigate the statistical properties of a special branching point process. The initial process is assumed to be a homogeneous Poisson point process (HPP). The initiating events at each branching stage are carried forward to the following stage. In addition, each initiating event independently contributes a nonstationary Poisson point process (whose rate is a specified function) located at that point. The additional contributions from all points of a given stage constitute a doubly stochastic Poisson point process (DSPP) whose rate is a filtered version of the initiating point process at that stage. The process studied is a generalization of a Poisson branching process in which random time delays are permitted in the generation of events. Particular attention is given to the limit in which the number of branching stages is infinite while the average number of added events per event of the previous stage is infinitesimal. In the special case when the branching is instantaneous this limit of continuous branching corresponds to the well-known Yule--Furry process with an initial Poisson population. The Poisson branching point process provides a useful description for many problems in various scientific disciplines, such as the behavior of electron multipliers, neutron chain reactions, and cosmic ray showers

Information transfer with rate-modulated Poisson processes: a simple model for nonstationary stochastic resonance.

Science.gov (United States)

Goychuk, I

2001-08-01

Stochastic resonance in a simple model of information transfer is studied for sensory neurons and ensembles of ion channels. An exact expression for the information gain is obtained for the Poisson process with the signal-modulated spiking rate. This result allows one to generalize the conventional stochastic resonance (SR) problem (with periodic input signal) to the arbitrary signals of finite duration (nonstationary SR). Moreover, in the case of a periodic signal, the rate of information gain is compared with the conventional signal-to-noise ratio. The paper establishes the general nonequivalence between both measures notwithstanding their apparent similarity in the limit of weak signals.

Some performance measures for vacation models with a batch Markovian arrival process

Directory of Open Access Journals (Sweden)

Sadrac K. Matendo

1994-01-01

Full Text Available We consider a single server infinite capacity queueing system, where the arrival process is a batch Markovian arrival process (BMAP. Particular BMAPs are the batch Poisson arrival process, the Markovian arrival process (MAP, many batch arrival processes with correlated interarrival times and batch sizes, and superpositions of these processes. We note that the MAP includes phase-type (PH renewal processes and non-renewal processes such as the Markov modulated Poisson process (MMPP.

Two-state Markov-chain Poisson nature of individual cellphone call statistics

Science.gov (United States)

Jiang, Zhi-Qiang; Xie, Wen-Jie; Li, Ming-Xia; Zhou, Wei-Xing; Sornette, Didier

2016-07-01

Unfolding the burst patterns in human activities and social interactions is a very important issue especially for understanding the spreading of disease and information and the formation of groups and organizations. Here, we conduct an in-depth study of the temporal patterns of cellphone conversation activities of 73 339 anonymous cellphone users, whose inter-call durations are Weibull distributed. We find that the individual call events exhibit a pattern of bursts, that high activity periods are alternated with low activity periods. In both periods, the number of calls are exponentially distributed for individuals, but power-law distributed for the population. Together with the exponential distributions of inter-call durations within bursts and of the intervals between consecutive bursts, we demonstrate that the individual call activities are driven by two independent Poisson processes, which can be combined within a minimal model in terms of a two-state first-order Markov chain, giving significant fits for nearly half of the individuals. By measuring directly the distributions of call rates across the population, which exhibit power-law tails, we purport the existence of power-law distributions, via the ‘superposition of distributions’ mechanism. Our findings shed light on the origins of bursty patterns in other human activities.

Reviving Markov processes and applications

International Nuclear Information System (INIS)

Cai, H.

1988-01-01

In this dissertation we study a procedure which restarts a Markov process when the process is killed by some arbitrary multiplicative functional. The regenerative nature of this revival procedure is characterized through a Markov renewal equation. An interesting duality between the revival procedure and the classical killing operation is found. Under the condition that the multiplicative functional possesses an intensity, the generators of the revival process can be written down explicitly. An intimate connection is also found between the perturbation of the sample path of a Markov process and the perturbation of a generator (in Kato's sense). The applications of the theory include the study of the processes like piecewise-deterministic Markov process, virtual waiting time process and the first entrance decomposition (taboo probability)

Histogram bin width selection for time-dependent Poisson processes

International Nuclear Information System (INIS)

Koyama, Shinsuke; Shinomoto, Shigeru

2004-01-01

In constructing a time histogram of the event sequences derived from a nonstationary point process, we wish to determine the bin width such that the mean squared error of the histogram from the underlying rate of occurrence is minimized. We find that the optimal bin widths obtained for a doubly stochastic Poisson process and a sinusoidally regulated Poisson process exhibit different scaling relations with respect to the number of sequences, time scale and amplitude of rate modulation, but both diverge under similar parametric conditions. This implies that under these conditions, no determination of the time-dependent rate can be made. We also apply the kernel method to these point processes, and find that the optimal kernels do not exhibit any critical phenomena, unlike the time histogram method

Histogram bin width selection for time-dependent Poisson processes

Energy Technology Data Exchange (ETDEWEB)

Koyama, Shinsuke; Shinomoto, Shigeru [Department of Physics, Graduate School of Science, Kyoto University, Sakyo-ku, Kyoto 606-8502 (Japan)

2004-07-23

In constructing a time histogram of the event sequences derived from a nonstationary point process, we wish to determine the bin width such that the mean squared error of the histogram from the underlying rate of occurrence is minimized. We find that the optimal bin widths obtained for a doubly stochastic Poisson process and a sinusoidally regulated Poisson process exhibit different scaling relations with respect to the number of sequences, time scale and amplitude of rate modulation, but both diverge under similar parametric conditions. This implies that under these conditions, no determination of the time-dependent rate can be made. We also apply the kernel method to these point processes, and find that the optimal kernels do not exhibit any critical phenomena, unlike the time histogram method.

A new approach for handling longitudinal count data with zero-inflation and overdispersion: poisson geometric process model.

Science.gov (United States)

Wan, Wai-Yin; Chan, Jennifer S K

2009-08-01

For time series of count data, correlated measurements, clustering as well as excessive zeros occur simultaneously in biomedical applications. Ignoring such effects might contribute to misleading treatment outcomes. A generalized mixture Poisson geometric process (GMPGP) model and a zero-altered mixture Poisson geometric process (ZMPGP) model are developed from the geometric process model, which was originally developed for modelling positive continuous data and was extended to handle count data. These models are motivated by evaluating the trend development of new tumour counts for bladder cancer patients as well as by identifying useful covariates which affect the count level. The models are implemented using Bayesian method with Markov chain Monte Carlo (MCMC) algorithms and are assessed using deviance information criterion (DIC).

Space-time-modulated stochastic processes

Science.gov (United States)

Giona, Massimiliano

2017-10-01

Starting from the physical problem associated with the Lorentzian transformation of a Poisson-Kac process in inertial frames, the concept of space-time-modulated stochastic processes is introduced for processes possessing finite propagation velocity. This class of stochastic processes provides a two-way coupling between the stochastic perturbation acting on a physical observable and the evolution of the physical observable itself, which in turn influences the statistical properties of the stochastic perturbation during its evolution. The definition of space-time-modulated processes requires the introduction of two functions: a nonlinear amplitude modulation, controlling the intensity of the stochastic perturbation, and a time-horizon function, which modulates its statistical properties, providing irreducible feedback between the stochastic perturbation and the physical observable influenced by it. The latter property is the peculiar fingerprint of this class of models that makes them suitable for extension to generic curved-space times. Considering Poisson-Kac processes as prototypical examples of stochastic processes possessing finite propagation velocity, the balance equations for the probability density functions associated with their space-time modulations are derived. Several examples highlighting the peculiarities of space-time-modulated processes are thoroughly analyzed.

(Quasi-)Poisson enveloping algebras

OpenAIRE

Yang, Yan-Hong; Yao, Yuan; Ye, Yu

2010-01-01

We introduce the quasi-Poisson enveloping algebra and Poisson enveloping algebra for a non-commutative Poisson algebra. We prove that for a non-commutative Poisson algebra, the category of quasi-Poisson modules is equivalent to the category of left modules over its quasi-Poisson enveloping algebra, and the category of Poisson modules is equivalent to the category of left modules over its Poisson enveloping algebra.

Process Algebra and Markov Chains

NARCIS (Netherlands)

Brinksma, Hendrik; Hermanns, H.; Brinksma, Hendrik; Hermanns, H.; Katoen, Joost P.

This paper surveys and relates the basic concepts of process algebra and the modelling of continuous time Markov chains. It provides basic introductions to both fields, where we also study the Markov chains from an algebraic perspective, viz. that of Markov chain algebra. We then proceed to study

Process algebra and Markov chains

NARCIS (Netherlands)

Brinksma, E.; Hermanns, H.; Brinksma, E.; Hermanns, H.; Katoen, J.P.

2001-01-01

This paper surveys and relates the basic concepts of process algebra and the modelling of continuous time Markov chains. It provides basic introductions to both fields, where we also study the Markov chains from an algebraic perspective, viz. that of Markov chain algebra. We then proceed to study

Nonlinearly perturbed semi-Markov processes

CERN Document Server

Silvestrov, Dmitrii

2017-01-01

The book presents new methods of asymptotic analysis for nonlinearly perturbed semi-Markov processes with a finite phase space. These methods are based on special time-space screening procedures for sequential phase space reduction of semi-Markov processes combined with the systematical use of operational calculus for Laurent asymptotic expansions. Effective recurrent algorithms are composed for getting asymptotic expansions, without and with explicit upper bounds for remainders, for power moments of hitting times, stationary and conditional quasi-stationary distributions for nonlinearly perturbed semi-Markov processes. These results are illustrated by asymptotic expansions for birth-death-type semi-Markov processes, which play an important role in various applications. The book will be a useful contribution to the continuing intensive studies in the area. It is an essential reference for theoretical and applied researchers in the field of stochastic processes and their applications that will cont...

Markov Chains and Markov Processes

OpenAIRE

Ogunbayo, Segun

2016-01-01

Markov chain, which was named after Andrew Markov is a mathematical system that transfers a state to another state. Many real world systems contain uncertainty. This study helps us to understand the basic idea of a Markov chain and how is been useful in our daily lives. For some times there had been suspense on distinct predictions and future existences. Also in different games there had been different expectations or results involved. That is the reason why we need Markov chains to predict o...

Semi-Markov Arnason-Schwarz models.

Science.gov (United States)

King, Ruth; Langrock, Roland

2016-06-01

We consider multi-state capture-recapture-recovery data where observed individuals are recorded in a set of possible discrete states. Traditionally, the Arnason-Schwarz model has been fitted to such data where the state process is modeled as a first-order Markov chain, though second-order models have also been proposed and fitted to data. However, low-order Markov models may not accurately represent the underlying biology. For example, specifying a (time-independent) first-order Markov process involves the assumption that the dwell time in each state (i.e., the duration of a stay in a given state) has a geometric distribution, and hence that the modal dwell time is one. Specifying time-dependent or higher-order processes provides additional flexibility, but at the expense of a potentially significant number of additional model parameters. We extend the Arnason-Schwarz model by specifying a semi-Markov model for the state process, where the dwell-time distribution is specified more generally, using, for example, a shifted Poisson or negative binomial distribution. A state expansion technique is applied in order to represent the resulting semi-Markov Arnason-Schwarz model in terms of a simpler and computationally tractable hidden Markov model. Semi-Markov Arnason-Schwarz models come with only a very modest increase in the number of parameters, yet permit a significantly more flexible state process. Model selection can be performed using standard procedures, and in particular via the use of information criteria. The semi-Markov approach allows for important biological inference to be drawn on the underlying state process, for example, on the times spent in the different states. The feasibility of the approach is demonstrated in a simulation study, before being applied to real data corresponding to house finches where the states correspond to the presence or absence of conjunctivitis. © 2015, The International Biometric Society.

On the fractal characterization of Paretian Poisson processes

Science.gov (United States)

Eliazar, Iddo I.; Sokolov, Igor M.

2012-06-01

Paretian Poisson processes are Poisson processes which are defined on the positive half-line, have maximal points, and are quantified by power-law intensities. Paretian Poisson processes are elemental in statistical physics, and are the bedrock of a host of power-law statistics ranging from Pareto's law to anomalous diffusion. In this paper we establish evenness-based fractal characterizations of Paretian Poisson processes. Considering an array of socioeconomic evenness-based measures of statistical heterogeneity, we show that: amongst the realm of Poisson processes which are defined on the positive half-line, and have maximal points, Paretian Poisson processes are the unique class of 'fractal processes' exhibiting scale-invariance. The results established in this paper are diametric to previous results asserting that the scale-invariance of Poisson processes-with respect to physical randomness-based measures of statistical heterogeneity-is characterized by exponential Poissonian intensities.

Compositions, Random Sums and Continued Random Fractions of Poisson and Fractional Poisson Processes

Science.gov (United States)

Orsingher, Enzo; Polito, Federico

2012-08-01

In this paper we consider the relation between random sums and compositions of different processes. In particular, for independent Poisson processes N α ( t), N β ( t), t>0, we have that N_{α}(N_{β}(t)) stackrel{d}{=} sum_{j=1}^{N_{β}(t)} Xj, where the X j s are Poisson random variables. We present a series of similar cases, where the outer process is Poisson with different inner processes. We highlight generalisations of these results where the external process is infinitely divisible. A section of the paper concerns compositions of the form N_{α}(tauk^{ν}), ν∈(0,1], where tauk^{ν} is the inverse of the fractional Poisson process, and we show how these compositions can be represented as random sums. Furthermore we study compositions of the form Θ( N( t)), t>0, which can be represented as random products. The last section is devoted to studying continued fractions of Cauchy random variables with a Poisson number of levels. We evaluate the exact distribution and derive the scale parameter in terms of ratios of Fibonacci numbers.

Timed Comparisons of Semi-Markov Processes

DEFF Research Database (Denmark)

Pedersen, Mathias Ruggaard; Larsen, Kim Guldstrand; Bacci, Giorgio

2018-01-01

-Markov processes, and investigate the question of how to compare two semi-Markov processes with respect to their time-dependent behaviour. To this end, we introduce the relation of being “faster than” between processes and study its algorithmic complexity. Through a connection to probabilistic automata we obtain...

A Martingale Characterization of Mixed Poisson Processes.

Science.gov (United States)

1985-10-01

03LA A 11. TITLE (Inciuae Security Clanafication, ",A martingale characterization of mixed Poisson processes " ________________ 12. PERSONAL AUTHOR... POISSON PROCESSES Jostification .......... . ... . . Di.;t ib,,jtion by Availability Codes Dietmar Pfeifer* Technical University Aachen Dist Special and...Mixed Poisson processes play an important role in many branches of applied probability, for instance in insurance mathematics and physics (see Albrecht

Inhomogeneous Markov point processes by transformation

DEFF Research Database (Denmark)

Jensen, Eva B. Vedel; Nielsen, Linda Stougaard

2000-01-01

We construct parametrized models for point processes, allowing for both inhomogeneity and interaction. The inhomogeneity is obtained by applying parametrized transformations to homogeneous Markov point processes. An interesting model class, which can be constructed by this transformation approach......, is that of exponential inhomogeneous Markov point processes. Statistical inference For such processes is discussed in some detail....

Generated dynamics of Markov and quantum processes

CERN Document Server

Janßen, Martin

2016-01-01

This book presents Markov and quantum processes as two sides of a coin called generated stochastic processes. It deals with quantum processes as reversible stochastic processes generated by one-step unitary operators, while Markov processes are irreversible stochastic processes generated by one-step stochastic operators. The characteristic feature of quantum processes are oscillations, interference, lots of stationary states in bounded systems and possible asymptotic stationary scattering states in open systems, while the characteristic feature of Markov processes are relaxations to a single stationary state. Quantum processes apply to systems where all variables, that control reversibility, are taken as relevant variables, while Markov processes emerge when some of those variables cannot be followed and are thus irrelevant for the dynamic description. Their absence renders the dynamic irreversible. A further aim is to demonstrate that almost any subdiscipline of theoretical physics can conceptually be put in...

Nonlinear Markov processes: Deterministic case

International Nuclear Information System (INIS)

Frank, T.D.

2008-01-01

Deterministic Markov processes that exhibit nonlinear transition mechanisms for probability densities are studied. In this context, the following issues are addressed: Markov property, conditional probability densities, propagation of probability densities, multistability in terms of multiple stationary distributions, stability analysis of stationary distributions, and basin of attraction of stationary distribution

Transforming spatial point processes into Poisson processes using random superposition

DEFF Research Database (Denmark)

Møller, Jesper; Berthelsen, Kasper Klitgaaard

with a complementary spatial point process Y  to obtain a Poisson process X∪Y  with intensity function β. Underlying this is a bivariate spatial birth-death process (Xt,Yt) which converges towards the distribution of (X,Y). We study the joint distribution of X and Y, and their marginal and conditional distributions....... In particular, we introduce a fast and easy simulation procedure for Y conditional on X. This may be used for model checking: given a model for the Papangelou intensity of the original spatial point process, this model is used to generate the complementary process, and the resulting superposition is a Poisson...... process with intensity function β if and only if the true Papangelou intensity is used. Whether the superposition is actually such a Poisson process can easily be examined using well known results and fast simulation procedures for Poisson processes. We illustrate this approach to model checking...

The Fractional Poisson Process and the Inverse Stable Subordinator

OpenAIRE

Meerschaert, Mark; Nane, Erkan; Vellaisamy, P.

2011-01-01

The fractional Poisson process is a renewal process with Mittag-Leffler waiting times. Its distributions solve a time-fractional analogue of the Kolmogorov forward equation for a Poisson process. This paper shows that a traditional Poisson process, with the time variable replaced by an independent inverse stable subordinator, is also a fractional Poisson process. This result unifies the two main approaches in the stochastic theory of time-fractional diffusion equations. The equivalence extend...

Fractional Poisson process (II)

International Nuclear Information System (INIS)

Wang Xiaotian; Wen Zhixiong; Zhang Shiying

2006-01-01

In this paper, we propose a stochastic process W H (t)(H-bar (12,1)) which we call fractional Poisson process. The process W H (t) is self-similar in wide sense, displays long range dependence, and has more fatter tail than Gaussian process. In addition, it converges to fractional Brownian motion in distribution

Portfolio Optimization in a Semi-Markov Modulated Market

International Nuclear Information System (INIS)

Ghosh, Mrinal K.; Goswami, Anindya; Kumar, Suresh K.

2009-01-01

We address a portfolio optimization problem in a semi-Markov modulated market. We study both the terminal expected utility optimization on finite time horizon and the risk-sensitive portfolio optimization on finite and infinite time horizon. We obtain optimal portfolios in relevant cases. A numerical procedure is also developed to compute the optimal expected terminal utility for finite horizon problem

Bayesian analysis of Markov point processes

DEFF Research Database (Denmark)

Berthelsen, Kasper Klitgaard; Møller, Jesper

2006-01-01

Recently Møller, Pettitt, Berthelsen and Reeves introduced a new MCMC methodology for drawing samples from a posterior distribution when the likelihood function is only specified up to a normalising constant. We illustrate the method in the setting of Bayesian inference for Markov point processes...... a partially ordered Markov point process as the auxiliary variable. As the method requires simulation from the "unknown" likelihood, perfect simulation algorithms for spatial point processes become useful....

NonMarkov Ito Processes with 1- state memory

Science.gov (United States)

McCauley, Joseph L.

2010-08-01

A Markov process, by definition, cannot depend on any previous state other than the last observed state. An Ito process implies the Fokker-Planck and Kolmogorov backward time partial differential eqns. for transition densities, which in turn imply the Chapman-Kolmogorov eqn., but without requiring the Markov condition. We present a class of Ito process superficially resembling Markov processes, but with 1-state memory. In finance, such processes would obey the efficient market hypothesis up through the level of pair correlations. These stochastic processes have been mislabeled in recent literature as 'nonlinear Markov processes'. Inspired by Doob and Feller, who pointed out that the ChapmanKolmogorov eqn. is not restricted to Markov processes, we exhibit a Gaussian Ito transition density with 1-state memory in the drift coefficient that satisfies both of Kolmogorov's partial differential eqns. and also the Chapman-Kolmogorov eqn. In addition, we show that three of the examples from McKean's seminal 1966 paper are also nonMarkov Ito processes. Last, we show that the transition density of the generalized Black-Scholes type partial differential eqn. describes a martingale, and satisfies the ChapmanKolmogorov eqn. This leads to the shortest-known proof that the Green function of the Black-Scholes eqn. with variable diffusion coefficient provides the so-called martingale measure of option pricing.

Markov chains of nonlinear Markov processes and an application to a winner-takes-all model for social conformity

Energy Technology Data Exchange (ETDEWEB)

Frank, T D [Center for the Ecological Study of Perception and Action, Department of Psychology, University of Connecticut, 406 Babbidge Road, Storrs, CT 06269 (United States)

2008-07-18

We discuss nonlinear Markov processes defined on discrete time points and discrete state spaces using Markov chains. In this context, special attention is paid to the distinction between linear and nonlinear Markov processes. We illustrate that the Chapman-Kolmogorov equation holds for nonlinear Markov processes by a winner-takes-all model for social conformity. (fast track communication)

Markov chains of nonlinear Markov processes and an application to a winner-takes-all model for social conformity

International Nuclear Information System (INIS)

Frank, T D

2008-01-01

We discuss nonlinear Markov processes defined on discrete time points and discrete state spaces using Markov chains. In this context, special attention is paid to the distinction between linear and nonlinear Markov processes. We illustrate that the Chapman-Kolmogorov equation holds for nonlinear Markov processes by a winner-takes-all model for social conformity. (fast track communication)

Multivariate fractional Poisson processes and compound sums

OpenAIRE

Beghin, Luisa; Macci, Claudio

2015-01-01

In this paper we present multivariate space-time fractional Poisson processes by considering common random time-changes of a (finite-dimensional) vector of independent classical (non-fractional) Poisson processes. In some cases we also consider compound processes. We obtain some equations in terms of some suitable fractional derivatives and fractional difference operators, which provides the extension of known equations for the univariate processes.

Markov processes characterization and convergence

CERN Document Server

Ethier, Stewart N

2009-01-01

The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists."[A]nyone who works with Markov processes whose state space is uncountably infinite will need this most impressive book as a guide and reference."-American Scientist"There is no question but that space should immediately be reserved for [this] book on the library shelf. Those who aspire to mastery of the contents should also reserve a large number of long winter evenings."-Zentralblatt f?r Mathematik und ihre Grenzgebiete/Mathematics Abstracts"Ethier and Kurtz have produced an excellent treatment of the modern theory of Markov processes that [is] useful both as a reference work and as a graduate textbook."-Journal of Statistical PhysicsMarkov Proce...

Finite Markov processes and their applications

CERN Document Server

Iosifescu, Marius

2007-01-01

A self-contained treatment of finite Markov chains and processes, this text covers both theory and applications. Author Marius Iosifescu, vice president of the Romanian Academy and director of its Center for Mathematical Statistics, begins with a review of relevant aspects of probability theory and linear algebra. Experienced readers may start with the second chapter, a treatment of fundamental concepts of homogeneous finite Markov chain theory that offers examples of applicable models.The text advances to studies of two basic types of homogeneous finite Markov chains: absorbing and ergodic ch

Multi-rate Poisson tree processes for single-locus species delimitation under maximum likelihood and Markov chain Monte Carlo.

Science.gov (United States)

Kapli, P; Lutteropp, S; Zhang, J; Kobert, K; Pavlidis, P; Stamatakis, A; Flouri, T

2017-06-01

In recent years, molecular species delimitation has become a routine approach for quantifying and classifying biodiversity. Barcoding methods are of particular importance in large-scale surveys as they promote fast species discovery and biodiversity estimates. Among those, distance-based methods are the most common choice as they scale well with large datasets; however, they are sensitive to similarity threshold parameters and they ignore evolutionary relationships. The recently introduced "Poisson Tree Processes" (PTP) method is a phylogeny-aware approach that does not rely on such thresholds. Yet, two weaknesses of PTP impact its accuracy and practicality when applied to large datasets; it does not account for divergent intraspecific variation and is slow for a large number of sequences. We introduce the multi-rate PTP (mPTP), an improved method that alleviates the theoretical and technical shortcomings of PTP. It incorporates different levels of intraspecific genetic diversity deriving from differences in either the evolutionary history or sampling of each species. Results on empirical data suggest that mPTP is superior to PTP and popular distance-based methods as it, consistently yields more accurate delimitations with respect to the taxonomy (i.e., identifies more taxonomic species, infers species numbers closer to the taxonomy). Moreover, mPTP does not require any similarity threshold as input. The novel dynamic programming algorithm attains a speedup of at least five orders of magnitude compared to PTP, allowing it to delimit species in large (meta-) barcoding data. In addition, Markov Chain Monte Carlo sampling provides a comprehensive evaluation of the inferred delimitation in just a few seconds for millions of steps, independently of tree size. mPTP is implemented in C and is available for download at http://github.com/Pas-Kapli/mptp under the GNU Affero 3 license. A web-service is available at http://mptp.h-its.org . : paschalia.kapli@h-its.org or

Derivation of Markov processes that violate detailed balance

Science.gov (United States)

Lee, Julian

2018-03-01

Time-reversal symmetry of the microscopic laws dictates that the equilibrium distribution of a stochastic process must obey the condition of detailed balance. However, cyclic Markov processes that do not admit equilibrium distributions with detailed balance are often used to model systems driven out of equilibrium by external agents. I show that for a Markov model without detailed balance, an extended Markov model can be constructed, which explicitly includes the degrees of freedom for the driving agent and satisfies the detailed balance condition. The original cyclic Markov model for the driven system is then recovered as an approximation at early times by summing over the degrees of freedom for the driving agent. I also show that the widely accepted expression for the entropy production in a cyclic Markov model is actually a time derivative of an entropy component in the extended model. Further, I present an analytic expression for the entropy component that is hidden in the cyclic Markov model.

Laplace-Laplace analysis of the fractional Poisson process

OpenAIRE

Gorenflo, Rudolf; Mainardi, Francesco

2013-01-01

We generate the fractional Poisson process by subordinating the standard Poisson process to the inverse stable subordinator. Our analysis is based on application of the Laplace transform with respect to both arguments of the evolving probability densities.

Markov processes from K. Ito's perspective (AM-155)

CERN Document Server

Stroock, Daniel W

2003-01-01

Kiyosi Itô''s greatest contribution to probability theory may be his introduction of stochastic differential equations to explain the Kolmogorov-Feller theory of Markov processes. Starting with the geometric ideas that guided him, this book gives an account of Itô''s program. The modern theory of Markov processes was initiated by A. N. Kolmogorov. However, Kolmogorov''s approach was too analytic to reveal the probabilistic foundations on which it rests. In particular, it hides the central role played by the simplest Markov processes: those with independent, identically distributed incremen

Harnessing the theoretical foundations of the exponential and beta-Poisson dose-response models to quantify parameter uncertainty using Markov Chain Monte Carlo.

Science.gov (United States)

Schmidt, Philip J; Pintar, Katarina D M; Fazil, Aamir M; Topp, Edward

2013-09-01

Dose-response models are the essential link between exposure assessment and computed risk values in quantitative microbial risk assessment, yet the uncertainty that is inherent to computed risks because the dose-response model parameters are estimated using limited epidemiological data is rarely quantified. Second-order risk characterization approaches incorporating uncertainty in dose-response model parameters can provide more complete information to decisionmakers by separating variability and uncertainty to quantify the uncertainty in computed risks. Therefore, the objective of this work is to develop procedures to sample from posterior distributions describing uncertainty in the parameters of exponential and beta-Poisson dose-response models using Bayes's theorem and Markov Chain Monte Carlo (in OpenBUGS). The theoretical origins of the beta-Poisson dose-response model are used to identify a decomposed version of the model that enables Bayesian analysis without the need to evaluate Kummer confluent hypergeometric functions. Herein, it is also established that the beta distribution in the beta-Poisson dose-response model cannot address variation among individual pathogens, criteria to validate use of the conventional approximation to the beta-Poisson model are proposed, and simple algorithms to evaluate actual beta-Poisson probabilities of infection are investigated. The developed MCMC procedures are applied to analysis of a case study data set, and it is demonstrated that an important region of the posterior distribution of the beta-Poisson dose-response model parameters is attributable to the absence of low-dose data. This region includes beta-Poisson models for which the conventional approximation is especially invalid and in which many beta distributions have an extreme shape with questionable plausibility. © Her Majesty the Queen in Right of Canada 2013. Reproduced with the permission of the Minister of the Public Health Agency of Canada.

Markov Chain Models for the Stochastic Modeling of Pitting Corrosion

Directory of Open Access Journals (Sweden)

A. Valor

2013-01-01

Full Text Available The stochastic nature of pitting corrosion of metallic structures has been widely recognized. It is assumed that this kind of deterioration retains no memory of the past, so only the current state of the damage influences its future development. This characteristic allows pitting corrosion to be categorized as a Markov process. In this paper, two different models of pitting corrosion, developed using Markov chains, are presented. Firstly, a continuous-time, nonhomogeneous linear growth (pure birth Markov process is used to model external pitting corrosion in underground pipelines. A closed-form solution of the system of Kolmogorov's forward equations is used to describe the transition probability function in a discrete pit depth space. The transition probability function is identified by correlating the stochastic pit depth mean with the empirical deterministic mean. In the second model, the distribution of maximum pit depths in a pitting experiment is successfully modeled after the combination of two stochastic processes: pit initiation and pit growth. Pit generation is modeled as a nonhomogeneous Poisson process, in which induction time is simulated as the realization of a Weibull process. Pit growth is simulated using a nonhomogeneous Markov process. An analytical solution of Kolmogorov's system of equations is also found for the transition probabilities from the first Markov state. Extreme value statistics is employed to find the distribution of maximum pit depths.

Stability of the trivial solution for linear stochastic differential equations with Poisson white noise

International Nuclear Information System (INIS)

Grigoriu, Mircea; Samorodnitsky, Gennady

2004-01-01

Two methods are considered for assessing the asymptotic stability of the trivial solution of linear stochastic differential equations driven by Poisson white noise, interpreted as the formal derivative of a compound Poisson process. The first method attempts to extend a result for diffusion processes satisfying linear stochastic differential equations to the case of linear equations with Poisson white noise. The developments for the method are based on Ito's formula for semimartingales and Lyapunov exponents. The second method is based on a geometric ergodic theorem for Markov chains providing a criterion for the asymptotic stability of the solution of linear stochastic differential equations with Poisson white noise. Two examples are presented to illustrate the use and evaluate the potential of the two methods. The examples demonstrate limitations of the first method and the generality of the second method

Test of Poisson Process for Earthquakes in and around Korea

International Nuclear Information System (INIS)

Noh, Myunghyun; Choi, Hoseon

2015-01-01

Since Cornell's work on the probabilistic seismic hazard analysis (hereafter, PSHA), majority of PSHA computer codes are assuming that the earthquake occurrence is Poissonian. To the author's knowledge, it is uncertain who first opened the issue of the Poisson process for the earthquake occurrence. The systematic PSHA in Korea, led by the nuclear industry, were carried out for more than 25 year with the assumption of the Poisson process. However, the assumption of the Poisson process has never been tested. Therefore, the test is of significance. We tested whether the Korean earthquakes follow the Poisson process or not. The Chi-square test with the significance level of 5% was applied. The test turned out that the Poisson process could not be rejected for the earthquakes of magnitude 2.9 or larger. However, it was still observed in the graphical comparison that some portion of the observed distribution significantly deviated from the Poisson distribution. We think this is due to the small earthquake data. The earthquakes of magnitude 2.9 or larger occurred only 376 times during 34 years. Therefore, the judgment on the Poisson process derived in the present study is not conclusive

Alternative Forms of Compound Fractional Poisson Processes

Directory of Open Access Journals (Sweden)

Luisa Beghin

2012-01-01

Full Text Available We study here different fractional versions of the compound Poisson process. The fractionality is introduced in the counting process representing the number of jumps as well as in the density of the jumps themselves. The corresponding distributions are obtained explicitly and proved to be solution of fractional equations of order less than one. Only in the final case treated in this paper, where the number of jumps is given by the fractional-difference Poisson process defined in Orsingher and Polito (2012, we have a fractional driving equation, with respect to the time argument, with order greater than one. Moreover, in this case, the compound Poisson process is Markovian and this is also true for the corresponding limiting process. All the processes considered here are proved to be compositions of continuous time random walks with stable processes (or inverse stable subordinators. These subordinating relationships hold, not only in the limit, but also in the finite domain. In some cases the densities satisfy master equations which are the fractional analogues of the well-known Kolmogorov one.

Detection of bursts in extracellular spike trains using hidden semi-Markov point process models.

Science.gov (United States)

Tokdar, Surya; Xi, Peiyi; Kelly, Ryan C; Kass, Robert E

2010-08-01

Neurons in vitro and in vivo have epochs of bursting or "up state" activity during which firing rates are dramatically elevated. Various methods of detecting bursts in extracellular spike trains have appeared in the literature, the most widely used apparently being Poisson Surprise (PS). A natural description of the phenomenon assumes (1) there are two hidden states, which we label "burst" and "non-burst," (2) the neuron evolves stochastically, switching at random between these two states, and (3) within each state the spike train follows a time-homogeneous point process. If in (2) the transitions from non-burst to burst and burst to non-burst states are memoryless, this becomes a hidden Markov model (HMM). For HMMs, the state transitions follow exponential distributions, and are highly irregular. Because observed bursting may in some cases be fairly regular-exhibiting inter-burst intervals with small variation-we relaxed this assumption. When more general probability distributions are used to describe the state transitions the two-state point process model becomes a hidden semi-Markov model (HSMM). We developed an efficient Bayesian computational scheme to fit HSMMs to spike train data. Numerical simulations indicate the method can perform well, sometimes yielding very different results than those based on PS.

Pathwise duals of monotone and additive Markov processes

Czech Academy of Sciences Publication Activity Database

Sturm, A.; Swart, Jan M.

-, - (2018) ISSN 0894-9840 R&D Projects: GA ČR GAP201/12/2613 Institutional support: RVO:67985556 Keywords : pathwise duality * monotone Markov process * additive Markov process * interacting particle system Subject RIV: BA - General Mathematics Impact factor: 0.854, year: 2016 http://library.utia.cas.cz/separaty/2016/SI/swart-0465436.pdf

Modeling laser velocimeter signals as triply stochastic Poisson processes

Science.gov (United States)

Mayo, W. T., Jr.

1976-01-01

Previous models of laser Doppler velocimeter (LDV) systems have not adequately described dual-scatter signals in a manner useful for analysis and simulation of low-level photon-limited signals. At low photon rates, an LDV signal at the output of a photomultiplier tube is a compound nonhomogeneous filtered Poisson process, whose intensity function is another (slower) Poisson process with the nonstationary rate and frequency parameters controlled by a random flow (slowest) process. In the present paper, generalized Poisson shot noise models are developed for low-level LDV signals. Theoretical results useful in detection error analysis and simulation are presented, along with measurements of burst amplitude statistics. Computer generated simulations illustrate the difference between Gaussian and Poisson models of low-level signals.

Non-Poisson Processes: Regression to Equilibrium Versus Equilibrium Correlation Functions

Science.gov (United States)

2004-07-07

ARTICLE IN PRESSPhysica A 347 (2005) 268–2880378-4371/$ - doi:10.1016/j Correspo E-mail adwww.elsevier.com/locate/physaNon- Poisson processes : regression...05.40.a; 89.75.k; 02.50.Ey Keywords: Stochastic processes; Non- Poisson processes ; Liouville and Liouville-like equations; Correlation function...which is not legitimate with renewal non- Poisson processes , is a correct property if the deviation from the exponential relaxation is obtained by time

Estimating Bird / Aircraft Collision Probabilities and Risk Utilizing Spatial Poisson Processes

Science.gov (United States)

2012-06-10

ESTIMATING BIRD/AIRCRAFT COLLISION PROBABILITIES AND RISK UTILIZING SPATIAL POISSON PROCESSES GRADUATE...AND RISK UTILIZING SPATIAL POISSON PROCESSES GRADUATE RESEARCH PAPER Presented to the Faculty Department of Operational Sciences...COLLISION PROBABILITIES AND RISK UTILIZING SPATIAL POISSON PROCESSES Brady J. Vaira, BS, MS Major, USAF Approved

Quantum Markov processes and applications in many-body systems

International Nuclear Information System (INIS)

Temme, P. K.

2010-01-01

This thesis is concerned with the investigation of quantum as well as classical Markov processes and their application in the field of strongly correlated many-body systems. A Markov process is a special kind of stochastic process, which is determined by an evolution that is independent of its history and only depends on the current state of the system. The application of Markov processes has a long history in the field of statistical mechanics and classical many-body theory. Not only are Markov processes used to describe the dynamics of stochastic systems, but they predominantly also serve as a practical method that allows for the computation of fundamental properties of complex many-body systems by means of probabilistic algorithms. The aim of this thesis is to investigate the properties of quantum Markov processes, i.e. Markov processes taking place in a quantum mechanical state space, and to gain a better insight into complex many-body systems by means thereof. Moreover, we formulate a novel quantum algorithm which allows for the computation of the thermal and ground states of quantum many-body systems. After a brief introduction to quantum Markov processes we turn to an investigation of their convergence properties. We find bounds on the convergence rate of the quantum process by generalizing geometric bounds found for classical processes. We generalize a distance measure that serves as the basis for our investigations, the chi-square divergence, to non-commuting probability spaces. This divergence allows for a convenient generalization of the detailed balance condition to quantum processes. We then devise the quantum algorithm that can be seen as the natural generalization of the ubiquitous Metropolis algorithm to simulate quantum many-body Hamiltonians. By this we intend to provide further evidence, that a quantum computer can serve as a fully-fledged quantum simulator, which is not only capable of describing the dynamical evolution of quantum systems, but

Bayesian regression of piecewise homogeneous Poisson processes

Directory of Open Access Journals (Sweden)

Diego Sevilla

2015-12-01

Full Text Available In this paper, a Bayesian method for piecewise regression is adapted to handle counting processes data distributed as Poisson. A numerical code in Mathematica is developed and tested analyzing simulated data. The resulting method is valuable for detecting breaking points in the count rate of time series for Poisson processes. Received: 2 November 2015, Accepted: 27 November 2015; Edited by: R. Dickman; Reviewed by: M. Hutter, Australian National University, Canberra, Australia.; DOI: http://dx.doi.org/10.4279/PIP.070018 Cite as: D J R Sevilla, Papers in Physics 7, 070018 (2015

Rate-optimal Bayesian intensity smoothing for inhomogeneous Poisson processes

NARCIS (Netherlands)

Belitser, E.N.; Serra, P.; van Zanten, H.

2015-01-01

We apply nonparametric Bayesian methods to study the problem of estimating the intensity function of an inhomogeneous Poisson process. To motivate our results we start by analyzing count data coming from a call center which we model as a Poisson process. This analysis is carried out using a certain

Markov processes an introduction for physical scientists

CERN Document Server

Gillespie, Daniel T

1991-01-01

Markov process theory is basically an extension of ordinary calculus to accommodate functions whos time evolutions are not entirely deterministic. It is a subject that is becoming increasingly important for many fields of science. This book develops the single-variable theory of both continuous and jump Markov processes in a way that should appeal especially to physicists and chemists at the senior and graduate level.Key Features* A self-contained, prgamatic exposition of the needed elements of random variable theory* Logically integrated derviations of the Chapman-Kolmogorov e

Markov decision processes in artificial intelligence

CERN Document Server

Sigaud, Olivier

2013-01-01

Markov Decision Processes (MDPs) are a mathematical framework for modeling sequential decision problems under uncertainty as well as Reinforcement Learning problems. Written by experts in the field, this book provides a global view of current research using MDPs in Artificial Intelligence. It starts with an introductory presentation of the fundamental aspects of MDPs (planning in MDPs, Reinforcement Learning, Partially Observable MDPs, Markov games and the use of non-classical criteria). Then it presents more advanced research trends in the domain and gives some concrete examples using illustr

Analysis of overdispersed count data by mixtures of Poisson variables and Poisson processes.

Science.gov (United States)

Hougaard, P; Lee, M L; Whitmore, G A

1997-12-01

Count data often show overdispersion compared to the Poisson distribution. Overdispersion is typically modeled by a random effect for the mean, based on the gamma distribution, leading to the negative binomial distribution for the count. This paper considers a larger family of mixture distributions, including the inverse Gaussian mixture distribution. It is demonstrated that it gives a significantly better fit for a data set on the frequency of epileptic seizures. The same approach can be used to generate counting processes from Poisson processes, where the rate or the time is random. A random rate corresponds to variation between patients, whereas a random time corresponds to variation within patients.

NHPoisson: An R Package for Fitting and Validating Nonhomogeneous Poisson Processes

Directory of Open Access Journals (Sweden)

Ana C. Cebrián

2015-03-01

Full Text Available NHPoisson is an R package for the modeling of nonhomogeneous Poisson processes in one dimension. It includes functions for data preparation, maximum likelihood estimation, covariate selection and inference based on asymptotic distributions and simulation methods. It also provides specific methods for the estimation of Poisson processes resulting from a peak over threshold approach. In addition, the package supports a wide range of model validation tools and functions for generating nonhomogenous Poisson process trajectories. This paper is a description of the package and aims to help those interested in modeling data using nonhomogeneous Poisson processes.

Modeling nonhomogeneous Markov processes via time transformation.

Science.gov (United States)

Hubbard, R A; Inoue, L Y T; Fann, J R

2008-09-01

Longitudinal studies are a powerful tool for characterizing the course of chronic disease. These studies are usually carried out with subjects observed at periodic visits giving rise to panel data. Under this observation scheme the exact times of disease state transitions and sequence of disease states visited are unknown and Markov process models are often used to describe disease progression. Most applications of Markov process models rely on the assumption of time homogeneity, that is, that the transition rates are constant over time. This assumption is not satisfied when transition rates depend on time from the process origin. However, limited statistical tools are available for dealing with nonhomogeneity. We propose models in which the time scale of a nonhomogeneous Markov process is transformed to an operational time scale on which the process is homogeneous. We develop a method for jointly estimating the time transformation and the transition intensity matrix for the time transformed homogeneous process. We assess maximum likelihood estimation using the Fisher scoring algorithm via simulation studies and compare performance of our method to homogeneous and piecewise homogeneous models. We apply our methodology to a study of delirium progression in a cohort of stem cell transplantation recipients and show that our method identifies temporal trends in delirium incidence and recovery.

The cylindrical K-function and Poisson line cluster point processes

DEFF Research Database (Denmark)

Møller, Jesper; Safavimanesh, Farzaneh; Rasmussen, Jakob G.

Poisson line cluster point processes, is also introduced. Parameter estimation based on moment methods or Bayesian inference for this model is discussed when the underlying Poisson line process and the cluster memberships are treated as hidden processes. To illustrate the methodologies, we analyze two...

Nonhomogeneous fractional Poisson processes

International Nuclear Information System (INIS)

Wang Xiaotian; Zhang Shiying; Fan Shen

2007-01-01

In this paper, we propose a class of non-Gaussian stationary increment processes, named nonhomogeneous fractional Poisson processes W H (j) (t), which permit the study of the effects of long-range dependance in a large number of fields including quantum physics and finance. The processes W H (j) (t) are self-similar in a wide sense, exhibit more fatter tail than Gaussian processes, and converge to the Gaussian processes in distribution in some cases. In addition, we also show that the intensity function λ(t) strongly influences the existence of the highest finite moment of W H (j) (t) and the behaviour of the tail probability of W H (j) (t)

A Markov Process Inspired Cellular Automata Model of Road Traffic

OpenAIRE

Wang, Fa; Li, Li; Hu, Jianming; Ji, Yan; Yao, Danya; Zhang, Yi; Jin, Xuexiang; Su, Yuelong; Wei, Zheng

2008-01-01

To provide a more accurate description of the driving behaviors in vehicle queues, a namely Markov-Gap cellular automata model is proposed in this paper. It views the variation of the gap between two consequent vehicles as a Markov process whose stationary distribution corresponds to the observed distribution of practical gaps. The multiformity of this Markov process provides the model enough flexibility to describe various driving behaviors. Two examples are given to show how to specialize i...

Bayesian inference on multiscale models for poisson intensity estimation: applications to photon-limited image denoising.

Science.gov (United States)

Lefkimmiatis, Stamatios; Maragos, Petros; Papandreou, George

2009-08-01

We present an improved statistical model for analyzing Poisson processes, with applications to photon-limited imaging. We build on previous work, adopting a multiscale representation of the Poisson process in which the ratios of the underlying Poisson intensities (rates) in adjacent scales are modeled as mixtures of conjugate parametric distributions. Our main contributions include: 1) a rigorous and robust regularized expectation-maximization (EM) algorithm for maximum-likelihood estimation of the rate-ratio density parameters directly from the noisy observed Poisson data (counts); 2) extension of the method to work under a multiscale hidden Markov tree model (HMT) which couples the mixture label assignments in consecutive scales, thus modeling interscale coefficient dependencies in the vicinity of image edges; 3) exploration of a 2-D recursive quad-tree image representation, involving Dirichlet-mixture rate-ratio densities, instead of the conventional separable binary-tree image representation involving beta-mixture rate-ratio densities; and 4) a novel multiscale image representation, which we term Poisson-Haar decomposition, that better models the image edge structure, thus yielding improved performance. Experimental results on standard images with artificially simulated Poisson noise and on real photon-limited images demonstrate the effectiveness of the proposed techniques.

Mixed Vehicle Flow At Signalized Intersection: Markov Chain Analysis

Directory of Open Access Journals (Sweden)

Gertsbakh Ilya B.

2015-09-01

Full Text Available We assume that a Poisson flow of vehicles arrives at isolated signalized intersection, and each vehicle, independently of others, represents a random number X of passenger car units (PCU’s. We analyze numerically the stationary distribution of the queue process {Zn}, where Zn is the number of PCU’s in a queue at the beginning of the n-th red phase, n → ∞. We approximate the number Yn of PCU’s arriving during one red-green cycle by a two-parameter Negative Binomial Distribution (NBD. The well-known fact is that {Zn} follow an infinite-state Markov chain. We approximate its stationary distribution using a finite-state Markov chain. We show numerically that there is a strong dependence of the mean queue length E[Zn] in equilibrium on the input distribution of Yn and, in particular, on the ”over dispersion” parameter γ= Var[Yn]/E[Yn]. For Poisson input, γ = 1. γ > 1 indicates presence of heavy-tailed input. In reality it means that a relatively large ”portion” of PCU’s, considerably exceeding the average, may arrive with high probability during one red-green cycle. Empirical formulas are presented for an accurate estimation of mean queue length as a function of load and g of the input flow. Using the Markov chain technique, we analyze the mean ”virtual” delay time for a car which always arrives at the beginning of the red phase.

Nonhomogeneous fractional Poisson processes

Energy Technology Data Exchange (ETDEWEB)

Wang Xiaotian [School of Management, Tianjin University, Tianjin 300072 (China)]. E-mail: swa001@126.com; Zhang Shiying [School of Management, Tianjin University, Tianjin 300072 (China); Fan Shen [Computer and Information School, Zhejiang Wanli University, Ningbo 315100 (China)

2007-01-15

In this paper, we propose a class of non-Gaussian stationary increment processes, named nonhomogeneous fractional Poisson processes W{sub H}{sup (j)}(t), which permit the study of the effects of long-range dependance in a large number of fields including quantum physics and finance. The processes W{sub H}{sup (j)}(t) are self-similar in a wide sense, exhibit more fatter tail than Gaussian processes, and converge to the Gaussian processes in distribution in some cases. In addition, we also show that the intensity function {lambda}(t) strongly influences the existence of the highest finite moment of W{sub H}{sup (j)}(t) and the behaviour of the tail probability of W{sub H}{sup (j)}(t)

Optimality of Poisson Processes Intensity Learning with Gaussian Processes

NARCIS (Netherlands)

Kirichenko, A.; van Zanten, H.

2015-01-01

In this paper we provide theoretical support for the so-called "Sigmoidal Gaussian Cox Process" approach to learning the intensity of an inhomogeneous Poisson process on a d-dimensional domain. This method was proposed by Adams, Murray and MacKay (ICML, 2009), who developed a tractable computational

Estimating the period of a cyclic non-homogeneous Poisson process

NARCIS (Netherlands)

Belitser, E.; Andrade Serra, De P.J.; Zanten, van J.H.

2013-01-01

Motivated by applications of Poisson processes for modelling periodic time-varying phenomena, we study a semi-parametric estimator of the period of cyclic intensity function of a non-homogeneous Poisson process. There are no parametric assumptions on the intensity function which is treated as an

Numerical methods for realizing nonstationary Poisson processes with piecewise-constant instantaneous-rate functions

DEFF Research Database (Denmark)

Harrod, Steven; Kelton, W. David

2006-01-01

Nonstationary Poisson processes are appropriate in many applications, including disease studies, transportation, finance, and social policy. The authors review the risks of ignoring nonstationarity in Poisson processes and demonstrate three algorithms for generation of Poisson processes...

Maintenance planning for a deteriorating production process

International Nuclear Information System (INIS)

Ahmadi, Reza; Fouladirad, Mitra

2017-01-01

We consider a system subject to degradation, more precisely a production process with three quality states evolving according to a homogeneous Markov process. The degradation decreases the income generated by the system. To maintain revenue stream and prevent the loss of revenue, the system is inspected according to a Markov-modulated Poisson process. It is assumed that each inspection at time t incurs a time dependent cost. Each inspection improves the system health and therefore the degradation level jumps to a less deteriorated state. In absence of inspections, the system state is prone to shift to a more deteriorated state with a constant rate. The problem is to determine an optimal operating (stopping) time which truly balances some flow of income and increasing costs due to inspections, and so maximizes the expected gain of the proposed policy. To demonstrate the applicability of the explored approach and its effectiveness, some numerical results are provided. - Highlights: • An integrated model based on a quality state-dependent reward structure is explored. • The model allows the revenue stream responds to variation in the quality state. • The production process is inspected according to a Markovmodulated Poisson process. • Assuming a Markovian structure, we predict the quality state behavior. • We determine an optimal production run length based on a stopping decision rule.

Markov Decision Processes in Practice

NARCIS (Netherlands)

Boucherie, Richardus J.; van Dijk, N.M.

2017-01-01

It is over 30 years ago since D.J. White started his series of surveys on practical applications of Markov decision processes (MDP), over 20 years after the phenomenal book by Martin Puterman on the theory of MDP, and over 10 years since Eugene A. Feinberg and Adam Shwartz published their Handbook

Comparison of INAR(1)-Poisson model and Markov prediction model in forecasting the number of DHF patients in west java Indonesia

Science.gov (United States)

Ahdika, Atina; Lusiyana, Novyan

2017-02-01

World Health Organization (WHO) noted Indonesia as the country with the highest dengue (DHF) cases in Southeast Asia. There are no vaccine and specific treatment for DHF. One of the efforts which can be done by both government and resident is doing a prevention action. In statistics, there are some methods to predict the number of DHF cases to be used as the reference to prevent the DHF cases. In this paper, a discrete time series model, INAR(1)-Poisson model in specific, and Markov prediction model are used to predict the number of DHF patients in West Java Indonesia. The result shows that MPM is the best model since it has the smallest value of MAE (mean absolute error) and MAPE (mean absolute percentage error).

? filtering for stochastic systems driven by Poisson processes

Science.gov (United States)

Song, Bo; Wu, Zheng-Guang; Park, Ju H.; Shi, Guodong; Zhang, Ya

2015-01-01

This paper investigates the ? filtering problem for stochastic systems driven by Poisson processes. By utilising the martingale theory such as the predictable projection operator and the dual predictable projection operator, this paper transforms the expectation of stochastic integral with respect to the Poisson process into the expectation of Lebesgue integral. Then, based on this, this paper designs an ? filter such that the filtering error system is mean-square asymptotically stable and satisfies a prescribed ? performance level. Finally, a simulation example is given to illustrate the effectiveness of the proposed filtering scheme.

Bisimulation on Markov Processes over Arbitrary Measurable Spaces

DEFF Research Database (Denmark)

Bacci, Giorgio; Bacci, Giovanni; Larsen, Kim Guldstrand

2014-01-01

We introduce a notion of bisimulation on labelled Markov Processes over generic measurable spaces in terms of arbitrary binary relations. Our notion of bisimulation is proven to coincide with the coalgebraic definition of Aczel and Mendler in terms of the Giry functor, which associates with a mea......We introduce a notion of bisimulation on labelled Markov Processes over generic measurable spaces in terms of arbitrary binary relations. Our notion of bisimulation is proven to coincide with the coalgebraic definition of Aczel and Mendler in terms of the Giry functor, which associates...

On mean reward variance in semi-Markov processes

Czech Academy of Sciences Publication Activity Database

Sladký, Karel

2005-01-01

Roč. 62, č. 3 (2005), s. 387-397 ISSN 1432-2994 R&D Projects: GA ČR(CZ) GA402/05/0115; GA ČR(CZ) GA402/04/1294 Institutional research plan: CEZ:AV0Z10750506 Keywords : Markov and semi-Markov processes with rewards * variance of cumulative reward * asymptotic behaviour Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 0.259, year: 2005

Perturbation approach to scaled type Markov renewal processes with infinite mean

OpenAIRE

Pajor-Gyulai, Zsolt; Szász, Domokos

2010-01-01

Scaled type Markov renewal processes generalize classical renewal processes: renewal times come from a one parameter family of probability laws and the sequence of the parameters is the trajectory of an ergodic Markov chain. Our primary interest here is the asymptotic distribution of the Markovian parameter at time t \\to \\infty. The limit, of course, depends on the stationary distribution of the Markov chain. The results, however, are essentially different depending on whether the expectation...

Intertime jump statistics of state-dependent Poisson processes.

Science.gov (United States)

Daly, Edoardo; Porporato, Amilcare

2007-01-01

A method to obtain the probability distribution of the interarrival times of jump occurrences in systems driven by state-dependent Poisson noise is proposed. Such a method uses the survivor function obtained by a modified version of the master equation associated to the stochastic process under analysis. A model for the timing of human activities shows the capability of state-dependent Poisson noise to generate power-law distributions. The application of the method to a model for neuron dynamics and to a hydrological model accounting for land-atmosphere interaction elucidates the origin of characteristic recurrence intervals and possible persistence in state-dependent Poisson models.

Continuity Properties of Distances for Markov Processes

DEFF Research Database (Denmark)

Jaeger, Manfred; Mao, Hua; Larsen, Kim Guldstrand

2014-01-01

In this paper we investigate distance functions on finite state Markov processes that measure the behavioural similarity of non-bisimilar processes. We consider both probabilistic bisimilarity metrics, and trace-based distances derived from standard Lp and Kullback-Leibler distances. Two desirable...

Rate estimation in partially observed Markov jump processes with measurement errors

OpenAIRE

Amrein, Michael; Kuensch, Hans R.

2010-01-01

We present a simulation methodology for Bayesian estimation of rate parameters in Markov jump processes arising for example in stochastic kinetic models. To handle the problem of missing components and measurement errors in observed data, we embed the Markov jump process into the framework of a general state space model. We do not use diffusion approximations. Markov chain Monte Carlo and particle filter type algorithms are introduced, which allow sampling from the posterior distribution of t...

On the entropy of a hidden Markov process.

Science.gov (United States)

Jacquet, Philippe; Seroussi, Gadiel; Szpankowski, Wojciech

2008-05-01

We study the entropy rate of a hidden Markov process (HMP) defined by observing the output of a binary symmetric channel whose input is a first-order binary Markov process. Despite the simplicity of the models involved, the characterization of this entropy is a long standing open problem. By presenting the probability of a sequence under the model as a product of random matrices, one can see that the entropy rate sought is equal to a top Lyapunov exponent of the product. This offers an explanation for the elusiveness of explicit expressions for the HMP entropy rate, as Lyapunov exponents are notoriously difficult to compute. Consequently, we focus on asymptotic estimates, and apply the same product of random matrices to derive an explicit expression for a Taylor approximation of the entropy rate with respect to the parameter of the binary symmetric channel. The accuracy of the approximation is validated against empirical simulation results. We also extend our results to higher-order Markov processes and to Rényi entropies of any order.

Road maintenance optimization through a discrete-time semi-Markov decision process

International Nuclear Information System (INIS)

Zhang Xueqing; Gao Hui

2012-01-01

Optimization models are necessary for efficient and cost-effective maintenance of a road network. In this regard, road deterioration is commonly modeled as a discrete-time Markov process such that an optimal maintenance policy can be obtained based on the Markov decision process, or as a renewal process such that an optimal maintenance policy can be obtained based on the renewal theory. However, the discrete-time Markov process cannot capture the real time at which the state transits while the renewal process considers only one state and one maintenance action. In this paper, road deterioration is modeled as a semi-Markov process in which the state transition has the Markov property and the holding time in each state is assumed to follow a discrete Weibull distribution. Based on this semi-Markov process, linear programming models are formulated for both infinite and finite planning horizons in order to derive optimal maintenance policies to minimize the life-cycle cost of a road network. A hypothetical road network is used to illustrate the application of the proposed optimization models. The results indicate that these linear programming models are practical for the maintenance of a road network having a large number of road segments and that they are convenient to incorporate various constraints on the decision process, for example, performance requirements and available budgets. Although the optimal maintenance policies obtained for the road network are randomized stationary policies, the extent of this randomness in decision making is limited. The maintenance actions are deterministic for most states and the randomness in selecting actions occurs only for a few states.

The semi-Markov process. Generalizations and calculation rules for application in the analysis of systems

International Nuclear Information System (INIS)

Hirschmann, H.

1983-06-01

The consequences of the basic assumptions of the semi-Markov process as defined from a homogeneous renewal process with a stationary Markov condition are reviewed. The notion of the semi-Markov process is generalized by its redefinition from a nonstationary Markov renewal process. For both the nongeneralized and the generalized case a representation of the first order conditional state probabilities is derived in terms of the transition probabilities of the Markov renewal process. Some useful calculation rules (regeneration rules) are derived for the conditional state probabilities of the semi-Markov process. Compared to the semi-Markov process in its usual definition the generalized process allows the analysis of a larger class of systems. For instance systems with arbitrarily distributed lifetimes of their components can be described. There is also a chance to describe systems which are modified during time by forces or manipulations from outside. (Auth.)

Identification of Optimal Policies in Markov Decision Processes

Czech Academy of Sciences Publication Activity Database

Sladký, Karel

46 2010, č. 3 (2010), s. 558-570 ISSN 0023-5954. [International Conference on Mathematical Methods in Economy and Industry. České Budějovice, 15.06.2009-18.06.2009] R&D Projects: GA ČR(CZ) GA402/08/0107; GA ČR GA402/07/1113 Institutional research plan: CEZ:AV0Z10750506 Keywords : finite state Markov decision processes * discounted and average costs * elimination of suboptimal policies Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 0.461, year: 2010 http://library.utia.cas.cz/separaty/2010/E/sladky-identification of optimal policies in markov decision processes.pdf

Markov decision processes: a tool for sequential decision making under uncertainty.

Science.gov (United States)

Alagoz, Oguzhan; Hsu, Heather; Schaefer, Andrew J; Roberts, Mark S

2010-01-01

We provide a tutorial on the construction and evaluation of Markov decision processes (MDPs), which are powerful analytical tools used for sequential decision making under uncertainty that have been widely used in many industrial and manufacturing applications but are underutilized in medical decision making (MDM). We demonstrate the use of an MDP to solve a sequential clinical treatment problem under uncertainty. Markov decision processes generalize standard Markov models in that a decision process is embedded in the model and multiple decisions are made over time. Furthermore, they have significant advantages over standard decision analysis. We compare MDPs to standard Markov-based simulation models by solving the problem of the optimal timing of living-donor liver transplantation using both methods. Both models result in the same optimal transplantation policy and the same total life expectancies for the same patient and living donor. The computation time for solving the MDP model is significantly smaller than that for solving the Markov model. We briefly describe the growing literature of MDPs applied to medical decisions.

Poisson point processes imaging, tracking, and sensing

CERN Document Server

Streit, Roy L

2010-01-01

This overview of non-homogeneous and multidimensional Poisson point processes and their applications features mathematical tools and applications from emission- and transmission-computed tomography to multiple target tracking and distributed sensor detection.

Discounted semi-Markov decision processes : linear programming and policy iteration

NARCIS (Netherlands)

Wessels, J.; van Nunen, J.A.E.E.

1975-01-01

For semi-Markov decision processes with discounted rewards we derive the well known results regarding the structure of optimal strategies (nonrandomized, stationary Markov strategies) and the standard algorithms (linear programming, policy iteration). Our analysis is completely based on a primal

Discounted semi-Markov decision processes : linear programming and policy iteration

NARCIS (Netherlands)

Wessels, J.; van Nunen, J.A.E.E.

1974-01-01

For semi-Markov decision processes with discounted rewards we derive the well known results regarding the structure of optimal strategies (nonrandomized, stationary Markov strategies) and the standard algorithms (linear programming, policy iteration). Our analysis is completely based on a primal

Statistical analysis of non-homogeneous Poisson processes. Statistical processing of a particle multidetector

International Nuclear Information System (INIS)

Lacombe, J.P.

1985-12-01

Statistic study of Poisson non-homogeneous and spatial processes is the first part of this thesis. A Neyman-Pearson type test is defined concerning the intensity measurement of these processes. Conditions are given for which consistency of the test is assured, and others giving the asymptotic normality of the test statistics. Then some techniques of statistic processing of Poisson fields and their applications to a particle multidetector study are given. Quality tests of the device are proposed togetherwith signal extraction methods [fr

Markov Processes in Image Processing

Science.gov (United States)

Petrov, E. P.; Kharina, N. L.

2018-05-01

Digital images are used as an information carrier in different sciences and technologies. The aspiration to increase the number of bits in the image pixels for the purpose of obtaining more information is observed. In the paper, some methods of compression and contour detection on the basis of two-dimensional Markov chain are offered. Increasing the number of bits on the image pixels will allow one to allocate fine object details more precisely, but it significantly complicates image processing. The methods of image processing do not concede by the efficiency to well-known analogues, but surpass them in processing speed. An image is separated into binary images, and processing is carried out in parallel with each without an increase in speed, when increasing the number of bits on the image pixels. One more advantage of methods is the low consumption of energy resources. Only logical procedures are used and there are no computing operations. The methods can be useful in processing images of any class and assignment in processing systems with a limited time and energy resources.

Monte Carlo Simulation of Markov, Semi-Markov, and Generalized Semi- Markov Processes in Probabilistic Risk Assessment

Science.gov (United States)

English, Thomas

2005-01-01

A standard tool of reliability analysis used at NASA-JSC is the event tree. An event tree is simply a probability tree, with the probabilities determining the next step through the tree specified at each node. The nodal probabilities are determined by a reliability study of the physical system at work for a particular node. The reliability study performed at a node is typically referred to as a fault tree analysis, with the potential of a fault tree existing.for each node on the event tree. When examining an event tree it is obvious why the event tree/fault tree approach has been adopted. Typical event trees are quite complex in nature, and the event tree/fault tree approach provides a systematic and organized approach to reliability analysis. The purpose of this study was two fold. Firstly, we wanted to explore the possibility that a semi-Markov process can create dependencies between sojourn times (the times it takes to transition from one state to the next) that can decrease the uncertainty when estimating time to failures. Using a generalized semi-Markov model, we studied a four element reliability model and were able to demonstrate such sojourn time dependencies. Secondly, we wanted to study the use of semi-Markov processes to introduce a time variable into the event tree diagrams that are commonly developed in PRA (Probabilistic Risk Assessment) analyses. Event tree end states which change with time are more representative of failure scenarios than are the usual static probability-derived end states.

A Metrized Duality Theorem for Markov Processes

DEFF Research Database (Denmark)

Kozen, Dexter; Mardare, Radu Iulian; Panangaden, Prakash

2014-01-01

We extend our previous duality theorem for Markov processes by equipping the processes with a pseudometric and the algebras with a notion of metric diameter. We are able to show that the isomorphisms of our previous duality theorem become isometries in this quantitative setting. This opens the wa...

Prediction and generation of binary Markov processes: Can a finite-state fox catch a Markov mouse?

Science.gov (United States)

Ruebeck, Joshua B.; James, Ryan G.; Mahoney, John R.; Crutchfield, James P.

2018-01-01

Understanding the generative mechanism of a natural system is a vital component of the scientific method. Here, we investigate one of the fundamental steps toward this goal by presenting the minimal generator of an arbitrary binary Markov process. This is a class of processes whose predictive model is well known. Surprisingly, the generative model requires three distinct topologies for different regions of parameter space. We show that a previously proposed generator for a particular set of binary Markov processes is, in fact, not minimal. Our results shed the first quantitative light on the relative (minimal) costs of prediction and generation. We find, for instance, that the difference between prediction and generation is maximized when the process is approximately independently, identically distributed.

Operational Markov Condition for Quantum Processes

Science.gov (United States)

Pollock, Felix A.; Rodríguez-Rosario, César; Frauenheim, Thomas; Paternostro, Mauro; Modi, Kavan

2018-01-01

We derive a necessary and sufficient condition for a quantum process to be Markovian which coincides with the classical one in the relevant limit. Our condition unifies all previously known definitions for quantum Markov processes by accounting for all potentially detectable memory effects. We then derive a family of measures of non-Markovianity with clear operational interpretations, such as the size of the memory required to simulate a process or the experimental falsifiability of a Markovian hypothesis.

Moments analysis of concurrent Poisson processes

International Nuclear Information System (INIS)

McBeth, G.W.; Cross, P.

1975-01-01

A moments analysis of concurrent Poisson processes has been carried out. Equations are given which relate combinations of distribution moments to sums of products involving the number of counts associated with the processes and the mean rate of the processes. Elimination of background is discussed and equations suitable for processing random radiation, parent-daughter pairs in the presence of background, and triple and double correlations in the presence of background are given. The theory of identification of the four principle radioactive series by moments analysis is discussed. (Auth.)

Spectral analysis of multi-dimensional self-similar Markov processes

International Nuclear Information System (INIS)

Modarresi, N; Rezakhah, S

2010-01-01

In this paper we consider a discrete scale invariant (DSI) process {X(t), t in R + } with scale l > 1. We consider a fixed number of observations in every scale, say T, and acquire our samples at discrete points α k , k in W, where α is obtained by the equality l = α T and W = {0, 1, ...}. We thus provide a discrete time scale invariant (DT-SI) process X(.) with the parameter space {α k , k in W}. We find the spectral representation of the covariance function of such a DT-SI process. By providing the harmonic-like representation of multi-dimensional self-similar processes, spectral density functions of them are presented. We assume that the process {X(t), t in R + } is also Markov in the wide sense and provide a discrete time scale invariant Markov (DT-SIM) process with the above scheme of sampling. We present an example of the DT-SIM process, simple Brownian motion, by the above sampling scheme and verify our results. Finally, we find the spectral density matrix of such a DT-SIM process and show that its associated T-dimensional self-similar Markov process is fully specified by {R H j (1), R j H (0), j = 0, 1, ..., T - 1}, where R H j (τ) is the covariance function of jth and (j + τ)th observations of the process.

A Local Poisson Graphical Model for inferring networks from sequencing data.

Science.gov (United States)

Allen, Genevera I; Liu, Zhandong

2013-09-01

Gaussian graphical models, a class of undirected graphs or Markov Networks, are often used to infer gene networks based on microarray expression data. Many scientists, however, have begun using high-throughput sequencing technologies such as RNA-sequencing or next generation sequencing to measure gene expression. As the resulting data consists of counts of sequencing reads for each gene, Gaussian graphical models are not optimal for this discrete data. In this paper, we propose a novel method for inferring gene networks from sequencing data: the Local Poisson Graphical Model. Our model assumes a Local Markov property where each variable conditional on all other variables is Poisson distributed. We develop a neighborhood selection algorithm to fit our model locally by performing a series of l1 penalized Poisson, or log-linear, regressions. This yields a fast parallel algorithm for estimating networks from next generation sequencing data. In simulations, we illustrate the effectiveness of our methods for recovering network structure from count data. A case study on breast cancer microRNAs (miRNAs), a novel application of graphical models, finds known regulators of breast cancer genes and discovers novel miRNA clusters and hubs that are targets for future research.

Modeling spiking behavior of neurons with time-dependent Poisson processes.

Science.gov (United States)

Shinomoto, S; Tsubo, Y

2001-10-01

Three kinds of interval statistics, as represented by the coefficient of variation, the skewness coefficient, and the correlation coefficient of consecutive intervals, are evaluated for three kinds of time-dependent Poisson processes: pulse regulated, sinusoidally regulated, and doubly stochastic. Among these three processes, the sinusoidally regulated and doubly stochastic Poisson processes, in the case when the spike rate varies slowly compared with the mean interval between spikes, are found to be consistent with the three statistical coefficients exhibited by data recorded from neurons in the prefrontal cortex of monkeys.

Poisson Autoregression

DEFF Research Database (Denmark)

Fokianos, Konstantinos; Rahbek, Anders Christian; Tjøstheim, Dag

This paper considers geometric ergodicity and likelihood based inference for linear and nonlinear Poisson autoregressions. In the linear case the conditional mean is linked linearly to its past values as well as the observed values of the Poisson process. This also applies to the conditional...... variance, implying an interpretation as an integer valued GARCH process. In a nonlinear conditional Poisson model, the conditional mean is a nonlinear function of its past values and a nonlinear function of past observations. As a particular example an exponential autoregressive Poisson model for time...

Poisson Autoregression

DEFF Research Database (Denmark)

Fokianos, Konstantinos; Rahbæk, Anders; Tjøstheim, Dag

This paper considers geometric ergodicity and likelihood based inference for linear and nonlinear Poisson autoregressions. In the linear case the conditional mean is linked linearly to its past values as well as the observed values of the Poisson process. This also applies to the conditional...... variance, making an interpretation as an integer valued GARCH process possible. In a nonlinear conditional Poisson model, the conditional mean is a nonlinear function of its past values and a nonlinear function of past observations. As a particular example an exponential autoregressive Poisson model...

Hidden Markov processes theory and applications to biology

CERN Document Server

Vidyasagar, M

2014-01-01

This book explores important aspects of Markov and hidden Markov processes and the applications of these ideas to various problems in computational biology. The book starts from first principles, so that no previous knowledge of probability is necessary. However, the work is rigorous and mathematical, making it useful to engineers and mathematicians, even those not interested in biological applications. A range of exercises is provided, including drills to familiarize the reader with concepts and more advanced problems that require deep thinking about the theory. Biological applications are t

The explicit form of the rate function for semi-Markov processes and its contractions

Science.gov (United States)

Sughiyama, Yuki; Kobayashi, Testuya J.

2018-03-01

We derive the explicit form of the rate function for semi-Markov processes. Here, the ‘random time change trick’ plays an essential role. Also, by exploiting the contraction principle of large deviation theory to the explicit form, we show that the fluctuation theorem (Gallavotti-Cohen symmetry) holds for semi-Markov cases. Furthermore, we elucidate that our rate function is an extension of the level 2.5 rate function for Markov processes to semi-Markov cases.

State Estimation for Linear Systems Driven Simultaneously by Wiener and Poisson Processes.

Science.gov (United States)

1978-12-01

The state estimation problem of linear stochastic systems driven simultaneously by Wiener and Poisson processes is considered, especially the case...where the incident intensities of the Poisson processes are low and the system is observed in an additive white Gaussian noise. The minimum mean squared

Reliability Analysis of a Cold Standby System with Imperfect Repair and under Poisson Shocks

Directory of Open Access Journals (Sweden)

Yutian Chen

2014-01-01

Full Text Available This paper considers the reliability analysis of a two-component cold standby system with a repairman who may have vacation. The system may fail due to intrinsic factors like aging or deteriorating, or external factors such as Poisson shocks. The arrival time of the shocks follows a Poisson process with the intensity λ>0. Whenever the magnitude of a shock is larger than the prespecified threshold of the operating component, the operating component will fail. The paper assumes that the intrinsic lifetime and the repair time on the component are an extended Poisson process, the magnitude of the shock and the threshold of the operating component are nonnegative random variables, and the vacation time of the repairman obeys the general continuous probability distribution. By using the vector Markov process theory, the supplementary variable method, Laplace transform, and Tauberian theory, the paper derives a number of reliability indices: system availability, system reliability, the rate of occurrence of the system failure, and the mean time to the first failure of the system. Finally, a numerical example is given to validate the derived indices.

Nonhomogeneous Poisson process with nonparametric frailty

International Nuclear Information System (INIS)

Slimacek, Vaclav; Lindqvist, Bo Henry

2016-01-01

The failure processes of heterogeneous repairable systems are often modeled by non-homogeneous Poisson processes. The common way to describe an unobserved heterogeneity between systems is to multiply the basic rate of occurrence of failures by a random variable (a so-called frailty) having a specified parametric distribution. Since the frailty is unobservable, the choice of its distribution is a problematic part of using these models, as are often the numerical computations needed in the estimation of these models. The main purpose of this paper is to develop a method for estimation of the parameters of a nonhomogeneous Poisson process with unobserved heterogeneity which does not require parametric assumptions about the heterogeneity and which avoids the frequently encountered numerical problems associated with the standard models for unobserved heterogeneity. The introduced method is illustrated on an example involving the power law process, and is compared to the standard gamma frailty model and to the classical model without unobserved heterogeneity. The derived results are confirmed in a simulation study which also reveals several not commonly known properties of the gamma frailty model and the classical model, and on a real life example. - Highlights: • A new method for estimation of a NHPP with frailty is introduced. • Introduced method does not require parametric assumptions about frailty. • The approach is illustrated on an example with the power law process. • The method is compared to the gamma frailty model and to the model without frailty.

Exact solution of the hidden Markov processes

Science.gov (United States)

Saakian, David B.

2017-11-01

We write a master equation for the distributions related to hidden Markov processes (HMPs) and solve it using a functional equation. Thus the solution of HMPs is mapped exactly to the solution of the functional equation. For a general case the latter can be solved only numerically. We derive an exact expression for the entropy of HMPs. Our expression for the entropy is an alternative to the ones given before by the solution of integral equations. The exact solution is possible because actually the model can be considered as a generalized random walk on a one-dimensional strip. While we give the solution for the two second-order matrices, our solution can be easily generalized for the L values of the Markov process and M values of observables: We should be able to solve a system of L functional equations in the space of dimension M -1 .

Critical Age-Dependent Branching Markov Processes and their ...

Indian Academy of Sciences (India)

This paper studies: (i) the long-time behaviour of the empirical distribution of age and normalized position of an age-dependent critical branching Markov process conditioned on non-extinction; and (ii) the super-process limit of a sequence of age-dependent critical branching Brownian motions.

Doubly stochastic Poisson processes in artificial neural learning.

Science.gov (United States)

Card, H C

1998-01-01

This paper investigates neuron activation statistics in artificial neural networks employing stochastic arithmetic. It is shown that a doubly stochastic Poisson process is an appropriate model for the signals in these circuits.

Dynamical fluctuations for semi-Markov processes

Czech Academy of Sciences Publication Activity Database

Maes, C.; Netočný, Karel; Wynants, B.

2009-01-01

Roč. 42, č. 36 (2009), 365002/1-365002/21 ISSN 1751-8113 R&D Projects: GA ČR GC202/07/J051 Institutional research plan: CEZ:AV0Z10100520 Keywords : nonequilibrium fluctuations * semi-Markov processes Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.577, year: 2009 http://www.iop.org/EJ/abstract/1751-8121/42/36/365002

Reduction of Poisson noise in measured time-resolved data for time-domain diffuse optical tomography.

Science.gov (United States)

Okawa, S; Endo, Y; Hoshi, Y; Yamada, Y

2012-01-01

A method to reduce noise for time-domain diffuse optical tomography (DOT) is proposed. Poisson noise which contaminates time-resolved photon counting data is reduced by use of maximum a posteriori estimation. The noise-free data are modeled as a Markov random process, and the measured time-resolved data are assumed as Poisson distributed random variables. The posterior probability of the occurrence of the noise-free data is formulated. By maximizing the probability, the noise-free data are estimated, and the Poisson noise is reduced as a result. The performances of the Poisson noise reduction are demonstrated in some experiments of the image reconstruction of time-domain DOT. In simulations, the proposed method reduces the relative error between the noise-free and noisy data to about one thirtieth, and the reconstructed DOT image was smoothed by the proposed noise reduction. The variance of the reconstructed absorption coefficients decreased by 22% in a phantom experiment. The quality of DOT, which can be applied to breast cancer screening etc., is improved by the proposed noise reduction.

Simulation based sequential Monte Carlo methods for discretely observed Markov processes

OpenAIRE

Neal, Peter

2014-01-01

Parameter estimation for discretely observed Markov processes is a challenging problem. However, simulation of Markov processes is straightforward using the Gillespie algorithm. We exploit this ease of simulation to develop an effective sequential Monte Carlo (SMC) algorithm for obtaining samples from the posterior distribution of the parameters. In particular, we introduce two key innovations, coupled simulations, which allow us to study multiple parameter values on the basis of a single sim...

Active Learning of Markov Decision Processes for System Verification

DEFF Research Database (Denmark)

Chen, Yingke; Nielsen, Thomas Dyhre

2012-01-01

deterministic Markov decision processes from data by actively guiding the selection of input actions. The algorithm is empirically analyzed by learning system models of slot machines, and it is demonstrated that the proposed active learning procedure can significantly reduce the amount of data required...... demanding process, and this shortcoming has motivated the development of algorithms for automatically learning system models from observed system behaviors. Recently, algorithms have been proposed for learning Markov decision process representations of reactive systems based on alternating sequences...... of input/output observations. While alleviating the problem of manually constructing a system model, the collection/generation of observed system behaviors can also prove demanding. Consequently we seek to minimize the amount of data required. In this paper we propose an algorithm for learning...

Stark interaction of identical particles with the vacuum electromagnetic field as quantum Poisson process suppressing collective spontaneous emission

International Nuclear Information System (INIS)

Basharov, A. M.

2011-01-01

The effective Hamiltonian describing resonant interaction of an ensemble of identical quantum particles with a photon-free vacuum electromagnetic field has been obtained with allowance for terms of second order in the coupling constant (the Stark interaction) by means of the perturbation theory on the basis of the unitary transformation of the system quantum state. It has been shown that in the Markov approximation the effective Hamiltonian terms of first order in the coupling constant are represented by the quantum Wiener process, whereas terms of second order are expressed by the quantum Poisson process. During the course of the investigation, it was established that the Stark interaction played a significant role in the ensemble dynamics, thus influencing the collective spontaneous decay of the ensemble of an appreciably high number of identical particles. Fundamental effects have been discovered, i.e., the excitation conservation in a sufficiently dense ensemble of identical particles and superradiance suppression in the collective decaying process of an excited ensemble with a determined number of particles.

Tests of a homogeneous Poisson process against clustering and other alternatives

International Nuclear Information System (INIS)

Atwood, C.L.

1994-05-01

This report presents three closely related tests of the hypothesis that data points come from a homogeneous Poisson process. If there is too much observed variation among the log-transformed between-point distances, the hypothesis is rejected. The tests are more powerful than the standard chi-squared test against the alternative hypothesis of event clustering, but not against the alternative hypothesis of a Poisson process with smoothly varying intensity

Poisson pre-processing of nonstationary photonic signals: Signals with equality between mean and variance.

Science.gov (United States)

Poplová, Michaela; Sovka, Pavel; Cifra, Michal

2017-01-01

Photonic signals are broadly exploited in communication and sensing and they typically exhibit Poisson-like statistics. In a common scenario where the intensity of the photonic signals is low and one needs to remove a nonstationary trend of the signals for any further analysis, one faces an obstacle: due to the dependence between the mean and variance typical for a Poisson-like process, information about the trend remains in the variance even after the trend has been subtracted, possibly yielding artifactual results in further analyses. Commonly available detrending or normalizing methods cannot cope with this issue. To alleviate this issue we developed a suitable pre-processing method for the signals that originate from a Poisson-like process. In this paper, a Poisson pre-processing method for nonstationary time series with Poisson distribution is developed and tested on computer-generated model data and experimental data of chemiluminescence from human neutrophils and mung seeds. The presented method transforms a nonstationary Poisson signal into a stationary signal with a Poisson distribution while preserving the type of photocount distribution and phase-space structure of the signal. The importance of the suggested pre-processing method is shown in Fano factor and Hurst exponent analysis of both computer-generated model signals and experimental photonic signals. It is demonstrated that our pre-processing method is superior to standard detrending-based methods whenever further signal analysis is sensitive to variance of the signal.

Poisson and Gaussian approximation of weighted local empirical processes

NARCIS (Netherlands)

Einmahl, J.H.J.

1995-01-01

We consider the local empirical process indexed by sets, a greatly generalized version of the well-studied uniform tail empirical process. We show that the weak limit of weighted versions of this process is Poisson under certain conditions, whereas it is Gaussian in other situations. Our main

Continuous-time Markov decision processes theory and applications

CERN Document Server

Guo, Xianping

2009-01-01

This volume provides the first book entirely devoted to recent developments on the theory and applications of continuous-time Markov decision processes (MDPs). The MDPs presented here include most of the cases that arise in applications.

Properly quantized history-dependent Parrondo games, Markov processes, and multiplexing circuits

Energy Technology Data Exchange (ETDEWEB)

Bleiler, Steven A. [Fariborz Maseeh Department of Mathematics and Statistics, Portland State University, PO Box 751, Portland, OR 97207 (United States); Khan, Faisal Shah, E-mail: faisal.khan@kustar.ac.a [Khalifa University of Science, Technology and Research, PO Box 127788, Abu Dhabi (United Arab Emirates)

2011-05-09

Highlights: History-dependent Parrondo games are viewed as Markov processes. Quantum mechanical analogues of these Markov processes are constructed. These quantum analogues restrict to the original process on measurement. Relationship between these analogues and a quantum circuits is exhibited. - Abstract: In the context of quantum information theory, 'quantization' of various mathematical and computational constructions is said to occur upon the replacement, at various points in the construction, of the classical randomization notion of probability distribution with higher order randomization notions from quantum mechanics such as quantum superposition with measurement. For this to be done 'properly', a faithful copy of the original construction is required to exist within the new quantum one, just as is required when a function is extended to a larger domain. Here procedures for extending history-dependent Parrondo games, Markov processes and multiplexing circuits to their quantum versions are analyzed from a game theoretic viewpoint, and from this viewpoint, proper quantizations developed.

A System of Poisson Equations for a Nonconstant Varadhan Functional on a Finite State Space

International Nuclear Information System (INIS)

Cavazos-Cadena, Rolando; Hernandez-Hernandez, Daniel

2006-01-01

Given a discrete-time Markov chain with finite state space and a stationary transition matrix, a system of 'local' Poisson equations characterizing the (exponential) Varadhan's functional J(.) is given. The main results, which are derived for an arbitrary transition structure so that J(.) may be nonconstant, are as follows: (i) Any solution to the local Poisson equations immediately renders Varadhan's functional, and (ii) a solution of the system always exist. The proof of this latter result is constructive and suggests a method to solve the local Poisson equations

Neyman, Markov processes and survival analysis.

Science.gov (United States)

Yang, Grace

2013-07-01

J. Neyman used stochastic processes extensively in his applied work. One example is the Fix and Neyman (F-N) competing risks model (1951) that uses finite homogeneous Markov processes to analyse clinical trials with breast cancer patients. We revisit the F-N model, and compare it with the Kaplan-Meier (K-M) formulation for right censored data. The comparison offers a way to generalize the K-M formulation to include risks of recovery and relapses in the calculation of a patient's survival probability. The generalization is to extend the F-N model to a nonhomogeneous Markov process. Closed-form solutions of the survival probability are available in special cases of the nonhomogeneous processes, like the popular multiple decrement model (including the K-M model) and Chiang's staging model, but these models do not consider recovery and relapses while the F-N model does. An analysis of sero-epidemiology current status data with recurrent events is illustrated. Fix and Neyman used Neyman's RBAN (regular best asymptotic normal) estimates for the risks, and provided a numerical example showing the importance of considering both the survival probability and the length of time of a patient living a normal life in the evaluation of clinical trials. The said extension would result in a complicated model and it is unlikely to find analytical closed-form solutions for survival analysis. With ever increasing computing power, numerical methods offer a viable way of investigating the problem.

Simulation on a computer the cascade probabilistic functions and theirs relation with Markov's processes

International Nuclear Information System (INIS)

Kupchishin, A.A.; Kupchishin, A.I.; Shmygaleva, T.A.

2002-01-01

Within framework of the cascade-probabilistic (CP) method the radiation and physical processes are studied, theirs relation with Markov's processes are found. The conclusion that CP-function for electrons, protons, alpha-particles and ions are describing by unhomogeneous Markov's chain is drawn. The algorithms are developed, the CP-functions calculations for charged particles, concentration of radiation defects in solids at ion irradiation are carried out as well. Tables for CPF different parameters and radiation defects concentration at charged particle interaction with solids are given. The book consists of the introduction and two chapters: (1) Cascade probabilistic function and the Markov's processes; (2) Radiation defects formation in solids as a part of the Markov's processes. The book is intended for specialists on the radiation defects mathematical stimulation, solid state physics, elementary particles physics and applied mathematics

The Markov process admits a consistent steady-state thermodynamic formalism

Science.gov (United States)

Peng, Liangrong; Zhu, Yi; Hong, Liu

2018-01-01

The search for a unified formulation for describing various non-equilibrium processes is a central task of modern non-equilibrium thermodynamics. In this paper, a novel steady-state thermodynamic formalism was established for general Markov processes described by the Chapman-Kolmogorov equation. Furthermore, corresponding formalisms of steady-state thermodynamics for the master equation and Fokker-Planck equation could be rigorously derived in mathematics. To be concrete, we proved that (1) in the limit of continuous time, the steady-state thermodynamic formalism for the Chapman-Kolmogorov equation fully agrees with that for the master equation; (2) a similar one-to-one correspondence could be established rigorously between the master equation and Fokker-Planck equation in the limit of large system size; (3) when a Markov process is restrained to one-step jump, the steady-state thermodynamic formalism for the Fokker-Planck equation with discrete state variables also goes to that for master equations, as the discretization step gets smaller and smaller. Our analysis indicated that general Markov processes admit a unified and self-consistent non-equilibrium steady-state thermodynamic formalism, regardless of underlying detailed models.

Poisson processes and a Bessel function integral

NARCIS (Netherlands)

Steutel, F.W.

1985-01-01

The probability of winning a simple game of competing Poisson processes turns out to be equal to the well-known Bessel function integral J(x, y) (cf. Y. L. Luke, Integrals of Bessel Functions, McGraw-Hill, New York, 1962). Several properties of J, some of which seem to be new, follow quite easily

Maximizing Entropy over Markov Processes

DEFF Research Database (Denmark)

Biondi, Fabrizio; Legay, Axel; Nielsen, Bo Friis

2013-01-01

The channel capacity of a deterministic system with confidential data is an upper bound on the amount of bits of data an attacker can learn from the system. We encode all possible attacks to a system using a probabilistic specification, an Interval Markov Chain. Then the channel capacity...... as a reward function, a polynomial algorithm to verify the existence of an system maximizing entropy among those respecting a specification, a procedure for the maximization of reward functions over Interval Markov Chains and its application to synthesize an implementation maximizing entropy. We show how...... to use Interval Markov Chains to model abstractions of deterministic systems with confidential data, and use the above results to compute their channel capacity. These results are a foundation for ongoing work on computing channel capacity for abstractions of programs derived from code....

Maximizing entropy over Markov processes

DEFF Research Database (Denmark)

Biondi, Fabrizio; Legay, Axel; Nielsen, Bo Friis

2014-01-01

The channel capacity of a deterministic system with confidential data is an upper bound on the amount of bits of data an attacker can learn from the system. We encode all possible attacks to a system using a probabilistic specification, an Interval Markov Chain. Then the channel capacity...... as a reward function, a polynomial algorithm to verify the existence of a system maximizing entropy among those respecting a specification, a procedure for the maximization of reward functions over Interval Markov Chains and its application to synthesize an implementation maximizing entropy. We show how...... to use Interval Markov Chains to model abstractions of deterministic systems with confidential data, and use the above results to compute their channel capacity. These results are a foundation for ongoing work on computing channel capacity for abstractions of programs derived from code. © 2014 Elsevier...

Quantum fields and Poisson processes. Pt. 2

International Nuclear Information System (INIS)

Bertrand, J.; Gaveau, B.; Rideau, G.

1985-01-01

Quantum field evolutions are written as expectation values with respect to Poisson processes in two simple models; interaction of two boson fields (with conservation of the number of particles in one field) and interaction of a boson with a fermion field. The introduction of a cutt-off ensures that the expectation values are well-defined. (orig.)

On the record process of time-reversible spectrally-negative Markov additive processes

NARCIS (Netherlands)

J. Ivanovs; M.R.H. Mandjes (Michel)

2009-01-01

htmlabstractWe study the record process of a spectrally-negative Markov additive process (MAP). Assuming time-reversibility, a number of key quantities can be given explicitly. It is shown how these key quantities can be used when analyzing the distribution of the all-time maximum attained by MAPs

Dependent Neyman type A processes based on common shock Poisson approach

Science.gov (United States)

Kadilar, Gamze Özel; Kadilar, Cem

2016-04-01

The Neyman type A process is used for describing clustered data since the Poisson process is insufficient for clustering of events. In a multivariate setting, there may be dependencies between multivarite Neyman type A processes. In this study, dependent form of the Neyman type A process is considered under common shock approach. Then, the joint probability function are derived for the dependent Neyman type A Poisson processes. Then, an application based on forest fires in Turkey are given. The results show that the joint probability function of the dependent Neyman type A processes, which is obtained in this study, can be a good tool for the probabilistic fitness for the total number of burned trees in Turkey.

Modeling environmental noise exceedances using non-homogeneous Poisson processes.

Science.gov (United States)

Guarnaccia, Claudio; Quartieri, Joseph; Barrios, Juan M; Rodrigues, Eliane R

2014-10-01

In this work a non-homogeneous Poisson model is considered to study noise exposure. The Poisson process, counting the number of times that a sound level surpasses a threshold, is used to estimate the probability that a population is exposed to high levels of noise a certain number of times in a given time interval. The rate function of the Poisson process is assumed to be of a Weibull type. The presented model is applied to community noise data from Messina, Sicily (Italy). Four sets of data are used to estimate the parameters involved in the model. After the estimation and tuning are made, a way of estimating the probability that an environmental noise threshold is exceeded a certain number of times in a given time interval is presented. This estimation can be very useful in the study of noise exposure of a population and also to predict, given the current behavior of the data, the probability of occurrence of high levels of noise in the near future. One of the most important features of the model is that it implicitly takes into account different noise sources, which need to be treated separately when using usual models.

Continuous strong Markov processes in dimension one a stochastic calculus approach

CERN Document Server

Assing, Sigurd

1998-01-01

The book presents an in-depth study of arbitrary one-dimensional continuous strong Markov processes using methods of stochastic calculus. Departing from the classical approaches, a unified investigation of regular as well as arbitrary non-regular diffusions is provided. A general construction method for such processes, based on a generalization of the concept of a perfect additive functional, is developed. The intrinsic decomposition of a continuous strong Markov semimartingale is discovered. The book also investigates relations to stochastic differential equations and fundamental examples of irregular diffusions.

Nonparametric Bayesian inference for multidimensional compound Poisson processes

NARCIS (Netherlands)

Gugushvili, S.; van der Meulen, F.; Spreij, P.

2015-01-01

Given a sample from a discretely observed multidimensional compound Poisson process, we study the problem of nonparametric estimation of its jump size density r0 and intensity λ0. We take a nonparametric Bayesian approach to the problem and determine posterior contraction rates in this context,

Poisson Autoregression

DEFF Research Database (Denmark)

Fokianos, Konstantinos; Rahbek, Anders Christian; Tjøstheim, Dag

2009-01-01

In this article we consider geometric ergodicity and likelihood-based inference for linear and nonlinear Poisson autoregression. In the linear case, the conditional mean is linked linearly to its past values, as well as to the observed values of the Poisson process. This also applies...... to the conditional variance, making possible interpretation as an integer-valued generalized autoregressive conditional heteroscedasticity process. In a nonlinear conditional Poisson model, the conditional mean is a nonlinear function of its past values and past observations. As a particular example, we consider...... an exponential autoregressive Poisson model for time series. Under geometric ergodicity, the maximum likelihood estimators are shown to be asymptotically Gaussian in the linear model. In addition, we provide a consistent estimator of their asymptotic covariance matrix. Our approach to verifying geometric...

Optimal linear filtering of Poisson process with dead time

International Nuclear Information System (INIS)

Glukhova, E.V.

1993-01-01

The paper presents a derivation of an integral equation defining the impulsed transient of optimum linear filtering for evaluation of the intensity of the fluctuating Poisson process with allowance for dead time of transducers

Markov Decision Process Measurement Model.

Science.gov (United States)

LaMar, Michelle M

2018-03-01

Within-task actions can provide additional information on student competencies but are challenging to model. This paper explores the potential of using a cognitive model for decision making, the Markov decision process, to provide a mapping between within-task actions and latent traits of interest. Psychometric properties of the model are explored, and simulation studies report on parameter recovery within the context of a simple strategy game. The model is then applied to empirical data from an educational game. Estimates from the model are found to correlate more strongly with posttest results than a partial-credit IRT model based on outcome data alone.

Testing the Adequacy of a Semi-Markov Process

Science.gov (United States)

2015-09-17

classical Brownian motion are two common examples of martingales. Submartingales and supermartingales are two extended classes of martingales. They... movements using Semi-Markov processes,” Tourism Management, Vol. 32, No. 4, 2011, pp. 844–851. [4] Titman, A. C. and Sharples, L. D., “Model

Risk Sensitive Filtering with Poisson Process Observations

International Nuclear Information System (INIS)

Malcolm, W. P.; James, M. R.; Elliott, R. J.

2000-01-01

In this paper we consider risk sensitive filtering for Poisson process observations. Risk sensitive filtering is a type of robust filtering which offers performance benefits in the presence of uncertainties. We derive a risk sensitive filter for a stochastic system where the signal variable has dynamics described by a diffusion equation and determines the rate function for an observation process. The filtering equations are stochastic integral equations. Computer simulations are presented to demonstrate the performance gain for the risk sensitive filter compared with the risk neutral filter

Poisson processes on groups and Feynman path integrals

International Nuclear Information System (INIS)

Combe, P.; Rodriguez, R.; Sirugue-Collin, M.; Centre National de la Recherche Scientifique, 13 - Marseille; Sirugue, M.

1979-09-01

An expression is given for the perturbed evolution of a free evolution by gentle, possibly velocity dependent, potential, in terms of the expectation with respect to a Poisson process on a group. Various applications are given in particular to usual quantum mechanics but also to Fermi and spin systems

Monitoring Poisson time series using multi-process models

DEFF Research Database (Denmark)

Engebjerg, Malene Dahl Skov; Lundbye-Christensen, Søren; Kjær, Birgitte B.

aspects of health resource management may also be addressed. In this paper we center on the detection of outbreaks of infectious diseases. This is achieved by a multi-process Poisson state space model taking autocorrelation and overdispersion into account, which has been applied to a data set concerning...

Doubly stochastic Poisson process models for precipitation at fine time-scales

Science.gov (United States)

Ramesh, Nadarajah I.; Onof, Christian; Xie, Dichao

2012-09-01

This paper considers a class of stochastic point process models, based on doubly stochastic Poisson processes, in the modelling of rainfall. We examine the application of this class of models, a neglected alternative to the widely-known Poisson cluster models, in the analysis of fine time-scale rainfall intensity. These models are mainly used to analyse tipping-bucket raingauge data from a single site but an extension to multiple sites is illustrated which reveals the potential of this class of models to study the temporal and spatial variability of precipitation at fine time-scales.

Is neutron evaporation from highly excited nuclei a poisson random process

International Nuclear Information System (INIS)

Simbel, M.H.

1982-01-01

It is suggested that neutron emission from highly excited nuclei follows a Poisson random process. The continuous variable of the process is the excitation energy excess over the binding energy of the emitted neutrons and the discrete variable is the number of emitted neutrons. Cross sections for (HI,xn) reactions are analyzed using a formula containing a Poisson distribution function. The post- and pre-equilibrium components of the cross section are treated separately. The agreement between the predictions of this formula and the experimental results is very good. (orig.)

Applied probability and stochastic processes. 2. ed.

Energy Technology Data Exchange (ETDEWEB)

Feldman, Richard M. [Texas A and M Univ., College Station, TX (United States). Industrial and Systems Engineering Dept.; Valdez-Flores, Ciriaco [Sielken and Associates Consulting, Inc., Bryan, TX (United States)

2010-07-01

This book presents applied probability and stochastic processes in an elementary but mathematically precise manner, with numerous examples and exercises to illustrate the range of engineering and science applications of the concepts. The book is designed to give the reader an intuitive understanding of probabilistic reasoning, in addition to an understanding of mathematical concepts and principles. The initial chapters present a summary of probability and statistics and then Poisson processes, Markov chains, Markov processes and queuing processes are introduced. Advanced topics include simulation, inventory theory, replacement theory, Markov decision theory, and the use of matrix geometric procedures in the analysis of queues. Included in the second edition are appendices at the end of several chapters giving suggestions for the use of Excel in solving the problems of the chapter. Also new in this edition are an introductory chapter on statistics and a chapter on Poisson processes that includes some techniques used in risk assessment. The old chapter on queues has been expanded and broken into two new chapters: one for simple queuing processes and one for queuing networks. Support is provided through the web site http://apsp.tamu.edu where students will have the answers to odd numbered problems and instructors will have access to full solutions and Excel files for homework. (orig.)

On terminating Poisson processes in some shock models

Energy Technology Data Exchange (ETDEWEB)

Finkelstein, Maxim, E-mail: FinkelMI@ufs.ac.z [Department of Mathematical Statistics, University of the Free State, Bloemfontein (South Africa); Max Planck Institute for Demographic Research, Rostock (Germany); Marais, Francois, E-mail: fmarais@csc.co [CSC, Cape Town (South Africa)

2010-08-15

A system subject to a point process of shocks is considered. Shocks occur in accordance with the homogeneous Poisson process. Different criteria of system failure (termination) are discussed and the corresponding probabilities of failure (accident)-free performance are derived. The described analytical approach is based on deriving integral equations for each setting and solving these equations through the Laplace transform. Some approximations are analyzed and further generalizations and applications are discussed.

On terminating Poisson processes in some shock models

International Nuclear Information System (INIS)

Finkelstein, Maxim; Marais, Francois

2010-01-01

A system subject to a point process of shocks is considered. Shocks occur in accordance with the homogeneous Poisson process. Different criteria of system failure (termination) are discussed and the corresponding probabilities of failure (accident)-free performance are derived. The described analytical approach is based on deriving integral equations for each setting and solving these equations through the Laplace transform. Some approximations are analyzed and further generalizations and applications are discussed.

Berman-Konsowa principle for reversible Markov jump processes

NARCIS (Netherlands)

Hollander, den W.Th.F.; Jansen, S.

2013-01-01

In this paper we prove a version of the Berman-Konsowa principle for reversible Markov jump processes on Polish spaces. The Berman-Konsowa principle provides a variational formula for the capacity of a pair of disjoint measurable sets. There are two versions, one involving a class of probability

Filtering of a Markov Jump Process with Counting Observations

International Nuclear Information System (INIS)

Ceci, C.; Gerardi, A.

2000-01-01

This paper concerns the filtering of an R d -valued Markov pure jump process when only the total number of jumps are observed. Strong and weak uniqueness for the solutions of the filtering equations are discussed

Poisson processes on groups and Feynamn path integrals

International Nuclear Information System (INIS)

Combe, P.; Rodriguez, R.; Aix-Marseille-2 Univ., 13 - Marseille; Sirugue, M.; Sirugue-Collin, M.; Centre National de la Recherche Scientifique, 13 - Marseille; Hoegh-Krohn, R.

1980-01-01

We give an expression for the perturbed evolution of a free evolution by gentle, possibly velocity dependent, potential, in terms of the expectation with respect to a Poisson process on a group. Various applications are given in particular to usual quantum mechanics but also to Fermi and spin systems. (orig.)

A reward semi-Markov process with memory for wind speed modeling

Science.gov (United States)

Petroni, F.; D'Amico, G.; Prattico, F.

2012-04-01

-order Markov chain with different number of states, and Weibull distribution. All this model use Markov chains to generate synthetic wind speed time series but the search for a better model is still open. Approaching this issue, we applied new models which are generalization of Markov models. More precisely we applied semi-Markov models to generate synthetic wind speed time series. The primary goal of this analysis is the study of the time history of the wind in order to assess its reliability as a source of power and to determine the associated storage levels required. In order to assess this issue we use a probabilistic model based on indexed semi-Markov process [4] to which a reward structure is attached. Our model is used to calculate the expected energy produced by a given turbine and its variability expressed by the variance of the process. Our results can be used to compare different wind farms based on their reward and also on the risk of missed production due to the intrinsic variability of the wind speed process. The model is used to generate synthetic time series for wind speed by means of Monte Carlo simulations and backtesting procedure is used to compare results on first and second oder moments of rewards between real and synthetic data. [1] A. Shamshad, M.A. Bawadi, W.M.W. Wan Hussin, T.A. Majid, S.A.M. Sanusi, First and second order Markov chain models for synthetic gen- eration of wind speed time series, Energy 30 (2005) 693-708. [2] H. Nfaoui, H. Essiarab, A.A.M. Sayigh, A stochastic Markov chain model for simulating wind speed time series at Tangiers, Morocco, Re- newable Energy 29 (2004) 1407-1418. [3] F. Youcef Ettoumi, H. Sauvageot, A.-E.-H. Adane, Statistical bivariate modeling of wind using first-order Markov chain and Weibull distribu- tion, Renewable Energy 28 (2003) 1787-1802. [4]F. Petroni, G. D'Amico, F. Prattico, Indexed semi-Markov process for wind speed modeling. To be submitted.

Irreversible thermodynamics of Poisson processes with reaction.

Science.gov (United States)

Méndez, V; Fort, J

1999-11-01

A kinetic model is derived to study the successive movements of particles, described by a Poisson process, as well as their generation. The irreversible thermodynamics of this system is also studied from the kinetic model. This makes it possible to evaluate the differences between thermodynamical quantities computed exactly and up to second-order. Such differences determine the range of validity of the second-order approximation to extended irreversible thermodynamics.

The application of Markov decision process with penalty function in restaurant delivery robot

Science.gov (United States)

Wang, Yong; Hu, Zhen; Wang, Ying

2017-05-01

As the restaurant delivery robot is often in a dynamic and complex environment, including the chairs inadvertently moved to the channel and customers coming and going. The traditional Markov decision process path planning algorithm is not save, the robot is very close to the table and chairs. To solve this problem, this paper proposes the Markov Decision Process with a penalty term called MDPPT path planning algorithm according to the traditional Markov decision process (MDP). For MDP, if the restaurant delivery robot bumps into an obstacle, the reward it receives is part of the current status reward. For the MDPPT, the reward it receives not only the part of the current status but also a negative constant term. Simulation results show that the MDPPT algorithm can plan a more secure path.

Markov process of muscle motors

International Nuclear Information System (INIS)

Kondratiev, Yu; Pechersky, E; Pirogov, S

2008-01-01

We study a Markov random process describing muscle molecular motor behaviour. Every motor is either bound up with a thin filament or unbound. In the bound state the motor creates a force proportional to its displacement from the neutral position. In both states the motor spends an exponential time depending on the state. The thin filament moves at a velocity proportional to the average of all displacements of all motors. We assume that the time which a motor stays in the bound state does not depend on its displacement. Then one can find an exact solution of a nonlinear equation appearing in the limit of an infinite number of motors

Semi-Markov Chains and Hidden Semi-Markov Models toward Applications Their Use in Reliability and DNA Analysis

CERN Document Server

Barbu, Vlad

2008-01-01

Semi-Markov processes are much more general and better adapted to applications than the Markov ones because sojourn times in any state can be arbitrarily distributed, as opposed to the geometrically distributed sojourn time in the Markov case. This book concerns with the estimation of discrete-time semi-Markov and hidden semi-Markov processes

A Method for Speeding Up Value Iteration in Partially Observable Markov Decision Processes

OpenAIRE

Zhang, Nevin Lianwen; Lee, Stephen S.; Zhang, Weihong

2013-01-01

We present a technique for speeding up the convergence of value iteration for partially observable Markov decisions processes (POMDPs). The underlying idea is similar to that behind modified policy iteration for fully observable Markov decision processes (MDPs). The technique can be easily incorporated into any existing POMDP value iteration algorithms. Experiments have been conducted on several test problems with one POMDP value iteration algorithm called incremental pruning. We find that th...

Identification d’une Classe de Processus de Poisson Filtres (Identification of a Class of Filtered Poisson Processes).

Science.gov (United States)

1983-05-20

Poisson processes is introduced: the amplitude has a law which is spherically invariant and the filter is real, linear and causal. It is shown how such a model can be identified from experimental data. (Author)

A new non-commutative representation of the Wiener and Poisson processes

International Nuclear Information System (INIS)

Privault, N.

1996-01-01

Using two different constructions of the chaotic and variational calculus on Poisson space, we show that the Wiener and Poisson processes have a non-commutative representation which is different from the one obtained by transfer of the Fock space creation and annihilation operators. We obtain in this way an extension of the non-commutative It calculus. The associated commutation relations show a link between the geometric and exponential distributions. (author). 11 refs

Embedding a State Space Model Into a Markov Decision Process

DEFF Research Database (Denmark)

Nielsen, Lars Relund; Jørgensen, Erik; Højsgaard, Søren

2011-01-01

In agriculture Markov decision processes (MDPs) with finite state and action space are often used to model sequential decision making over time. For instance, states in the process represent possible levels of traits of the animal and transition probabilities are based on biological models...

On Characterisation of Markov Processes Via Martingale Problems

Indian Academy of Sciences (India)

This extension is used to improve on a criterion for a probability measure to be invariant for the semigroup associated with the Markov process. We also give examples of martingale problems that are well-posed in the class of solutions which are continuous in probability but for which no r.c.l.l. solution exists.

A Markovian approach for modeling packet traffic with long range dependence

DEFF Research Database (Denmark)

Andersen, Allan T.; Nielsen, Bo Friis

1998-01-01

-state Markov modulated Poisson processes (MMPPs). We illustrate that a superposition of four two-state MMPPs suffices to model second-order self-similar behavior over several time scales. Our modeling approach allows us to fit to additional descriptors while maintaining the second-order behavior...

Rate-optimal Bayesian intensity smoothing for inhomogeneous Poisson processes

NARCIS (Netherlands)

Belitser, E.; Andrade Serra, De P.J.; Zanten, van J.H.

2013-01-01

We apply nonparametric Bayesian methods to study the problem of estimating the intensity function of an inhomogeneous Poisson process. We exhibit a prior on intensities which both leads to a computationally feasible method and enjoys desirable theoretical optimality properties. The prior we use is

Non-parametric Bayesian inference for inhomogeneous Markov point processes

DEFF Research Database (Denmark)

Berthelsen, Kasper Klitgaard; Møller, Jesper; Johansen, Per Michael

is a shot noise process, and the interaction function for a pair of points depends only on the distance between the two points and is a piecewise linear function modelled by a marked Poisson process. Simulation of the resulting posterior using a Metropolis-Hastings algorithm in the "conventional" way...

Mean-Variance Optimization in Markov Decision Processes

OpenAIRE

Mannor, Shie; Tsitsiklis, John N.

2011-01-01

We consider finite horizon Markov decision processes under performance measures that involve both the mean and the variance of the cumulative reward. We show that either randomized or history-based policies can improve performance. We prove that the complexity of computing a policy that maximizes the mean reward under a variance constraint is NP-hard for some cases, and strongly NP-hard for others. We finally offer pseudo-polynomial exact and approximation algorithms.

A Family of Poisson Processes for Use in Stochastic Models of Precipitation

Science.gov (United States)

Penland, C.

2013-12-01

Both modified Poisson processes and compound Poisson processes can be relevant to stochastic parameterization of precipitation. This presentation compares the dynamical properties of these systems and discusses the physical situations in which each might be appropriate. If the parameters describing either class of systems originate in hydrodynamics, then proper consideration of stochastic calculus is required during numerical implementation of the parameterization. It is shown here that an improper numerical treatment can have severe implications for estimating rainfall distributions, particularly in the tails of the distributions and, thus, on the frequency of extreme events.

Poisson Coordinates.

Science.gov (United States)

Li, Xian-Ying; Hu, Shi-Min

2013-02-01

Harmonic functions are the critical points of a Dirichlet energy functional, the linear projections of conformal maps. They play an important role in computer graphics, particularly for gradient-domain image processing and shape-preserving geometric computation. We propose Poisson coordinates, a novel transfinite interpolation scheme based on the Poisson integral formula, as a rapid way to estimate a harmonic function on a certain domain with desired boundary values. Poisson coordinates are an extension of the Mean Value coordinates (MVCs) which inherit their linear precision, smoothness, and kernel positivity. We give explicit formulas for Poisson coordinates in both continuous and 2D discrete forms. Superior to MVCs, Poisson coordinates are proved to be pseudoharmonic (i.e., they reproduce harmonic functions on n-dimensional balls). Our experimental results show that Poisson coordinates have lower Dirichlet energies than MVCs on a number of typical 2D domains (particularly convex domains). As well as presenting a formula, our approach provides useful insights for further studies on coordinates-based interpolation and fast estimation of harmonic functions.

Generalized Poisson processes in quantum mechanics and field theory

International Nuclear Information System (INIS)

Combe, P.; Rodriguez, R.; Centre National de la Recherche Scientifique, 13 - Marseille; Hoegh-Krohn, R.; Centre National de la Recherche Scientifique, 13 - Marseille; Sirugue, M.; Sirugue-Collin, M.; Centre National de la Recherche Scientifique, 13 - Marseille

1981-01-01

In section 2 we describe more carefully the generalized Poisson processes, giving a realization of the underlying probability space, and we characterize these processes by their characteristic functionals. Section 3 is devoted to the proof of the previous formula for quantum mechanical systems, with possibly velocity dependent potentials and in section 4 we give an application of the previous theory to some relativistic Bose field models. (orig.)

Cascade probabilistic function and the Markov's processes. Chapter 1

International Nuclear Information System (INIS)

2002-01-01

In the Chapter 1 the physical and mathematical descriptions of radiation processes are carried out. The relation of the cascade probabilistic functions (CPF) for electrons, protons, alpha-particles and ions with Markov's chain is shown. The algorithms for CPF calculation with accounting energy losses are given

Importance Sampling for a Markov Modulated Queuing Network with Customer Impatience until the End of Service

Directory of Open Access Journals (Sweden)

Ebrahim MAHDIPOUR

2009-01-01

Full Text Available For more than two decades, there has been a growing of interest in fast simulation techniques for estimating probabilities of rare events in queuing networks. Importance sampling is a variance reduction method for simulating rare events. The present paper carries out strict deadlines to the paper by Dupuis et al for a two node tandem network with feedback whose arrival and service rates are modulated by an exogenous finite state Markov process. We derive a closed form solution for the probability of missing deadlines. Then we have employed the results to an importance sampling technique to estimate the probability of total population overflow which is a rare event. We have also shown that the probability of this rare event may be affected by various deadline values.

Scalable approximate policies for Markov decision process models of hospital elective admissions.

Science.gov (United States)

Zhu, George; Lizotte, Dan; Hoey, Jesse

2014-05-01

To demonstrate the feasibility of using stochastic simulation methods for the solution of a large-scale Markov decision process model of on-line patient admissions scheduling. The problem of admissions scheduling is modeled as a Markov decision process in which the states represent numbers of patients using each of a number of resources. We investigate current state-of-the-art real time planning methods to compute solutions to this Markov decision process. Due to the complexity of the model, traditional model-based planners are limited in scalability since they require an explicit enumeration of the model dynamics. To overcome this challenge, we apply sample-based planners along with efficient simulation techniques that given an initial start state, generate an action on-demand while avoiding portions of the model that are irrelevant to the start state. We also propose a novel variant of a popular sample-based planner that is particularly well suited to the elective admissions problem. Results show that the stochastic simulation methods allow for the problem size to be scaled by a factor of almost 10 in the action space, and exponentially in the state space. We have demonstrated our approach on a problem with 81 actions, four specialities and four treatment patterns, and shown that we can generate solutions that are near-optimal in about 100s. Sample-based planners are a viable alternative to state-based planners for large Markov decision process models of elective admissions scheduling. Copyright © 2014 Elsevier B.V. All rights reserved.

On Markov processes in the hadron-nuclear and nuclear-nuclear collisions at superhigh energies

International Nuclear Information System (INIS)

Lebedeva, A.A.; Rus'kin, V.I.

2001-01-01

In the article the possibility of the Markov processes use as simulation method for mean characteristics of hadron-nuclear and nucleus-nuclear collisions at superhigh energies is discussed. The simple (hadron-nuclear collisions) and non-simple (nucleus-nuclear collisions) non-uniform Markov process of output constant spectrum and absorption in a nucleon's nucleus-target with rapidity y are considered. The expression allowing to simulate the different collision modes were obtained

Markov LIMID processes for representing and solving renewal problems

DEFF Research Database (Denmark)

Jørgensen, Erik; Kristensen, Anders Ringgaard; Nilsson, Dennis

2014-01-01

to model a Markov Limid Process, where each TemLimid represents a macro action. Algorithms are presented to find optimal plans for a sequence of such macro actions. Use of algorithms is illustrated based on an extended version of an example from pig production originally used to introduce the Limid concept...

Modeling Visit Behaviour in Smart Homes using Unsupervised Learning

NARCIS (Netherlands)

Nait Aicha, A.; Englebienne, G.; Kröse, B.

2014-01-01

Many algorithms on health monitoring from ambient sensor networks assume that only a single person is present in the home. We present an unsupervised method that models visit behaviour. A Markov modulated multidimensional non-homogeneous Poisson process (M3P2) is described that allows us to model

TCP (truncated compound Poisson) process for multiplicity distributions in high energy collisions

International Nuclear Information System (INIS)

Srivastave, P.P.

1990-01-01

On using the Poisson distribution truncated at zero for intermediate cluster decay in a compound Poisson process, the authors obtain TCP distribution which describes quite well the multiplicity distributions in high energy collisions. A detailed comparison is made between TCP and NB for UA5 data. The reduced moments up to the fifth agree very well with the observed ones. The TCP curves are narrower than NB at high multiplicity tail, look narrower at very high energy and develop shoulders and oscillations which become increasingly pronounced as the energy grows. At lower energies the distributions, of the data for fixed intervals of rapidity for UA5 data and for the data (at low energy) for e + e - annihilation and pion-proton, proton-proton and muon-proton scattering. A discussion of compound Poisson distribution, expression of reduced moments and Poisson transforms are also given. The TCP curves and curves of the reduced moments for different values of the parameters are also presented

Process Modeling for Energy Usage in “Smart House” System with a Help of Markov Discrete Chain

Directory of Open Access Journals (Sweden)

Victor Kravets

2016-05-01

Full Text Available Method for evaluating economic efficiency of technical systems using discrete Markov chains modelling illustrated by the system of “Smart house”, consisting, for example, of the three independently functioning elements. Dynamic model of a random power consumption process in the form of a symmetrical state graph of heterogeneous discrete Markov chain is built. The corresponding mathematical model of a random Markov process of power consumption in the “smart house” system in recurrent matrix form is being developed. Technique of statistical determination of probability of random transition elements of the system and the corresponding to the transition probability matrix of the discrete inhomogeneous Markov chain are developed. Statistically determined random transitions of system elements power consumption and the corresponding distribution laws are introduced. The matrix of transition prices, expectations for the possible states of a system price transition and, eventually, the cost of Markov process of power consumption throughout the day.

Envelopes of Sets of Measures, Tightness, and Markov Control Processes

International Nuclear Information System (INIS)

Gonzalez-Hernandez, J.; Hernandez-Lerma, O.

1999-01-01

We introduce upper and lower envelopes for sets of measures on an arbitrary topological space, which are then used to give a tightness criterion. These concepts are applied to show the existence of optimal policies for a class of Markov control processes

Modeling of Electrokinetic Processes Using the Nernst-Plank-Poisson System

DEFF Research Database (Denmark)

Paz-Garcia, Juan Manuel; Johannesson, Björn; Ottosen, Lisbeth M.

2010-01-01

Electrokinetic processes are known as the mobilization of species within the pore solution of porous materials under the effect of an external electric field. A finite elements model was implemented and used for the integration of the coupled Nernst-Plank-Poisson system of equations in order...

Investigation of Random Switching Driven by a Poisson Point Process

DEFF Research Database (Denmark)

Simonsen, Maria; Schiøler, Henrik; Leth, John-Josef

2015-01-01

This paper investigates the switching mechanism of a two-dimensional switched system, when the switching events are generated by a Poisson point process. A model, in the shape of a stochastic process, for such a system is derived and the distribution of the trajectory's position is developed...... together with marginal density functions for the coordinate functions. Furthermore, the joint probability distribution is given explicitly....

Generalization bounds of ERM-based learning processes for continuous-time Markov chains.

Science.gov (United States)

Zhang, Chao; Tao, Dacheng

2012-12-01

Many existing results on statistical learning theory are based on the assumption that samples are independently and identically distributed (i.i.d.). However, the assumption of i.i.d. samples is not suitable for practical application to problems in which samples are time dependent. In this paper, we are mainly concerned with the empirical risk minimization (ERM) based learning process for time-dependent samples drawn from a continuous-time Markov chain. This learning process covers many kinds of practical applications, e.g., the prediction for a time series and the estimation of channel state information. Thus, it is significant to study its theoretical properties including the generalization bound, the asymptotic convergence, and the rate of convergence. It is noteworthy that, since samples are time dependent in this learning process, the concerns of this paper cannot (at least straightforwardly) be addressed by existing methods developed under the sample i.i.d. assumption. We first develop a deviation inequality for a sequence of time-dependent samples drawn from a continuous-time Markov chain and present a symmetrization inequality for such a sequence. By using the resultant deviation inequality and symmetrization inequality, we then obtain the generalization bounds of the ERM-based learning process for time-dependent samples drawn from a continuous-time Markov chain. Finally, based on the resultant generalization bounds, we analyze the asymptotic convergence and the rate of convergence of the learning process.

A test for judging the presence of additional scatter in a Poisson process

International Nuclear Information System (INIS)

Mueller, J.W.

1978-01-01

The effect of additional scatter on a Poisson process is studied. Possible causes for such fluctuations are insufficient stability of the detection efficiency or of the associated electronics. It is shown with a simple model that the presence of fluctuations results in a characteristic broadening of the counting distribution. Comparison of the observed distribution with the one expected for a Poisson process with the same mean value will show three different regions, each with predictable sign of the deviation; the presence of scatter can thus be decided upon by a sign test. Experimental results are in excellent agreement with this expectation

Efficient tests for equivalence of hidden Markov processes and quantum random walks

NARCIS (Netherlands)

U. Faigle; A. Schönhuth (Alexander)

2011-01-01

htmlabstractWhile two hidden Markov process (HMP) resp.~quantum random walk (QRW) parametrizations can differ from one another, the stochastic processes arising from them can be equivalent. Here a polynomial-time algorithm is presented which can determine equivalence of two HMP parametrizations

Recombination Processes and Nonlinear Markov Chains.

Science.gov (United States)

Pirogov, Sergey; Rybko, Alexander; Kalinina, Anastasia; Gelfand, Mikhail

2016-09-01

Bacteria are known to exchange genetic information by horizontal gene transfer. Since the frequency of homologous recombination depends on the similarity between the recombining segments, several studies examined whether this could lead to the emergence of subspecies. Most of them simulated fixed-size Wright-Fisher populations, in which the genetic drift should be taken into account. Here, we use nonlinear Markov processes to describe a bacterial population evolving under mutation and recombination. We consider a population structure as a probability measure on the space of genomes. This approach implies the infinite population size limit, and thus, the genetic drift is not assumed. We prove that under these conditions, the emergence of subspecies is impossible.

Ruin probabilities for a regenerative Poisson gap generated risk process

DEFF Research Database (Denmark)

Asmussen, Søren; Biard, Romain

A risk process with constant premium rate c and Poisson arrivals of claims is considered. A threshold r is defined for claim interarrival times, such that if k consecutive interarrival times are larger than r, then the next claim has distribution G. Otherwise, the claim size distribution is F...

Stochastic Interest Model Based on Compound Poisson Process and Applications in Actuarial Science

OpenAIRE

Li, Shilong; Yin, Chuancun; Zhao, Xia; Dai, Hongshuai

2017-01-01

Considering stochastic behavior of interest rates in financial market, we construct a new class of interest models based on compound Poisson process. Different from the references, this paper describes the randomness of interest rates by modeling the force of interest with Poisson random jumps directly. To solve the problem in calculation of accumulated interest force function, one important integral technique is employed. And a conception called the critical value is introduced to investigat...

Stochastic modeling for neural spiking events based on fractional superstatistical Poisson process

Science.gov (United States)

Konno, Hidetoshi; Tamura, Yoshiyasu

2018-01-01

In neural spike counting experiments, it is known that there are two main features: (i) the counting number has a fractional power-law growth with time and (ii) the waiting time (i.e., the inter-spike-interval) distribution has a heavy tail. The method of superstatistical Poisson processes (SSPPs) is examined whether these main features are properly modeled. Although various mixed/compound Poisson processes are generated with selecting a suitable distribution of the birth-rate of spiking neurons, only the second feature (ii) can be modeled by the method of SSPPs. Namely, the first one (i) associated with the effect of long-memory cannot be modeled properly. Then, it is shown that the two main features can be modeled successfully by a class of fractional SSPP (FSSPP).

Neural pulse frequency modulation of an exponentially correlated Gaussian process

Science.gov (United States)

Hutchinson, C. E.; Chon, Y.-T.

1976-01-01

The effect of NPFM (Neural Pulse Frequency Modulation) on a stationary Gaussian input, namely an exponentially correlated Gaussian input, is investigated with special emphasis on the determination of the average number of pulses in unit time, known also as the average frequency of pulse occurrence. For some classes of stationary input processes where the formulation of the appropriate multidimensional Markov diffusion model of the input-plus-NPFM system is possible, the average impulse frequency may be obtained by a generalization of the approach adopted. The results are approximate and numerical, but are in close agreement with Monte Carlo computer simulation results.

On the Fractional Poisson Process and the Discretized Stable Subordinator

Directory of Open Access Journals (Sweden)

Rudolf Gorenflo

2015-08-01

Full Text Available We consider the renewal counting number process N = N(t as a forward march over the non-negative integers with independent identically distributed waiting times. We embed the values of the counting numbers N in a “pseudo-spatial” non-negative half-line x ≥ 0 and observe that for physical time likewise we have t ≥ 0. Thus we apply the Laplace transform with respect to both variables x and t. Applying then a modification of the Montroll-Weiss-Cox formalism of continuous time random walk we obtain the essential characteristics of a renewal process in the transform domain and, if we are lucky, also in the physical domain. The process t = t(N of accumulation of waiting times is inverse to the counting number process, in honour of the Danish mathematician and telecommunication engineer A.K. Erlang we call it the Erlang process. It yields the probability of exactly n renewal events in the interval (0; t]. We apply our Laplace-Laplace formalism to the fractional Poisson process whose waiting times are of Mittag-Leffler type and to a renewal process whose waiting times are of Wright type. The process of Mittag-Leffler type includes as a limiting case the classical Poisson process, the process of Wright type represents the discretized stable subordinator and a re-scaled version of it was used in our method of parametric subordination of time-space fractional diffusion processes. Properly rescaling the counting number process N(t and the Erlang process t(N yields as diffusion limits the inverse stable and the stable subordinator, respectively.

A fast exact simulation method for a class of Markov jump processes.

Science.gov (United States)

Li, Yao; Hu, Lili

2015-11-14

A new method of the stochastic simulation algorithm (SSA), named the Hashing-Leaping method (HLM), for exact simulations of a class of Markov jump processes, is presented in this paper. The HLM has a conditional constant computational cost per event, which is independent of the number of exponential clocks in the Markov process. The main idea of the HLM is to repeatedly implement a hash-table-like bucket sort algorithm for all times of occurrence covered by a time step with length τ. This paper serves as an introduction to this new SSA method. We introduce the method, demonstrate its implementation, analyze its properties, and compare its performance with three other commonly used SSA methods in four examples. Our performance tests and CPU operation statistics show certain advantages of the HLM for large scale problems.

A Unified Framework for Complex Networks with Degree Trichotomy Based on Markov Chains.

Science.gov (United States)

Hui, David Shui Wing; Chen, Yi-Chao; Zhang, Gong; Wu, Weijie; Chen, Guanrong; Lui, John C S; Li, Yingtao

2017-06-16

This paper establishes a Markov chain model as a unified framework for describing the evolution processes in complex networks. The unique feature of the proposed model is its capability in addressing the formation mechanism that can reflect the "trichotomy" observed in degree distributions, based on which closed-form solutions can be derived. Important special cases of the proposed unified framework are those classical models, including Poisson, Exponential, Power-law distributed networks. Both simulation and experimental results demonstrate a good match of the proposed model with real datasets, showing its superiority over the classical models. Implications of the model to various applications including citation analysis, online social networks, and vehicular networks design, are also discussed in the paper.

Stochastic modeling for neural spiking events based on fractional superstatistical Poisson process

Directory of Open Access Journals (Sweden)

Hidetoshi Konno

2018-01-01

Full Text Available In neural spike counting experiments, it is known that there are two main features: (i the counting number has a fractional power-law growth with time and (ii the waiting time (i.e., the inter-spike-interval distribution has a heavy tail. The method of superstatistical Poisson processes (SSPPs is examined whether these main features are properly modeled. Although various mixed/compound Poisson processes are generated with selecting a suitable distribution of the birth-rate of spiking neurons, only the second feature (ii can be modeled by the method of SSPPs. Namely, the first one (i associated with the effect of long-memory cannot be modeled properly. Then, it is shown that the two main features can be modeled successfully by a class of fractional SSPP (FSSPP.

Advanced Models and Algorithms for Self-Similar IP Network Traffic Simulation and Performance Analysis

Science.gov (United States)

Radev, Dimitar; Lokshina, Izabella

2010-11-01

The paper examines self-similar (or fractal) properties of real communication network traffic data over a wide range of time scales. These self-similar properties are very different from the properties of traditional models based on Poisson and Markov-modulated Poisson processes. Advanced fractal models of sequentional generators and fixed-length sequence generators, and efficient algorithms that are used to simulate self-similar behavior of IP network traffic data are developed and applied. Numerical examples are provided; and simulation results are obtained and analyzed.

A Correlated Random Effects Model for Non-homogeneous Markov Processes with Nonignorable Missingness.

Science.gov (United States)

Chen, Baojiang; Zhou, Xiao-Hua

2013-05-01

Life history data arising in clusters with prespecified assessment time points for patients often feature incomplete data since patients may choose to visit the clinic based on their needs. Markov process models provide a useful tool describing disease progression for life history data. The literature mainly focuses on time homogeneous process. In this paper we develop methods to deal with non-homogeneous Markov process with incomplete clustered life history data. A correlated random effects model is developed to deal with the nonignorable missingness, and a time transformation is employed to address the non-homogeneity in the transition model. Maximum likelihood estimate based on the Monte-Carlo EM algorithm is advocated for parameter estimation. Simulation studies demonstrate that the proposed method works well in many situations. We also apply this method to an Alzheimer's disease study.

Elements of the theory of Markov processes and their applications

CERN Document Server

Bharucha-Reid, A T

2010-01-01

This graduate-level text and reference in probability, with numerous applications to several fields of science, presents nonmeasure-theoretic introduction to theory of Markov processes. The work also covers mathematical models based on the theory, employed in various applied fields. Prerequisites are a knowledge of elementary probability theory, mathematical statistics, and analysis. Appendixes. Bibliographies. 1960 edition.

Group-buying inventory policy with demand under Poisson process

Directory of Open Access Journals (Sweden)

Tammarat Kleebmek

2016-02-01

Full Text Available The group-buying is the modern business of selling in the uncertain market. With an objective to minimize costs for sellers arising from ordering and reordering, we present in this paper the group buying inventory model, with the demand governed by a Poisson process and the product sale distributed as Binomial distribution. The inventory level is under continuous review, while the lead time is fixed. A numerical example is illustrated.

On poisson-stopped-sums that are mixed poisson

OpenAIRE

Valero Baya, Jordi; Pérez Casany, Marta; Ginebra Molins, Josep

2013-01-01

Maceda (1948) characterized the mixed Poisson distributions that are Poisson-stopped-sum distributions based on the mixing distribution. In an alternative characterization of the same set of distributions here the Poisson-stopped-sum distributions that are mixed Poisson distributions is proved to be the set of Poisson-stopped-sums of either a mixture of zero-truncated Poisson distributions or a zero-modification of it. Peer Reviewed

WAITING TIME DISTRIBUTION OF SOLAR ENERGETIC PARTICLE EVENTS MODELED WITH A NON-STATIONARY POISSON PROCESS

International Nuclear Information System (INIS)

Li, C.; Su, W.; Fang, C.; Zhong, S. J.; Wang, L.

2014-01-01

We present a study of the waiting time distributions (WTDs) of solar energetic particle (SEP) events observed with the spacecraft WIND and GOES. The WTDs of both solar electron events (SEEs) and solar proton events (SPEs) display a power-law tail of ∼Δt –γ . The SEEs display a broken power-law WTD. The power-law index is γ 1 = 0.99 for the short waiting times (<70 hr) and γ 2 = 1.92 for large waiting times (>100 hr). The break of the WTD of SEEs is probably due to the modulation of the corotating interaction regions. The power-law index, γ ∼ 1.82, is derived for the WTD of the SPEs which is consistent with the WTD of type II radio bursts, indicating a close relationship between the shock wave and the production of energetic protons. The WTDs of SEP events can be modeled with a non-stationary Poisson process, which was proposed to understand the waiting time statistics of solar flares. We generalize the method and find that, if the SEP event rate λ = 1/Δt varies as the time distribution of event rate f(λ) = Aλ –α exp (– βλ), the time-dependent Poisson distribution can produce a power-law tail WTD of ∼Δt α –3 , where 0 ≤ α < 2

Reliability analysis of nuclear component cooling water system using semi-Markov process model

International Nuclear Information System (INIS)

Veeramany, Arun; Pandey, Mahesh D.

2011-01-01

Research highlights: → Semi-Markov process (SMP) model is used to evaluate system failure probability of the nuclear component cooling water (NCCW) system. → SMP is used because it can solve reliability block diagram with a mixture of redundant repairable and non-repairable components. → The primary objective is to demonstrate that SMP can consider Weibull failure time distribution for components while a Markov model cannot → Result: the variability in component failure time is directly proportional to the NCCW system failure probability. → The result can be utilized as an initiating event probability in probabilistic safety assessment projects. - Abstract: A reliability analysis of nuclear component cooling water (NCCW) system is carried out. Semi-Markov process model is used in the analysis because it has potential to solve a reliability block diagram with a mixture of repairable and non-repairable components. With Markov models it is only possible to assume an exponential profile for component failure times. An advantage of the proposed model is the ability to assume Weibull distribution for the failure time of components. In an attempt to reduce the number of states in the model, it is shown that usage of poly-Weibull distribution arises. The objective of the paper is to determine system failure probability under these assumptions. Monte Carlo simulation is used to validate the model result. This result can be utilized as an initiating event probability in probabilistic safety assessment projects.

Availability Control for Means of Transport in Decisive Semi-Markov Models of Exploitation Process

Science.gov (United States)

Migawa, Klaudiusz

2012-12-01

The issues presented in this research paper refer to problems connected with the control process for exploitation implemented in the complex systems of exploitation for technical objects. The article presents the description of the method concerning the control availability for technical objects (means of transport) on the basis of the mathematical model of the exploitation process with the implementation of the decisive processes by semi-Markov. The presented method means focused on the preparing the decisive for the exploitation process for technical objects (semi-Markov model) and after that specifying the best control strategy (optimal strategy) from among possible decisive variants in accordance with the approved criterion (criteria) of the activity evaluation of the system of exploitation for technical objects. In the presented method specifying the optimal strategy for control availability in the technical objects means a choice of a sequence of control decisions made in individual states of modelled exploitation process for which the function being a criterion of evaluation reaches the extreme value. In order to choose the optimal control strategy the implementation of the genetic algorithm was chosen. The opinions were presented on the example of the exploitation process of the means of transport implemented in the real system of the bus municipal transport. The model of the exploitation process for the means of transports was prepared on the basis of the results implemented in the real transport system. The mathematical model of the exploitation process was built taking into consideration the fact that the model of the process constitutes the homogenous semi-Markov process.

Data-based inference of generators for Markov jump processes using convex optimization

NARCIS (Netherlands)

D.T. Crommelin (Daan); E. Vanden-Eijnden (Eric)

2009-01-01

textabstractA variational approach to the estimation of generators for Markov jump processes from discretely sampled data is discussed and generalized. In this approach, one first calculates the spectrum of the discrete maximum likelihood estimator for the transition matrix consistent with

Applied probability and stochastic processes

CERN Document Server

Sumita, Ushio

1999-01-01

Applied Probability and Stochastic Processes is an edited work written in honor of Julien Keilson. This volume has attracted a host of scholars in applied probability, who have made major contributions to the field, and have written survey and state-of-the-art papers on a variety of applied probability topics, including, but not limited to: perturbation method, time reversible Markov chains, Poisson processes, Brownian techniques, Bayesian probability, optimal quality control, Markov decision processes, random matrices, queueing theory and a variety of applications of stochastic processes. The book has a mixture of theoretical, algorithmic, and application chapters providing examples of the cutting-edge work that Professor Keilson has done or influenced over the course of his highly-productive and energetic career in applied probability and stochastic processes. The book will be of interest to academic researchers, students, and industrial practitioners who seek to use the mathematics of applied probability i...

A Multi-stage Representation of Cell Proliferation as a Markov Process.

Science.gov (United States)

Yates, Christian A; Ford, Matthew J; Mort, Richard L

2017-12-01

The stochastic simulation algorithm commonly known as Gillespie's algorithm (originally derived for modelling well-mixed systems of chemical reactions) is now used ubiquitously in the modelling of biological processes in which stochastic effects play an important role. In well-mixed scenarios at the sub-cellular level it is often reasonable to assume that times between successive reaction/interaction events are exponentially distributed and can be appropriately modelled as a Markov process and hence simulated by the Gillespie algorithm. However, Gillespie's algorithm is routinely applied to model biological systems for which it was never intended. In particular, processes in which cell proliferation is important (e.g. embryonic development, cancer formation) should not be simulated naively using the Gillespie algorithm since the history-dependent nature of the cell cycle breaks the Markov process. The variance in experimentally measured cell cycle times is far less than in an exponential cell cycle time distribution with the same mean.Here we suggest a method of modelling the cell cycle that restores the memoryless property to the system and is therefore consistent with simulation via the Gillespie algorithm. By breaking the cell cycle into a number of independent exponentially distributed stages, we can restore the Markov property at the same time as more accurately approximating the appropriate cell cycle time distributions. The consequences of our revised mathematical model are explored analytically as far as possible. We demonstrate the importance of employing the correct cell cycle time distribution by recapitulating the results from two models incorporating cellular proliferation (one spatial and one non-spatial) and demonstrating that changing the cell cycle time distribution makes quantitative and qualitative differences to the outcome of the models. Our adaptation will allow modellers and experimentalists alike to appropriately represent cellular

Theoretical analysis of radiographic images by nonstationary Poisson processes

International Nuclear Information System (INIS)

Tanaka, Kazuo; Uchida, Suguru; Yamada, Isao.

1980-01-01

This paper deals with the noise analysis of radiographic images obtained in the usual fluorescent screen-film system. The theory of nonstationary Poisson processes is applied to the analysis of the radiographic images containing the object information. The ensemble averages, the autocorrelation functions, and the Wiener spectrum densities of the light-energy distribution at the fluorescent screen and of the film optical-density distribution are obtained. The detection characteristics of the system are evaluated theoretically. Numerical examples one-dimensional image are shown and the results are compared with those obtained under the assumption that the object image is related to the background noise by the additive process. (author)

An application of modulated poisson processes to the reliability analysis of repairable systems

Energy Technology Data Exchange (ETDEWEB)

Saldanha, Pedro L.C. [Comissao Nacional de Energia Nuclear (CNEN), Rio de Janeiro, RJ (Brazil). Coordenacao de Reatores]. E-mail: saldanha@cnen.gov.br; Melo, P.F. Frutuoso e [Universidade Federal, Rio de Janeiro, RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia. Programa de Engenharia Nuclear]. E-mail: frutuoso@con.ufrj.br; Noriega, Hector C. [Universidad Austral de Chile (UACh), Valdivia (Chile). Faculdad de Ciencias de la Ingeniaria]. E-mail: hnoriega@uach.cl

2005-07-01

This paper discusses the application of the modulated power law process (MPLP) model to the rate of occurrence of failures of active repairable systems in reliability engineering. Traditionally, two ways of modeling repairable systems, in what concerns maintenance policies, are: a pessimistic approach (non-homogeneous process - NHPP), and a very optimistic approach (renewal processes - RP). It is important to build a generalized model that might consider characteristics and properties both of the NHPP and of the RP models as particular cases. In practice, by considering the pattern of times between failures, the MPLP appears to be more realistic to represent the occurrence of failures of repairable systems in order to define whether they can be modeled by a homogeneous or a non-homogeneous process. The study has shown that the model can be used to make decisions concerning the evaluation of the qualified life of plant equipment. By controlling and monitoring two of the three parameters of the MPLP model during the equipment operation, it is possible to check whether and how the equipment is following the basis of its qualification process, and so identify how the effects of time, degradation and operation modes are influencing the equipment performance. The discussion is illustrated by an application to the service water pumps of a typical PWR plant. (author)

Phasic Triplet Markov Chains.

Science.gov (United States)

El Yazid Boudaren, Mohamed; Monfrini, Emmanuel; Pieczynski, Wojciech; Aïssani, Amar

2014-11-01

Hidden Markov chains have been shown to be inadequate for data modeling under some complex conditions. In this work, we address the problem of statistical modeling of phenomena involving two heterogeneous system states. Such phenomena may arise in biology or communications, among other fields. Namely, we consider that a sequence of meaningful words is to be searched within a whole observation that also contains arbitrary one-by-one symbols. Moreover, a word may be interrupted at some site to be carried on later. Applying plain hidden Markov chains to such data, while ignoring their specificity, yields unsatisfactory results. The Phasic triplet Markov chain, proposed in this paper, overcomes this difficulty by means of an auxiliary underlying process in accordance with the triplet Markov chains theory. Related Bayesian restoration techniques and parameters estimation procedures according to the new model are then described. Finally, to assess the performance of the proposed model against the conventional hidden Markov chain model, experiments are conducted on synthetic and real data.

POISSON SUPERFISH, Poisson Equation Solver for Radio Frequency Cavity

International Nuclear Information System (INIS)

Colman, J.

2001-01-01

field specification defined by the user. PAN-T calculates the temperature distribution in the walls of a RF-cavity given the electric field at the walls, the thermal conductivity of the wall materials, and the temperature at the outer surface of the wall. TEKPLOT plots the physical boundaries and mesh resulting from a LATTICE run and equipotential or field lines generated as a result of POISSON, PANDIRA, MIRT, or SUPERFISH runs. SF01 and SHY process results from SUPERFISH runs. SF01 calculates quantities useful for a drift-tube linac. SHY calculates the value of the electric field in the TM mode over an area in the XY-plane. 2 - Method of solution: The POISSON group of codes solves Maxwell's static equations (MSE's) in integral form and in two dimensions. When the MSE's are taken together with the boundary conditions, they are equivalent to a generalized form of Poisson's equations in two dimensions. POISSON uses a successive point over-relaxation (SPOR) method to solve the equations, while PANDIRA directly solves the block tridiagonal system of difference equations, and iteration is required only for nonlinear problems. After solving the equations, both compute the derivatives of the potential, namely the fields and their gradients, and calculate the stored energy. SUPERFISH uses the same direct solution method as PANDIRA for the Helmholtz eigenvalue problem. 3 - Restrictions on the complexity of the problem: POISSON: 16000 mesh points, 30 regions; SUPERFISH: 32000 mesh points; 125 max value for k max and/or l max , 60 segments and 3 regions

Zeroth Poisson Homology, Foliated Cohomology and Perfect Poisson Manifolds

Science.gov (United States)

Martínez-Torres, David; Miranda, Eva

2018-01-01

We prove that, for compact regular Poisson manifolds, the zeroth homology group is isomorphic to the top foliated cohomology group, and we give some applications. In particular, we show that, for regular unimodular Poisson manifolds, top Poisson and foliated cohomology groups are isomorphic. Inspired by the symplectic setting, we define what a perfect Poisson manifold is. We use these Poisson homology computations to provide families of perfect Poisson manifolds.

Markov Tail Chains

OpenAIRE

janssen, Anja; Segers, Johan

2013-01-01

The extremes of a univariate Markov chain with regularly varying stationary marginal distribution and asymptotically linear behavior are known to exhibit a multiplicative random walk structure called the tail chain. In this paper we extend this fact to Markov chains with multivariate regularly varying marginal distributions in Rd. We analyze both the forward and the backward tail process and show that they mutually determine each other through a kind of adjoint relation. In ...

Stochastic model of milk homogenization process using Markov's chain

Directory of Open Access Journals (Sweden)

A. A. Khvostov

2016-01-01

Full Text Available The process of development of a mathematical model of the process of homogenization of dairy products is considered in the work. The theory of Markov's chains was used in the development of the mathematical model, Markov's chain with discrete states and continuous parameter for which the homogenisation pressure is taken, being the basis for the model structure. Machine realization of the model is implemented in the medium of structural modeling MathWorks Simulink™. Identification of the model parameters was carried out by minimizing the standard deviation calculated from the experimental data for each fraction of dairy products fat phase. As the set of experimental data processing results of the micrographic images of fat globules of whole milk samples distribution which were subjected to homogenization at different pressures were used. Pattern Search method was used as optimization method with the Latin Hypercube search algorithm from Global Optimization Тoolbox library. The accuracy of calculations averaged over all fractions of 0.88% (the relative share of units, the maximum relative error was 3.7% with the homogenization pressure of 30 MPa, which may be due to the very abrupt change in properties from the original milk in the particle size distribution at the beginning of the homogenization process and the lack of experimental data at homogenization pressures of below the specified value. The mathematical model proposed allows to calculate the profile of volume and mass distribution of the fat phase (fat globules in the product, depending on the homogenization pressure and can be used in the laboratory and research of dairy products composition, as well as in the calculation, design and modeling of the process equipment of the dairy industry enterprises.

A Partially Observed Markov Decision Process for Dynamic Pricing

OpenAIRE

Yossi Aviv; Amit Pazgal

2005-01-01

In this paper, we develop a stylized partially observed Markov decision process (POMDP) framework to study a dynamic pricing problem faced by sellers of fashion-like goods. We consider a retailer that plans to sell a given stock of items during a finite sales season. The objective of the retailer is to dynamically price the product in a way that maximizes expected revenues. Our model brings together various types of uncertainties about the demand, some of which are resolvable through sales ob...

Polynomial Poisson algebras: Gel'fand-Kirillov problem and Poisson spectra

OpenAIRE

Lecoutre, César

2014-01-01

We study the fields of fractions and the Poisson spectra of polynomial Poisson algebras.\\ud \\ud First we investigate a Poisson birational equivalence problem for polynomial Poisson algebras over a field of arbitrary characteristic. Namely, the quadratic Poisson Gel'fand-Kirillov problem asks whether the field of fractions of a Poisson algebra is isomorphic to the field of fractions of a Poisson affine space, i.e. a polynomial algebra such that the Poisson bracket of two generators is equal to...

Strategy Complexity of Finite-Horizon Markov Decision Processes and Simple Stochastic Games

DEFF Research Database (Denmark)

Ibsen-Jensen, Rasmus; Chatterjee, Krishnendu

2012-01-01

Markov decision processes (MDPs) and simple stochastic games (SSGs) provide a rich mathematical framework to study many important problems related to probabilistic systems. MDPs and SSGs with finite-horizon objectives, where the goal is to maximize the probability to reach a target state in a given...

Bearing Degradation Process Prediction Based on the Support Vector Machine and Markov Model

Directory of Open Access Journals (Sweden)

Shaojiang Dong

2014-01-01

Full Text Available Predicting the degradation process of bearings before they reach the failure threshold is extremely important in industry. This paper proposed a novel method based on the support vector machine (SVM and the Markov model to achieve this goal. Firstly, the features are extracted by time and time-frequency domain methods. However, the extracted original features are still with high dimensional and include superfluous information, and the nonlinear multifeatures fusion technique LTSA is used to merge the features and reduces the dimension. Then, based on the extracted features, the SVM model is used to predict the bearings degradation process, and the CAO method is used to determine the embedding dimension of the SVM model. After the bearing degradation process is predicted by SVM model, the Markov model is used to improve the prediction accuracy. The proposed method was validated by two bearing run-to-failure experiments, and the results proved the effectiveness of the methodology.

Detecting critical state before phase transition of complex biological systems by hidden Markov model.

Science.gov (United States)

Chen, Pei; Liu, Rui; Li, Yongjun; Chen, Luonan

2016-07-15

Identifying the critical state or pre-transition state just before the occurrence of a phase transition is a challenging task, because the state of the system may show little apparent change before this critical transition during the gradual parameter variations. Such dynamics of phase transition is generally composed of three stages, i.e. before-transition state, pre-transition state and after-transition state, which can be considered as three different Markov processes. By exploring the rich dynamical information provided by high-throughput data, we present a novel computational method, i.e. hidden Markov model (HMM) based approach, to detect the switching point of the two Markov processes from the before-transition state (a stationary Markov process) to the pre-transition state (a time-varying Markov process), thereby identifying the pre-transition state or early-warning signals of the phase transition. To validate the effectiveness, we apply this method to detect the signals of the imminent phase transitions of complex systems based on the simulated datasets, and further identify the pre-transition states as well as their critical modules for three real datasets, i.e. the acute lung injury triggered by phosgene inhalation, MCF-7 human breast cancer caused by heregulin and HCV-induced dysplasia and hepatocellular carcinoma. Both functional and pathway enrichment analyses validate the computational results. The source code and some supporting files are available at https://github.com/rabbitpei/HMM_based-method lnchen@sibs.ac.cn or liyj@scut.edu.cn Supplementary data are available at Bioinformatics online. © The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

DISEÑO Y MANIPULACIÓN DE MODELOS OCULTOS DE MARKOV, UTILIZANDO HERRAMIENTAS HTK: UNA TUTORÍA DESIGN AND MANIPULATION OF HIDDEN MARKOV MODELS USING HTK TOOLS: A TUTORIAL

Directory of Open Access Journals (Sweden)

Roberto Carrillo Aguilar

2007-04-01

Full Text Available Este trabajo da a conocer el sistema de desarrollo de software para el diseño y manipulación de modelos ocultos de Markov, denominado HTK. Actualmente, la técnica de modelos ocultos de Markov es la herramienta más efectiva para implementar sistemas reconocedores del habla. HTK está orientado principalmente a ese aspecto. Su arquitectura es robusta y autosuficiente. Permite: la entrada lógica y natural desde un micrófono, dispone de módulos para la conversión A/D, preprocesado y parametrización de la información, posee herramientas para definir y manipular modelos ocultos de Markov, tiene librerías para entrenamiento y manipulación de los modelos ocultos de Markov ya definidos, considera funciones para definir la gramática, y además: Una serie de herramientas adicionales permiten lograr el objetivo final de obtener una hipotética transcripción del habla (conversión voz - texto.This paper presents HTK, a software development platform for the design and management of Hidden Markov Models. Nowadays, the Hidden Markov Models technique is the more effective one to implement voice recognition systems. HTK is mainly oriented to this application. Its architecture is robust and self-sufficient. It allows a natural input from a microphone, it has modules for A/D conversion, it allows pre-processing and parameterization of information, it possesses tools to define and manage the Hidden Markov Models, libraries for training and use the already defined Hidden Markov Models. It has functions to define the grammar and it has additional tools to reach the final objective, to obtain an hypothetical transcription of the talking (voice to text translation.

Processing module operating methods, processing modules, and communications systems

Science.gov (United States)

McCown, Steven Harvey; Derr, Kurt W.; Moore, Troy

2014-09-09

A processing module operating method includes using a processing module physically connected to a wireless communications device, requesting that the wireless communications device retrieve encrypted code from a web site and receiving the encrypted code from the wireless communications device. The wireless communications device is unable to decrypt the encrypted code. The method further includes using the processing module, decrypting the encrypted code, executing the decrypted code, and preventing the wireless communications device from accessing the decrypted code. Another processing module operating method includes using a processing module physically connected to a host device, executing an application within the processing module, allowing the application to exchange user interaction data communicated using a user interface of the host device with the host device, and allowing the application to use the host device as a communications device for exchanging information with a remote device distinct from the host device.

Learning Markov Decision Processes for Model Checking

DEFF Research Database (Denmark)

Mao, Hua; Chen, Yingke; Jaeger, Manfred

2012-01-01

. The proposed learning algorithm is adapted from algorithms for learning deterministic probabilistic finite automata, and extended to include both probabilistic and nondeterministic transitions. The algorithm is empirically analyzed and evaluated by learning system models of slot machines. The evaluation......Constructing an accurate system model for formal model verification can be both resource demanding and time-consuming. To alleviate this shortcoming, algorithms have been proposed for automatically learning system models based on observed system behaviors. In this paper we extend the algorithm...... on learning probabilistic automata to reactive systems, where the observed system behavior is in the form of alternating sequences of inputs and outputs. We propose an algorithm for automatically learning a deterministic labeled Markov decision process model from the observed behavior of a reactive system...

Generalization of the Wide-Sense Markov Concept to a Widely Linear Processing

International Nuclear Information System (INIS)

Espinosa-Pulido, Juan Antonio; Navarro-Moreno, Jesús; Fernández-Alcalá, Rosa María; Ruiz-Molina, Juan Carlos; Oya-Lechuga, Antonia; Ruiz-Fuentes, Nuria

2014-01-01

In this paper we show that the classical definition and the associated characterizations of wide-sense Markov (WSM) signals are not valid for improper complex signals. For that, we propose an extension of the concept of WSM to a widely linear (WL) setting and the study of new characterizations. Specifically, we introduce a new class of signals, called widely linear Markov (WLM) signals, and we analyze some of their properties based either on second-order properties or on state-space models from a WL processing standpoint. The study is performed in both the forwards and backwards directions of time. Thus, we provide two forwards and backwards Markovian representations for WLM signals. Finally, different estimation recursive algorithms are obtained for these models

A high-fidelity weather time series generator using the Markov Chain process on a piecewise level

Science.gov (United States)

Hersvik, K.; Endrerud, O.-E. V.

2017-12-01

A method is developed for generating a set of unique weather time-series based on an existing weather series. The method allows statistically valid weather variations to take place within repeated simulations of offshore operations. The numerous generated time series need to share the same statistical qualities as the original time series. Statistical qualities here refer mainly to the distribution of weather windows available for work, including durations and frequencies of such weather windows, and seasonal characteristics. The method is based on the Markov chain process. The core new development lies in how the Markov Process is used, specifically by joining small pieces of random length time series together rather than joining individual weather states, each from a single time step, which is a common solution found in the literature. This new Markov model shows favorable characteristics with respect to the requirements set forth and all aspects of the validation performed.

Simulating the formation of keratin filament networks by a piecewise-deterministic Markov process.

Science.gov (United States)

Beil, Michael; Lück, Sebastian; Fleischer, Frank; Portet, Stéphanie; Arendt, Wolfgang; Schmidt, Volker

2009-02-21

Keratin intermediate filament networks are part of the cytoskeleton in epithelial cells. They were found to regulate viscoelastic properties and motility of cancer cells. Due to unique biochemical properties of keratin polymers, the knowledge of the mechanisms controlling keratin network formation is incomplete. A combination of deterministic and stochastic modeling techniques can be a valuable source of information since they can describe known mechanisms of network evolution while reflecting the uncertainty with respect to a variety of molecular events. We applied the concept of piecewise-deterministic Markov processes to the modeling of keratin network formation with high spatiotemporal resolution. The deterministic component describes the diffusion-driven evolution of a pool of soluble keratin filament precursors fueling various network formation processes. Instants of network formation events are determined by a stochastic point process on the time axis. A probability distribution controlled by model parameters exercises control over the frequency of different mechanisms of network formation to be triggered. Locations of the network formation events are assigned dependent on the spatial distribution of the soluble pool of filament precursors. Based on this modeling approach, simulation studies revealed that the architecture of keratin networks mostly depends on the balance between filament elongation and branching processes. The spatial distribution of network mesh size, which strongly influences the mechanical characteristics of filament networks, is modulated by lateral annealing processes. This mechanism which is a specific feature of intermediate filament networks appears to be a major and fast regulator of cell mechanics.

Stencil method: a Markov model for transport in porous media

Science.gov (United States)

Delgoshaie, A. H.; Tchelepi, H.; Jenny, P.

2016-12-01

In porous media the transport of fluid is dominated by flow-field heterogeneity resulting from the underlying transmissibility field. Since the transmissibility is highly uncertain, many realizations of a geological model are used to describe the statistics of the transport phenomena in a Monte Carlo framework. One possible way to avoid the high computational cost of physics-based Monte Carlo simulations is to model the velocity field as a Markov process and use Markov Chain Monte Carlo. In previous works multiple Markov models for discrete velocity processes have been proposed. These models can be divided into two general classes of Markov models in time and Markov models in space. Both of these choices have been shown to be effective to some extent. However some studies have suggested that the Markov property cannot be confirmed for a temporal Markov process; Therefore there is not a consensus about the validity and value of Markov models in time. Moreover, previous spacial Markov models have only been used for modeling transport on structured networks and can not be readily applied to model transport in unstructured networks. In this work we propose a novel approach for constructing a Markov model in time (stencil method) for a discrete velocity process. The results form the stencil method are compared to previously proposed spacial Markov models for structured networks. The stencil method is also applied to unstructured networks and can successfully describe the dispersion of particles in this setting. Our conclusion is that both temporal Markov models and spacial Markov models for discrete velocity processes can be valid for a range of model parameters. Moreover, we show that the stencil model can be more efficient in many practical settings and is suited to model dispersion both on structured and unstructured networks.

Stationary and non-stationary occurrences of miniature end plate potentials are well described as stationary and non-stationary Poisson processes in the mollusc Navanax inermis.

Science.gov (United States)

Cappell, M S; Spray, D C; Bennett, M V

1988-06-28

Protractor muscles in the gastropod mollusc Navanax inermis exhibit typical spontaneous miniature end plate potentials with mean amplitude 1.71 +/- 1.19 (standard deviation) mV. The evoked end plate potential is quantized, with a quantum equal to the miniature end plate potential amplitude. When their rate is stationary, occurrence of miniature end plate potentials is a random, Poisson process. When non-stationary, spontaneous miniature end plate potential occurrence is a non-stationary Poisson process, a Poisson process with the mean frequency changing with time. This extends the random Poisson model for miniature end plate potentials to the frequently observed non-stationary occurrence. Reported deviations from a Poisson process can sometimes be accounted for by the non-stationary Poisson process and more complex models, such as clustered release, are not always needed.

«Concurrency» in M-L-Parallel Semi-Markov Process

Directory of Open Access Journals (Sweden)

Larkin Eugene

2017-01-01

Full Text Available This article investigates the functioning of a swarm of robots, each of which receives instructions from the external human operator and autonomously executes them. An abstract model of functioning of a robot, a group of robots and multiple groups of robots was obtained using the notion of semi-Markov process. The concepts of aggregated initial and aggregated absorbing states were introduced. Correspondences for calculation of time parameters of concurrency were obtained.

Discrimination of shot-noise-driven Poisson processes by external dead time - Application of radioluminescence from glass

Science.gov (United States)

Saleh, B. E. A.; Tavolacci, J. T.; Teich, M. C.

1981-01-01

Ways in which dead time can be used to constructively enhance or diminish the effects of point processes that display bunching in the shot-noise-driven doubly stochastic Poisson point process (SNDP) are discussed. Interrelations between photocount bunching arising in the SNDP and the antibunching character arising from dead-time effects are investigated. It is demonstrated that the dead-time-modified count mean and variance for an arbitrary doubly stochastic Poisson point process can be obtained from the Laplace transform of the single-fold and joint-moment-generating functions for the driving rate process. The theory is in good agreement with experimental values for radioluminescence radiation in fused silica, quartz, and glass, and the process has many applications in pulse, particle, and photon detection.

Stochastic foundations of undulatory transport phenomena: generalized Poisson-Kac processes—part II Irreversibility, norms and entropies

Science.gov (United States)

Giona, Massimiliano; Brasiello, Antonio; Crescitelli, Silvestro

2017-08-01

In this second part, we analyze the dissipation properties of generalized Poisson-Kac (GPK) processes, considering the decay of suitable L 2-norms and the definition of entropy functions. In both cases, consistent energy dissipation and entropy functions depend on the whole system of primitive statistical variables, the partial probability density functions \\{ p_α({x}, t) \\}α=1N , while the corresponding energy dissipation and entropy functions based on the overall probability density p({x}, t) do not satisfy monotonicity requirements as a function of time. These results provide new insights on the theory of Markov operators associated with irreversible stochastic dynamics. Examples from chaotic advection (standard map coupled to stochastic GPK processes) illustrate this phenomenon. Some complementary physical issues are also addressed: the ergodicity breaking in the presence of attractive potentials, and the use of GPK perturbations to mollify stochastic field equations.

Regeneration and general Markov chains

Directory of Open Access Journals (Sweden)

Vladimir V. Kalashnikov

1994-01-01

Full Text Available Ergodicity, continuity, finite approximations and rare visits of general Markov chains are investigated. The obtained results permit further quantitative analysis of characteristics, such as, rates of convergence, continuity (measured as a distance between perturbed and non-perturbed characteristics, deviations between Markov chains, accuracy of approximations and bounds on the distribution function of the first visit time to a chosen subset, etc. The underlying techniques use the embedding of the general Markov chain into a wide sense regenerative process with the help of splitting construction.

Markov Processes: Exploring the Use of Dynamic Visualizations to Enhance Student Understanding

Science.gov (United States)

Pfannkuch, Maxine; Budgett, Stephanie

2016-01-01

Finding ways to enhance introductory students' understanding of probability ideas and theory is a goal of many first-year probability courses. In this article, we explore the potential of a prototype tool for Markov processes using dynamic visualizations to develop in students a deeper understanding of the equilibrium and hitting times…

Variance reduction techniques in the simulation of Markov processes

International Nuclear Information System (INIS)

Lessi, O.

1987-01-01

We study a functional r of the stationary distribution of a homogeneous Markov chain. It is often difficult or impossible to perform the analytical calculation of r and so it is reasonable to estimate r by a simulation process. A consistent estimator r(n) of r is obtained with respect to a chain with a countable state space. Suitably modifying the estimator r(n) of r one obtains a new consistent estimator which has a smaller variance than r(n). The same is obtained in the case of finite state space

Modeling of IP scanning activities with Hidden Markov Models: Darknet case study

OpenAIRE

De Santis , Giulia; Lahmadi , Abdelkader; Francois , Jerome; Festor , Olivier

2016-01-01

International audience; We propose a methodology based on Hidden Markov Models (HMMs) to model scanning activities monitored by a darknet. The HMMs of scanning activities are built on the basis of the number of scanned IP addresses within a time window and fitted using mixtures of Poisson distributions. Our methodology is applied on real data traces collected from a darknet and generated by two large scale scanners, ZMap and Shodan. We demonstrated that the built models are able to characteri...

The application of Markov decision process in restaurant delivery robot

Science.gov (United States)

Wang, Yong; Hu, Zhen; Wang, Ying

2017-05-01

As the restaurant delivery robot is often in a dynamic and complex environment, including the chairs inadvertently moved to the channel and customers coming and going. The traditional path planning algorithm is not very ideal. To solve this problem, this paper proposes the Markov dynamic state immediate reward (MDR) path planning algorithm according to the traditional Markov decision process. First of all, it uses MDR to plan a global path, then navigates along this path. When the sensor detects there is no obstructions in front state, increase its immediate state reward value; when the sensor detects there is an obstacle in front, plan a global path that can avoid obstacle with the current position as the new starting point and reduce its state immediate reward value. This continues until the target is reached. When the robot learns for a period of time, it can avoid those places where obstacles are often present when planning the path. By analyzing the simulation experiment, the algorithm has achieved good results in the global path planning under the dynamic environment.

Markov chains theory and applications

CERN Document Server

Sericola, Bruno

2013-01-01

Markov chains are a fundamental class of stochastic processes. They are widely used to solve problems in a large number of domains such as operational research, computer science, communication networks and manufacturing systems. The success of Markov chains is mainly due to their simplicity of use, the large number of available theoretical results and the quality of algorithms developed for the numerical evaluation of many metrics of interest.The author presents the theory of both discrete-time and continuous-time homogeneous Markov chains. He carefully examines the explosion phenomenon, the

Normal forms for Poisson maps and symplectic groupoids around Poisson transversals.

Science.gov (United States)

Frejlich, Pedro; Mărcuț, Ioan

2018-01-01

Poisson transversals are submanifolds in a Poisson manifold which intersect all symplectic leaves transversally and symplectically. In this communication, we prove a normal form theorem for Poisson maps around Poisson transversals. A Poisson map pulls a Poisson transversal back to a Poisson transversal, and our first main result states that simultaneous normal forms exist around such transversals, for which the Poisson map becomes transversally linear, and intertwines the normal form data of the transversals. Our second result concerns symplectic integrations. We prove that a neighborhood of a Poisson transversal is integrable exactly when the Poisson transversal itself is integrable, and in that case we prove a normal form theorem for the symplectic groupoid around its restriction to the Poisson transversal, which puts all structure maps in normal form. We conclude by illustrating our results with examples arising from Lie algebras.

Comparison of Poisson structures and Poisson-Lie dynamical r-matrices

OpenAIRE

Enriquez, B.; Etingof, P.; Marshall, I.

2004-01-01

We construct a Poisson isomorphism between the formal Poisson manifolds g^* and G^*, where g is a finite dimensional quasitriangular Lie bialgebra. Here g^* is equipped with its Lie-Poisson (or Kostant-Kirillov-Souriau) structure, and G^* with its Poisson-Lie structure. We also quantize Poisson-Lie dynamical r-matrices of Balog-Feher-Palla.

Repairable-conditionally repairable damage model based on dual Poisson processes.

Science.gov (United States)

Lind, B K; Persson, L M; Edgren, M R; Hedlöf, I; Brahme, A

2003-09-01

The advent of intensity-modulated radiation therapy makes it increasingly important to model the response accurately when large volumes of normal tissues are irradiated by controlled graded dose distributions aimed at maximizing tumor cure and minimizing normal tissue toxicity. The cell survival model proposed here is very useful and flexible for accurate description of the response of healthy tissues as well as tumors in classical and truly radiobiologically optimized radiation therapy. The repairable-conditionally repairable (RCR) model distinguishes between two different types of damage, namely the potentially repairable, which may also be lethal, i.e. if unrepaired or misrepaired, and the conditionally repairable, which may be repaired or may lead to apoptosis if it has not been repaired correctly. When potentially repairable damage is being repaired, for example by nonhomologous end joining, conditionally repairable damage may require in addition a high-fidelity correction by homologous repair. The induction of both types of damage is assumed to be described by Poisson statistics. The resultant cell survival expression has the unique ability to fit most experimental data well at low doses (the initial hypersensitive range), intermediate doses (on the shoulder of the survival curve), and high doses (on the quasi-exponential region of the survival curve). The complete Poisson expression can be approximated well by a simple bi-exponential cell survival expression, S(D) = e(-aD) + bDe(-cD), where the first term describes the survival of undamaged cells and the last term represents survival after complete repair of sublethal damage. The bi-exponential expression makes it easy to derive D(0), D(q), n and alpha, beta values to facilitate comparison with classical cell survival models.

Bayesian Inference and Online Learning in Poisson Neuronal Networks.

Science.gov (United States)

Huang, Yanping; Rao, Rajesh P N

2016-08-01

Motivated by the growing evidence for Bayesian computation in the brain, we show how a two-layer recurrent network of Poisson neurons can perform both approximate Bayesian inference and learning for any hidden Markov model. The lower-layer sensory neurons receive noisy measurements of hidden world states. The higher-layer neurons infer a posterior distribution over world states via Bayesian inference from inputs generated by sensory neurons. We demonstrate how such a neuronal network with synaptic plasticity can implement a form of Bayesian inference similar to Monte Carlo methods such as particle filtering. Each spike in a higher-layer neuron represents a sample of a particular hidden world state. The spiking activity across the neural population approximates the posterior distribution over hidden states. In this model, variability in spiking is regarded not as a nuisance but as an integral feature that provides the variability necessary for sampling during inference. We demonstrate how the network can learn the likelihood model, as well as the transition probabilities underlying the dynamics, using a Hebbian learning rule. We present results illustrating the ability of the network to perform inference and learning for arbitrary hidden Markov models.

On Poisson functions

OpenAIRE

Terashima, Yuji

2008-01-01

In this paper, defining Poisson functions on super manifolds, we show that the graphs of Poisson functions are Dirac structures, and find Poisson functions which include as special cases both quasi-Poisson structures and twisted Poisson structures.

Assistive system for people with Apraxia using a Markov decision process.

Science.gov (United States)

Jean-Baptiste, Emilie M D; Russell, Martin; Rothstein, Pia

2014-01-01

CogWatch is an assistive system to re-train stroke survivors suffering from Apraxia or Action Disorganization Syndrome (AADS) to complete activities of daily living (ADLs). This paper describes the approach to real-time planning based on a Markov Decision Process (MDP), and demonstrates its ability to improve task's performance via user simulation. The paper concludes with a discussion of the remaining challenges and future enhancements.

Poisson INAR(1)过程的质量控制%Quality control chart for poisson INAR(1) process

Institute of Scientific and Technical Information of China (English)

睢立伟; 宋向东

2017-01-01

为解决在实际生产中,过程数据并不总能满足彼此独立的假设前提,从而使得一些控制图不再适用于具有相关性的过程的问题,以免在监控过程中出现大量的虚假警报.论文采用取整法研究一阶自回归泊松计数过程模型,首先将一阶自回归模型与泊松计数过程结合起来,然后对原有的模型就行修正,在新模型的基础上重新构造了c控制图和残差控制图的控制限,以使得这两种控制图能够适应新的模型.研究结果表明:两种控制图都只是在一定的情况下使用,研究结论对于研究具有相关性的统计过程有着重要的推进作用.%To solve the problem that in actual production,the process data is not always satisfied with the assumption of independence,which makes some control charts no longer suitable for the process of correlation,so as to avoid a large number of false alarm.This paper studied the poisson INAR(1) process with rounding method.Firstly,the AR(1) process was combined with the poisson counting process,and the original model was corrected.Based on the new model,the control limits of c-chart and residual chart were constructed,in order to adapt the new model.The results of the study indicate the application of the two control charts.The research results have important promoting effect on the study of statistical process.

Speech parts as Poisson processes.

Science.gov (United States)

Badalamenti, A F

2001-09-01

This paper presents evidence that six of the seven parts of speech occur in written text as Poisson processes, simple or recurring. The six major parts are nouns, verbs, adjectives, adverbs, prepositions, and conjunctions, with the interjection occurring too infrequently to support a model. The data consist of more than the first 5000 words of works by four major authors coded to label the parts of speech, as well as periods (sentence terminators). Sentence length is measured via the period and found to be normally distributed with no stochastic model identified for its occurrence. The models for all six speech parts but the noun significantly distinguish some pairs of authors and likewise for the joint use of all words types. Any one author is significantly distinguished from any other by at least one word type and sentence length very significantly distinguishes each from all others. The variety of word type use, measured by Shannon entropy, builds to about 90% of its maximum possible value. The rate constants for nouns are close to the fractions of maximum entropy achieved. This finding together with the stochastic models and the relations among them suggest that the noun may be a primitive organizer of written text.

Capacity of a bosonic memory channel with Gauss-Markov noise

International Nuclear Information System (INIS)

Schaefer, Joachim; Daems, David; Karpov, Evgueni; Cerf, Nicolas J.

2009-01-01

We address the classical capacity of a quantum bosonic memory channel with additive noise, subject to an input energy constraint. The memory is modeled by correlated noise emerging from a Gauss-Markov process. Under reasonable assumptions, we show that the optimal modulation results from a 'quantum water-filling' solution above a certain input energy threshold, similar to the optimal modulation for parallel classical Gaussian channels. We also derive analytically the optimal multimode input state above this threshold, which enables us to compute the capacity of this memory channel in the limit of an infinite number of modes. The method can also be applied to a more general noise environment which is constructed by a stationary Gauss process. The extension of our results to the case of broadband bosonic channels with colored Gaussian noise should also be straightforward.

Quantum Markov Chain Mixing and Dissipative Engineering

DEFF Research Database (Denmark)

Kastoryano, Michael James

2012-01-01

This thesis is the fruit of investigations on the extension of ideas of Markov chain mixing to the quantum setting, and its application to problems of dissipative engineering. A Markov chain describes a statistical process where the probability of future events depends only on the state...... of the system at the present point in time, but not on the history of events. Very many important processes in nature are of this type, therefore a good understanding of their behaviour has turned out to be very fruitful for science. Markov chains always have a non-empty set of limiting distributions...... (stationary states). The aim of Markov chain mixing is to obtain (upper and/or lower) bounds on the number of steps it takes for the Markov chain to reach a stationary state. The natural quantum extensions of these notions are density matrices and quantum channels. We set out to develop a general mathematical...

Birth and Death Process Modeling Leads to the Poisson Distribution: A Journey Worth Taking

Science.gov (United States)

Rash, Agnes M.; Winkel, Brian J.

2009-01-01

This paper describes details of development of the general birth and death process from which we can extract the Poisson process as a special case. This general process is appropriate for a number of courses and units in courses and can enrich the study of mathematics for students as it touches and uses a diverse set of mathematical topics, e.g.,…

Spectral methods for quantum Markov chains

Energy Technology Data Exchange (ETDEWEB)

Szehr, Oleg

2014-05-08

The aim of this project is to contribute to our understanding of quantum time evolutions, whereby we focus on quantum Markov chains. The latter constitute a natural generalization of the ubiquitous concept of a classical Markov chain to describe evolutions of quantum mechanical systems. We contribute to the theory of such processes by introducing novel methods that allow us to relate the eigenvalue spectrum of the transition map to convergence as well as stability properties of the Markov chain.

Spectral methods for quantum Markov chains

International Nuclear Information System (INIS)

Szehr, Oleg

2014-01-01

The aim of this project is to contribute to our understanding of quantum time evolutions, whereby we focus on quantum Markov chains. The latter constitute a natural generalization of the ubiquitous concept of a classical Markov chain to describe evolutions of quantum mechanical systems. We contribute to the theory of such processes by introducing novel methods that allow us to relate the eigenvalue spectrum of the transition map to convergence as well as stability properties of the Markov chain.

Optimal dividend distribution under Markov regime switching

NARCIS (Netherlands)

Jiang, Z.; Pistorius, M.

2012-01-01

We investigate the problem of optimal dividend distribution for a company in the presence of regime shifts. We consider a company whose cumulative net revenues evolve as a Brownian motion with positive drift that is modulated by a finite state Markov chain, and model the discount rate as a

An integrated Markov decision process and nested logit consumer response model of air ticket pricing

NARCIS (Netherlands)

Lu, J.; Feng, T.; Timmermans, H.P.J.; Yang, Z.

2017-01-01

The paper attempts to propose an optimal air ticket pricing model during the booking horizon by taking into account passengers' purchasing behavior of air tickets. A Markov decision process incorporating a nested logit consumer response model is established to modeling the dynamic pricing process.

Pavement maintenance optimization model using Markov Decision Processes

Science.gov (United States)

Mandiartha, P.; Duffield, C. F.; Razelan, I. S. b. M.; Ismail, A. b. H.

2017-09-01

This paper presents an optimization model for selection of pavement maintenance intervention using a theory of Markov Decision Processes (MDP). There are some particular characteristics of the MDP developed in this paper which distinguish it from other similar studies or optimization models intended for pavement maintenance policy development. These unique characteristics include a direct inclusion of constraints into the formulation of MDP, the use of an average cost method of MDP, and the policy development process based on the dual linear programming solution. The limited information or discussions that are available on these matters in terms of stochastic based optimization model in road network management motivates this study. This paper uses a data set acquired from road authorities of state of Victoria, Australia, to test the model and recommends steps in the computation of MDP based stochastic optimization model, leading to the development of optimum pavement maintenance policy.

Stochastic Interest Model Based on Compound Poisson Process and Applications in Actuarial Science

Directory of Open Access Journals (Sweden)

Shilong Li

2017-01-01

Full Text Available Considering stochastic behavior of interest rates in financial market, we construct a new class of interest models based on compound Poisson process. Different from the references, this paper describes the randomness of interest rates by modeling the force of interest with Poisson random jumps directly. To solve the problem in calculation of accumulated interest force function, one important integral technique is employed. And a conception called the critical value is introduced to investigate the validity condition of this new model. We also discuss actuarial present values of several life annuities under this new interest model. Simulations are done to illustrate the theoretical results and the effect of parameters in interest model on actuarial present values is also analyzed.

Asymptotics for Estimating Equations in Hidden Markov Models

DEFF Research Database (Denmark)

Hansen, Jørgen Vinsløv; Jensen, Jens Ledet

Results on asymptotic normality for the maximum likelihood estimate in hidden Markov models are extended in two directions. The stationarity assumption is relaxed, which allows for a covariate process influencing the hidden Markov process. Furthermore a class of estimating equations is considered...

Formal equivalence of Poisson structures around Poisson submanifolds

NARCIS (Netherlands)

Marcut, I.T.

2012-01-01

Let (M,π) be a Poisson manifold. A Poisson submanifold P ⊂ M gives rise to a Lie algebroid AP → P. Formal deformations of π around P are controlled by certain cohomology groups associated to AP. Assuming that these groups vanish, we prove that π is formally rigid around P; that is, any other Poisson

Graph theoretical calculation of systems reliability with semi-Markov processes

International Nuclear Information System (INIS)

Widmer, U.

1984-06-01

The determination of the state probabilities and related quantities of a system characterized by an SMP (or a homogeneous MP) can be performed by means of graph-theoretical methods. The calculation procedures for semi-Markov processes based on signal flow graphs are reviewed. Some methods from electrotechnics are adapted in order to obtain a representation of the state probabilities by means of trees. From this some formulas are derived for the asymptotic state probabilities and for the mean life-time in reliability considerations. (Auth.)

Asymptotic behavior of local times of compound Poisson processes with drift in the infinite variance case

NARCIS (Netherlands)

Lambert, A.; Simatos, F.

2015-01-01

Consider compound Poisson processes with negative drift and no negative jumps, which converge to some spectrally positive Lévy process with nonzero Lévy measure. In this paper, we study the asymptotic behavior of the local time process, in the spatial variable, of these processes killed at two

Asymptotic behavior of local times of compound Poisson processes with drift in the infinite variance case

NARCIS (Netherlands)

Lambert, A.; Simatos, F.

2012-01-01

Consider compound Poisson processes with negative drift and no negative jumps, which converge to some spectrally positive L\\'evy process with non-zero L\\'evy measure. In this paper we study the asymptotic behavior of the local time process, in the spatial variable, of these processes killed at two

On the Modeling and Analysis of Heterogeneous Radio Access Networks using a Poisson Cluster Process

DEFF Research Database (Denmark)

Suryaprakash, Vinay; Møller, Jesper; Fettweis, Gerhard P.

processes, some of which are alluded to (later) in this paper. We model a heterogeneous network consisting of two types of base stations by using a particular Poisson cluster process model. The main contributions are two-fold. First, a complete description of the interference in heterogeneous networks...

First Passage Moments of Finite-State Semi-Markov Processes

Energy Technology Data Exchange (ETDEWEB)

Warr, Richard [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Cordeiro, James [Air Force Research Lab. (AFRL), Wright-Patterson AFB, OH (United States)

2014-03-31

In this paper, we discuss the computation of first-passage moments of a regular time-homogeneous semi-Markov process (SMP) with a finite state space to certain of its states that possess the property of universal accessibility (UA). A UA state is one which is accessible from any other state of the SMP, but which may or may not connect back to one or more other states. An important characteristic of UA is that it is the state-level version of the oft-invoked process-level property of irreducibility. We adapt existing results for irreducible SMPs to the derivation of an analytical matrix expression for the first passage moments to a single UA state of the SMP. In addition, consistent point estimators for these first passage moments, together with relevant R code, are provided.

The exit-time problem for a Markov jump process

Science.gov (United States)

Burch, N.; D'Elia, M.; Lehoucq, R. B.

2014-12-01

The purpose of this paper is to consider the exit-time problem for a finite-range Markov jump process, i.e, the distance the particle can jump is bounded independent of its location. Such jump diffusions are expedient models for anomalous transport exhibiting super-diffusion or nonstandard normal diffusion. We refer to the associated deterministic equation as a volume-constrained nonlocal diffusion equation. The volume constraint is the nonlocal analogue of a boundary condition necessary to demonstrate that the nonlocal diffusion equation is well-posed and is consistent with the jump process. A critical aspect of the analysis is a variational formulation and a recently developed nonlocal vector calculus. This calculus allows us to pose nonlocal backward and forward Kolmogorov equations, the former equation granting the various moments of the exit-time distribution.

On the application of nonhomogeneous Poisson process to the reliability analysis of service water pumps of nuclear power plants

International Nuclear Information System (INIS)

Cruz Saldanha, Pedro Luiz da.

1995-12-01

The purpose of this study is to evaluate the nonhomogeneous Poisson process as a model to rate of occurrence of failures when it is not constant, and the times between failures are not independent nor identically distributed. To this evaluation, an analyse of reliability of service water pumps of a typical nuclear power plant is made considering the model discussed in the last paragraph, as long as the pumps are effectively repairable components. Standard statistical techniques, such as maximum likelihood and linear regression, are applied to estimate parameters of nonhomogeneous Poisson process model. As a conclusion of the study, the nonhomogeneous Poisson process is adequate to model rate of occurrence of failures that are function of time, and can be used where the aging mechanisms are present in operation of repairable systems. (author). 72 refs., 45 figs., 21 tabs

Cumulative sum control charts for monitoring geometrically inflated Poisson processes: An application to infectious disease counts data.

Science.gov (United States)

Rakitzis, Athanasios C; Castagliola, Philippe; Maravelakis, Petros E

2018-02-01

In this work, we study upper-sided cumulative sum control charts that are suitable for monitoring geometrically inflated Poisson processes. We assume that a process is properly described by a two-parameter extension of the zero-inflated Poisson distribution, which can be used for modeling count data with an excessive number of zero and non-zero values. Two different upper-sided cumulative sum-type schemes are considered, both suitable for the detection of increasing shifts in the average of the process. Aspects of their statistical design are discussed and their performance is compared under various out-of-control situations. Changes in both parameters of the process are considered. Finally, the monitoring of the monthly cases of poliomyelitis in the USA is given as an illustrative example.

Consistent Estimation of Partition Markov Models

Directory of Open Access Journals (Sweden)

Jesús E. García

2017-04-01

Full Text Available The Partition Markov Model characterizes the process by a partition L of the state space, where the elements in each part of L share the same transition probability to an arbitrary element in the alphabet. This model aims to answer the following questions: what is the minimal number of parameters needed to specify a Markov chain and how to estimate these parameters. In order to answer these questions, we build a consistent strategy for model selection which consist of: giving a size n realization of the process, finding a model within the Partition Markov class, with a minimal number of parts to represent the process law. From the strategy, we derive a measure that establishes a metric in the state space. In addition, we show that if the law of the process is Markovian, then, eventually, when n goes to infinity, L will be retrieved. We show an application to model internet navigation patterns.

The cascade probabilistic functions and the Markov's processes. Chapter 1

International Nuclear Information System (INIS)

2003-01-01

In the Chapter 1 the physical and mathematical descriptions of radiation processes are carried out. The relation of the cascade probabilistic functions (CPF) with Markov's chain is shown. The CPF calculation for electrons with the energy losses taking into account are given. The calculation of the CPF on the computer was carried out. The estimation of energy losses contribution in the CPFs and radiation defects concentration are made. Besides calculation of the primarily knock-on atoms and radiation defects at electron irradiation with use of the CPF with taking into account energy losses are conducted

Stochastic interest model driven by compound Poisson process andBrownian motion with applications in life contingencies

Directory of Open Access Journals (Sweden)

Shilong Li

2018-03-01

Full Text Available In this paper, we introduce a class of stochastic interest model driven by a compoundPoisson process and a Brownian motion, in which the jumping times of force of interest obeyscompound Poisson process and the continuous tiny fluctuations are described by Brownian motion, andthe adjustment in each jump of interest force is assumed to be random. Based on the proposed interestmodel, we discuss the expected discounted function, the validity of the model and actuarial presentvalues of life annuities and life insurances under different parameters and distribution settings. Ournumerical results show actuarial values could be sensitive to the parameters and distribution settings,which shows the importance of introducing this kind interest model.

Non-homogeneous Markov process models with informative observations with an application to Alzheimer's disease.

Science.gov (United States)

Chen, Baojiang; Zhou, Xiao-Hua

2011-05-01

Identifying risk factors for transition rates among normal cognition, mildly cognitive impairment, dementia and death in an Alzheimer's disease study is very important. It is known that transition rates among these states are strongly time dependent. While Markov process models are often used to describe these disease progressions, the literature mainly focuses on time homogeneous processes, and limited tools are available for dealing with non-homogeneity. Further, patients may choose when they want to visit the clinics, which creates informative observations. In this paper, we develop methods to deal with non-homogeneous Markov processes through time scale transformation when observation times are pre-planned with some observations missing. Maximum likelihood estimation via the EM algorithm is derived for parameter estimation. Simulation studies demonstrate that the proposed method works well under a variety of situations. An application to the Alzheimer's disease study identifies that there is a significant increase in transition rates as a function of time. Furthermore, our models reveal that the non-ignorable missing mechanism is perhaps reasonable. Copyright © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Segmenting Continuous Motions with Hidden Semi-markov Models and Gaussian Processes

Directory of Open Access Journals (Sweden)

Tomoaki Nakamura

2017-12-01

Full Text Available Humans divide perceived continuous information into segments to facilitate recognition. For example, humans can segment speech waves into recognizable morphemes. Analogously, continuous motions are segmented into recognizable unit actions. People can divide continuous information into segments without using explicit segment points. This capacity for unsupervised segmentation is also useful for robots, because it enables them to flexibly learn languages, gestures, and actions. In this paper, we propose a Gaussian process-hidden semi-Markov model (GP-HSMM that can divide continuous time series data into segments in an unsupervised manner. Our proposed method consists of a generative model based on the hidden semi-Markov model (HSMM, the emission distributions of which are Gaussian processes (GPs. Continuous time series data is generated by connecting segments generated by the GP. Segmentation can be achieved by using forward filtering-backward sampling to estimate the model's parameters, including the lengths and classes of the segments. In an experiment using the CMU motion capture dataset, we tested GP-HSMM with motion capture data containing simple exercise motions; the results of this experiment showed that the proposed GP-HSMM was comparable with other methods. We also conducted an experiment using karate motion capture data, which is more complex than exercise motion capture data; in this experiment, the segmentation accuracy of GP-HSMM was 0.92, which outperformed other methods.

A Poisson process approximation for generalized K-5 confidence regions

Science.gov (United States)

Arsham, H.; Miller, D. R.

1982-01-01

One-sided confidence regions for continuous cumulative distribution functions are constructed using empirical cumulative distribution functions and the generalized Kolmogorov-Smirnov distance. The band width of such regions becomes narrower in the right or left tail of the distribution. To avoid tedious computation of confidence levels and critical values, an approximation based on the Poisson process is introduced. This aproximation provides a conservative confidence region; moreover, the approximation error decreases monotonically to 0 as sample size increases. Critical values necessary for implementation are given. Applications are made to the areas of risk analysis, investment modeling, reliability assessment, and analysis of fault tolerant systems.

Decisive Markov Chains

OpenAIRE

Abdulla, Parosh Aziz; Henda, Noomene Ben; Mayr, Richard

2007-01-01

We consider qualitative and quantitative verification problems for infinite-state Markov chains. We call a Markov chain decisive w.r.t. a given set of target states F if it almost certainly eventually reaches either F or a state from which F can no longer be reached. While all finite Markov chains are trivially decisive (for every set F), this also holds for many classes of infinite Markov chains. Infinite Markov chains which contain a finite attractor are decisive w.r.t. every set F. In part...

Portfolio allocation under the vendor managed inventory: A Markov ...

African Journals Online (AJOL)

Portfolio allocation under the vendor managed inventory: A Markov decision process. ... Journal of Applied Sciences and Environmental Management ... This study provides a review of Markov decision processes and investigates its suitability for solutions to portfolio allocation problems under vendor managed inventory in ...

Simulation-based algorithms for Markov decision processes

CERN Document Server

Chang, Hyeong Soo; Fu, Michael C; Marcus, Steven I

2013-01-01

Markov decision process (MDP) models are widely used for modeling sequential decision-making problems that arise in engineering, economics, computer science, and the social sciences.  Many real-world problems modeled by MDPs have huge state and/or action spaces, giving an opening to the curse of dimensionality and so making practical solution of the resulting models intractable.  In other cases, the system of interest is too complex to allow explicit specification of some of the MDP model parameters, but simulation samples are readily available (e.g., for random transitions and costs). For these settings, various sampling and population-based algorithms have been developed to overcome the difficulties of computing an optimal solution in terms of a policy and/or value function.  Specific approaches include adaptive sampling, evolutionary policy iteration, evolutionary random policy search, and model reference adaptive search. This substantially enlarged new edition reflects the latest developments in novel ...

Markov Jump Processes Approximating a Non-Symmetric Generalized Diffusion

International Nuclear Information System (INIS)

Limić, Nedžad

2011-01-01

Consider a non-symmetric generalized diffusion X(⋅) in ℝ d determined by the differential operator A(x) = -Σ ij ∂ i a ij (x)∂ j + Σ i b i (x)∂ i . In this paper the diffusion process is approximated by Markov jump processes X n (⋅), in homogeneous and isotropic grids G n ⊂ℝ d , which converge in distribution in the Skorokhod space D([0,∞),ℝ d ) to the diffusion X(⋅). The generators of X n (⋅) are constructed explicitly. Due to the homogeneity and isotropy of grids, the proposed method for d≥3 can be applied to processes for which the diffusion tensor {a ij (x)} 11 dd fulfills an additional condition. The proposed construction offers a simple method for simulation of sample paths of non-symmetric generalized diffusion. Simulations are carried out in terms of jump processes X n (⋅). For piece-wise constant functions a ij on ℝ d and piece-wise continuous functions a ij on ℝ 2 the construction and principal algorithm are described enabling an easy implementation into a computer code.

Topological Poisson Sigma models on Poisson-Lie groups

International Nuclear Information System (INIS)

Calvo, Ivan; Falceto, Fernando; Garcia-Alvarez, David

2003-01-01

We solve the topological Poisson Sigma model for a Poisson-Lie group G and its dual G*. We show that the gauge symmetry for each model is given by its dual group that acts by dressing transformations on the target. The resolution of both models in the open geometry reveals that there exists a map from the reduced phase of each model (P and P*) to the main symplectic leaf of the Heisenberg double (D 0 ) such that the symplectic forms on P, P* are obtained as the pull-back by those maps of the symplectic structure on D 0 . This uncovers a duality between P and P* under the exchange of bulk degrees of freedom of one model with boundary degrees of freedom of the other one. We finally solve the Poisson Sigma model for the Poisson structure on G given by a pair of r-matrices that generalizes the Poisson-Lie case. The Hamiltonian analysis of the theory requires the introduction of a deformation of the Heisenberg double. (author)

Markov chain aggregation for agent-based models

CERN Document Server

Banisch, Sven

2016-01-01

This self-contained text develops a Markov chain approach that makes the rigorous analysis of a class of microscopic models that specify the dynamics of complex systems at the individual level possible. It presents a general framework of aggregation in agent-based and related computational models, one which makes use of lumpability and information theory in order to link the micro and macro levels of observation. The starting point is a microscopic Markov chain description of the dynamical process in complete correspondence with the dynamical behavior of the agent-based model (ABM), which is obtained by considering the set of all possible agent configurations as the state space of a huge Markov chain. An explicit formal representation of a resulting “micro-chain” including microscopic transition rates is derived for a class of models by using the random mapping representation of a Markov process. The type of probability distribution used to implement the stochastic part of the model, which defines the upd...

Poisson distribution

NARCIS (Netherlands)

Hallin, M.; Piegorsch, W.; El Shaarawi, A.

2012-01-01

The random variable X taking values 0,1,2,…,x,… with probabilities pλ(x) = e−λλx/x!, where λ∈R0+ is called a Poisson variable, and its distribution a Poisson distribution, with parameter λ. The Poisson distribution with parameter λ can be obtained as the limit, as n → ∞ and p → 0 in such a way that

Reduced equations of motion for quantum systems driven by diffusive Markov processes.

Science.gov (United States)

Sarovar, Mohan; Grace, Matthew D

2012-09-28

The expansion of a stochastic Liouville equation for the coupled evolution of a quantum system and an Ornstein-Uhlenbeck process into a hierarchy of coupled differential equations is a useful technique that simplifies the simulation of stochastically driven quantum systems. We expand the applicability of this technique by completely characterizing the class of diffusive Markov processes for which a useful hierarchy of equations can be derived. The expansion of this technique enables the examination of quantum systems driven by non-Gaussian stochastic processes with bounded range. We present an application of this extended technique by simulating Stark-tuned Förster resonance transfer in Rydberg atoms with nonperturbative position fluctuations.

Fermionic Markov Chains

OpenAIRE

Fannes, Mark; Wouters, Jeroen

2012-01-01

We study a quantum process that can be considered as a quantum analogue for the classical Markov process. We specifically construct a version of these processes for free Fermions. For such free Fermionic processes we calculate the entropy density. This can be done either directly using Szeg\\"o's theorem for asymptotic densities of functions of Toeplitz matrices, or through an extension of said theorem to rates of functions, which we present in this article.

Markov and mixed models with applications

DEFF Research Database (Denmark)

Mortensen, Stig Bousgaard

This thesis deals with mathematical and statistical models with focus on applications in pharmacokinetic and pharmacodynamic (PK/PD) modelling. These models are today an important aspect of the drug development in the pharmaceutical industry and continued research in statistical methodology within...... or uncontrollable factors in an individual. Modelling using SDEs also provides new tools for estimation of unknown inputs to a system and is illustrated with an application to estimation of insulin secretion rates in diabetic patients. Models for the eect of a drug is a broader area since drugs may affect...... for non-parametric estimation of Markov processes are proposed to give a detailed description of the sleep process during the night. Statistically the Markov models considered for sleep states are closely related to the PK models based on SDEs as both models share the Markov property. When the models...

Markov stochasticity coordinates

International Nuclear Information System (INIS)

Eliazar, Iddo

2017-01-01

Markov dynamics constitute one of the most fundamental models of random motion between the states of a system of interest. Markov dynamics have diverse applications in many fields of science and engineering, and are particularly applicable in the context of random motion in networks. In this paper we present a two-dimensional gauging method of the randomness of Markov dynamics. The method–termed Markov Stochasticity Coordinates–is established, discussed, and exemplified. Also, the method is tweaked to quantify the stochasticity of the first-passage-times of Markov dynamics, and the socioeconomic equality and mobility in human societies.

Markov stochasticity coordinates

Energy Technology Data Exchange (ETDEWEB)

Eliazar, Iddo, E-mail: iddo.eliazar@intel.com

2017-01-15

Markov dynamics constitute one of the most fundamental models of random motion between the states of a system of interest. Markov dynamics have diverse applications in many fields of science and engineering, and are particularly applicable in the context of random motion in networks. In this paper we present a two-dimensional gauging method of the randomness of Markov dynamics. The method–termed Markov Stochasticity Coordinates–is established, discussed, and exemplified. Also, the method is tweaked to quantify the stochasticity of the first-passage-times of Markov dynamics, and the socioeconomic equality and mobility in human societies.

Experimental dead-time distortions of Poisson processes

International Nuclear Information System (INIS)

Faraci, G.; Pennisi, A.R.; Consiglio Nazionale delle Ricerche, Catania

1983-01-01

In order to check the distortions, introduced by a non-extended dead time on the Poisson statistics, accurate experiments have been made in single channel counting. At a given measuring time, the dependence on the choice of the time origin and on the width of the dead time has been verified. An excellent agreement has been found between the theoretical expressions and the experimental curves. (orig.)

Observation uncertainty in reversible Markov chains.

Science.gov (United States)

Metzner, Philipp; Weber, Marcus; Schütte, Christof

2010-09-01

In many applications one is interested in finding a simplified model which captures the essential dynamical behavior of a real life process. If the essential dynamics can be assumed to be (approximately) memoryless then a reasonable choice for a model is a Markov model whose parameters are estimated by means of Bayesian inference from an observed time series. We propose an efficient Monte Carlo Markov chain framework to assess the uncertainty of the Markov model and related observables. The derived Gibbs sampler allows for sampling distributions of transition matrices subject to reversibility and/or sparsity constraints. The performance of the suggested sampling scheme is demonstrated and discussed for a variety of model examples. The uncertainty analysis of functions of the Markov model under investigation is discussed in application to the identification of conformations of the trialanine molecule via Robust Perron Cluster Analysis (PCCA+) .

Context Tree Estimation in Variable Length Hidden Markov Models

OpenAIRE

Dumont, Thierry

2011-01-01

We address the issue of context tree estimation in variable length hidden Markov models. We propose an estimator of the context tree of the hidden Markov process which needs no prior upper bound on the depth of the context tree. We prove that the estimator is strongly consistent. This uses information-theoretic mixture inequalities in the spirit of Finesso and Lorenzo(Consistent estimation of the order for Markov and hidden Markov chains(1990)) and E.Gassiat and S.Boucheron (Optimal error exp...

Estimation of a Non-homogeneous Poisson Model: An Empirical ...

African Journals Online (AJOL)

This article aims at applying the Nonhomogeneous Poisson process to trends of economic development. For this purpose, a modified Nonhomogeneous Poisson process is derived when the intensity rate is considered as a solution of stochastic differential equation which satisfies the geometric Brownian motion. The mean ...

Microergodicity effects on ebullition of methane modelled by Mixed Poisson process with Pareto mixing variable

Czech Academy of Sciences Publication Activity Database

Jordanova, P.; Dušek, Jiří; Stehlík, M.

2013-01-01

Roč. 128, OCT 15 (2013), s. 124-134 ISSN 0169-7439 R&D Projects: GA ČR(CZ) GAP504/11/1151; GA MŠk(CZ) ED1.1.00/02.0073 Institutional support: RVO:67179843 Keywords : environmental chemistry * ebullition of methane * mixed poisson processes * renewal process * pareto distribution * moving average process * robust statistics * sedge–grass marsh Subject RIV: EH - Ecology, Behaviour Impact factor: 2.381, year: 2013

Logics and Models for Stochastic Analysis Beyond Markov Chains

DEFF Research Database (Denmark)

Zeng, Kebin

, because of the generality of ME distributions, we have to leave the world of Markov chains. To support ME distributions with multiple exits, we introduce a multi-exits ME distribution together with a process algebra MEME to express the systems having the semantics as Markov renewal processes with ME...

Mixed-Poisson Point Process with Partially-Observed Covariates: Ecological Momentary Assessment of Smoking.

Science.gov (United States)

Neustifter, Benjamin; Rathbun, Stephen L; Shiffman, Saul

2012-01-01

Ecological Momentary Assessment is an emerging method of data collection in behavioral research that may be used to capture the times of repeated behavioral events on electronic devices, and information on subjects' psychological states through the electronic administration of questionnaires at times selected from a probability-based design as well as the event times. A method for fitting a mixed Poisson point process model is proposed for the impact of partially-observed, time-varying covariates on the timing of repeated behavioral events. A random frailty is included in the point-process intensity to describe variation among subjects in baseline rates of event occurrence. Covariate coefficients are estimated using estimating equations constructed by replacing the integrated intensity in the Poisson score equations with a design-unbiased estimator. An estimator is also proposed for the variance of the random frailties. Our estimators are robust in the sense that no model assumptions are made regarding the distribution of the time-varying covariates or the distribution of the random effects. However, subject effects are estimated under gamma frailties using an approximate hierarchical likelihood. The proposed approach is illustrated using smoking data.

Markov Chain Modelling for Short-Term NDVI Time Series Forecasting

Directory of Open Access Journals (Sweden)

Stepčenko Artūrs

2016-12-01

Full Text Available In this paper, the NDVI time series forecasting model has been developed based on the use of discrete time, continuous state Markov chain of suitable order. The normalised difference vegetation index (NDVI is an indicator that describes the amount of chlorophyll (the green mass and shows the relative density and health of vegetation; therefore, it is an important variable for vegetation forecasting. A Markov chain is a stochastic process that consists of a state space. This stochastic process undergoes transitions from one state to another in the state space with some probabilities. A Markov chain forecast model is flexible in accommodating various forecast assumptions and structures. The present paper discusses the considerations and techniques in building a Markov chain forecast model at each step. Continuous state Markov chain model is analytically described. Finally, the application of the proposed Markov chain model is illustrated with reference to a set of NDVI time series data.

Seasonally adjusted birth frequencies follow the Poisson distribution.

Science.gov (United States)

Barra, Mathias; Lindstrøm, Jonas C; Adams, Samantha S; Augestad, Liv A

2015-12-15

Variations in birth frequencies have an impact on activity planning in maternity wards. Previous studies of this phenomenon have commonly included elective births. A Danish study of spontaneous births found that birth frequencies were well modelled by a Poisson process. Somewhat unexpectedly, there were also weekly variations in the frequency of spontaneous births. Another study claimed that birth frequencies follow the Benford distribution. Our objective was to test these results. We analysed 50,017 spontaneous births at Akershus University Hospital in the period 1999-2014. To investigate the Poisson distribution of these births, we plotted their variance over a sliding average. We specified various Poisson regression models, with the number of births on a given day as the outcome variable. The explanatory variables included various combinations of years, months, days of the week and the digit sum of the date. The relationship between the variance and the average fits well with an underlying Poisson process. A Benford distribution was disproved by a goodness-of-fit test (p Poisson process when monthly and day-of-the-week variation is included. The frequency is highest in summer towards June and July, Friday and Tuesday stand out as particularly busy days, and the activity level is at its lowest during weekends.

Nonparametric Inference of Doubly Stochastic Poisson Process Data via the Kernel Method.

Science.gov (United States)

Zhang, Tingting; Kou, S C

2010-01-01

Doubly stochastic Poisson processes, also known as the Cox processes, frequently occur in various scientific fields. In this article, motivated primarily by analyzing Cox process data in biophysics, we propose a nonparametric kernel-based inference method. We conduct a detailed study, including an asymptotic analysis, of the proposed method, and provide guidelines for its practical use, introducing a fast and stable regression method for bandwidth selection. We apply our method to real photon arrival data from recent single-molecule biophysical experiments, investigating proteins' conformational dynamics. Our result shows that conformational fluctuation is widely present in protein systems, and that the fluctuation covers a broad range of time scales, highlighting the dynamic and complex nature of proteins' structure.

Segmentation algorithm for non-stationary compound Poisson processes. With an application to inventory time series of market members in a financial market

Science.gov (United States)

Tóth, B.; Lillo, F.; Farmer, J. D.

2010-11-01

We introduce an algorithm for the segmentation of a class of regime switching processes. The segmentation algorithm is a non parametric statistical method able to identify the regimes (patches) of a time series. The process is composed of consecutive patches of variable length. In each patch the process is described by a stationary compound Poisson process, i.e. a Poisson process where each count is associated with a fluctuating signal. The parameters of the process are different in each patch and therefore the time series is non-stationary. Our method is a generalization of the algorithm introduced by Bernaola-Galván, et al. [Phys. Rev. Lett. 87, 168105 (2001)]. We show that the new algorithm outperforms the original one for regime switching models of compound Poisson processes. As an application we use the algorithm to segment the time series of the inventory of market members of the London Stock Exchange and we observe that our method finds almost three times more patches than the original one.

A Multilayer Hidden Markov Models-Based Method for Human-Robot Interaction

Directory of Open Access Journals (Sweden)

Chongben Tao

2013-01-01

Full Text Available To achieve Human-Robot Interaction (HRI by using gestures, a continuous gesture recognition approach based on Multilayer Hidden Markov Models (MHMMs is proposed, which consists of two parts. One part is gesture spotting and segment module, the other part is continuous gesture recognition module. Firstly, a Kinect sensor is used to capture 3D acceleration and 3D angular velocity data of hand gestures. And then, a Feed-forward Neural Networks (FNNs and a threshold criterion are used for gesture spotting and segment, respectively. Afterwards, the segmented gesture signals are respectively preprocessed and vector symbolized by a sliding window and a K-means clustering method. Finally, symbolized data are sent into Lower Hidden Markov Models (LHMMs to identify individual gestures, and then, a Bayesian filter with sequential constraints among gestures in Upper Hidden Markov Models (UHMMs is used to correct recognition errors created in LHMMs. Five predefined gestures are used to interact with a Kinect mobile robot in experiments. The experimental results show that the proposed method not only has good effectiveness and accuracy, but also has favorable real-time performance.

Statistical error in simulations of Poisson processes: Example of diffusion in solids

Science.gov (United States)

Nilsson, Johan O.; Leetmaa, Mikael; Vekilova, Olga Yu.; Simak, Sergei I.; Skorodumova, Natalia V.

2016-08-01

Simulations of diffusion in solids often produce poor statistics of diffusion events. We present an analytical expression for the statistical error in ion conductivity obtained in such simulations. The error expression is not restricted to any computational method in particular, but valid in the context of simulation of Poisson processes in general. This analytical error expression is verified numerically for the case of Gd-doped ceria by running a large number of kinetic Monte Carlo calculations.

Markov Chain Monte Carlo Methods

Indian Academy of Sciences (India)

Keywords. Markov chain; state space; stationary transition probability; stationary distribution; irreducibility; aperiodicity; stationarity; M-H algorithm; proposal distribution; acceptance probability; image processing; Gibbs sampler.

A sow replacement model using Bayesian updating in a three-level hierarchic Markov process. I. Biological model

DEFF Research Database (Denmark)

Kristensen, Anders Ringgaard; Søllested, Thomas Algot

2004-01-01

that really uses all these methodological improvements. In this paper, the biological model describing the performance and feed intake of sows is presented. In particular, estimation of herd specific parameters is emphasized. The optimization model is described in a subsequent paper......Several replacement models have been presented in literature. In other applicational areas like dairy cow replacement, various methodological improvements like hierarchical Markov processes and Bayesian updating have been implemented, but not in sow models. Furthermore, there are methodological...... improvements like multi-level hierarchical Markov processes with decisions on multiple time scales, efficient methods for parameter estimations at herd level and standard software that has been hardly implemented at all in any replacement model. The aim of this study is to present a sow replacement model...

Singular Perturbation for the Discounted Continuous Control of Piecewise Deterministic Markov Processes

International Nuclear Information System (INIS)

Costa, O. L. V.; Dufour, F.

2011-01-01

This paper deals with the expected discounted continuous control of piecewise deterministic Markov processes (PDMP’s) using a singular perturbation approach for dealing with rapidly oscillating parameters. The state space of the PDMP is written as the product of a finite set and a subset of the Euclidean space ℝ n . The discrete part of the state, called the regime, characterizes the mode of operation of the physical system under consideration, and is supposed to have a fast (associated to a small parameter ε>0) and a slow behavior. By using a similar approach as developed in Yin and Zhang (Continuous-Time Markov Chains and Applications: A Singular Perturbation Approach, Applications of Mathematics, vol. 37, Springer, New York, 1998, Chaps. 1 and 3) the idea in this paper is to reduce the number of regimes by considering an averaged model in which the regimes within the same class are aggregated through the quasi-stationary distribution so that the different states in this class are replaced by a single one. The main goal is to show that the value function of the control problem for the system driven by the perturbed Markov chain converges to the value function of this limit control problem as ε goes to zero. This convergence is obtained by, roughly speaking, showing that the infimum and supremum limits of the value functions satisfy two optimality inequalities as ε goes to zero. This enables us to show the result by invoking a uniqueness argument, without needing any kind of Lipschitz continuity condition.

The Green-Kubo formula for general Markov processes with a continuous time parameter

International Nuclear Information System (INIS)

Yang Fengxia; Liu Yong; Chen Yong

2010-01-01

For general Markov processes, the Green-Kubo formula is shown to be valid under a mild condition. A class of stochastic evolution equations on a separable Hilbert space and three typical infinite systems of locally interacting diffusions on Z d (irreversible in most cases) are shown to satisfy the Green-Kubo formula, and the Einstein relations for these stochastic evolution equations are shown explicitly as a corollary.

Climate changes and their effects in the public health: use of poisson regression models

Directory of Open Access Journals (Sweden)

Jonas Bodini Alonso

2010-08-01

Full Text Available In this paper, we analyze the daily number of hospitalizations in São Paulo City, Brazil, in the period of January 01, 2002 to December 31, 2005. This data set relates to pneumonia, coronary ischemic diseases, diabetes and chronic diseases in different age categories. In order to verify the effect of climate changes the following covariates are considered: atmosphere pressure, air humidity, temperature, year season and also a covariate related to the week day when the hospitalization occurred. The possible effects of the assumed covariates in the number of hospitalization are studied using a Poisson regression model in the presence or not of a random effect which captures the possible correlation among the hospitalization accounting for the different age categories in the same day and the extra-Poisson variability for the longitudinal data. The inferences of interest are obtained using the Bayesian paradigm and MCMC (Markov chain Monte Carlo methods.Neste artigo, analisamos os dados relativos aos números diários de hospitalizações na cidade de São Paulo, Brasil no período de 01/01/2002 a 31/12/2005 devido a pneumonia, doenças isquêmicas, diabetes e doenças crônicas e de acordo com a faixa etária. Com o objetivo de estudar o efeito de mudanças climáticas são consideradas algumas covariáveis climáticas os índices diários de pressão atmosférica, umidade do ar, temperatura e estação do ano, e uma covariável relacionada ao dia da semana da ocorrência de hospitalização. Para verificar os efeitos das covariáveis nas respostas dadas pelo numero de hospitalizações, consideramos um modelo de regressão de Poisson na presença ou não de um efeito aleatório que captura a possível correlação entre as contagens para as faixas etárias de um mesmo dia e a variabilidade extra-poisson para os dados longitudinais. As inferências de interesse são obtidas usando o paradigma bayesiano e métodos de simulação MCMC (Monte Carlo

Approximate quantum Markov chains

CERN Document Server

Sutter, David

2018-01-01

This book is an introduction to quantum Markov chains and explains how this concept is connected to the question of how well a lost quantum mechanical system can be recovered from a correlated subsystem. To achieve this goal, we strengthen the data-processing inequality such that it reveals a statement about the reconstruction of lost information. The main difficulty in order to understand the behavior of quantum Markov chains arises from the fact that quantum mechanical operators do not commute in general. As a result we start by explaining two techniques of how to deal with non-commuting matrices: the spectral pinching method and complex interpolation theory. Once the reader is familiar with these techniques a novel inequality is presented that extends the celebrated Golden-Thompson inequality to arbitrarily many matrices. This inequality is the key ingredient in understanding approximate quantum Markov chains and it answers a question from matrix analysis that was open since 1973, i.e., if Lieb's triple ma...

Description of quantum-mechanical motion by using the formalism of non-Markov stochastic process

International Nuclear Information System (INIS)

Skorobogatov, G.A.; Svertilov, S.I.

1999-01-01

The principle possibilities of mathematical modeling of quantum mechanical motion by the theory of a real stochastic processes is considered. The set of equations corresponding to the simplest case of a two-level system undergoing transitions under the influence of electromagnetic field are obtained. It is shown that quantum-mechanical processes are purely discrete processes of non-Markovian type. They are continuous processes in the space of probability amplitudes and posses the properties of quantum Markovity. The formulation of quantum mechanics in terms of the theory of stochastic processes is necessary for its generalization on small space-time intervals [ru

Effective degree Markov-chain approach for discrete-time epidemic processes on uncorrelated networks.

Science.gov (United States)

Cai, Chao-Ran; Wu, Zhi-Xi; Guan, Jian-Yue

2014-11-01

Recently, Gómez et al. proposed a microscopic Markov-chain approach (MMCA) [S. Gómez, J. Gómez-Gardeñes, Y. Moreno, and A. Arenas, Phys. Rev. E 84, 036105 (2011)PLEEE81539-375510.1103/PhysRevE.84.036105] to the discrete-time susceptible-infected-susceptible (SIS) epidemic process and found that the epidemic prevalence obtained by this approach agrees well with that by simulations. However, we found that the approach cannot be straightforwardly extended to a susceptible-infected-recovered (SIR) epidemic process (due to its irreversible property), and the epidemic prevalences obtained by MMCA and Monte Carlo simulations do not match well when the infection probability is just slightly above the epidemic threshold. In this contribution we extend the effective degree Markov-chain approach, proposed for analyzing continuous-time epidemic processes [J. Lindquist, J. Ma, P. Driessche, and F. Willeboordse, J. Math. Biol. 62, 143 (2011)JMBLAJ0303-681210.1007/s00285-010-0331-2], to address discrete-time binary-state (SIS) or three-state (SIR) epidemic processes on uncorrelated complex networks. It is shown that the final epidemic size as well as the time series of infected individuals obtained from this approach agree very well with those by Monte Carlo simulations. Our results are robust to the change of different parameters, including the total population size, the infection probability, the recovery probability, the average degree, and the degree distribution of the underlying networks.

Risk aversion and risk seeking in multicriteria forest management: a Markov decision process approach

Science.gov (United States)

Joseph Buongiorno; Mo Zhou; Craig Johnston

2017-01-01

Markov decision process models were extended to reflect some consequences of the risk attitude of forestry decision makers. One approach consisted of maximizing the expected value of a criterion subject to an upper bound on the variance or, symmetrically, minimizing the variance subject to a lower bound on the expected value.  The other method used the certainty...

Universal Poisson Statistics of mRNAs with Complex Decay Pathways.

Science.gov (United States)

Thattai, Mukund

2016-01-19

Messenger RNA (mRNA) dynamics in single cells are often modeled as a memoryless birth-death process with a constant probability per unit time that an mRNA molecule is synthesized or degraded. This predicts a Poisson steady-state distribution of mRNA number, in close agreement with experiments. This is surprising, since mRNA decay is known to be a complex process. The paradox is resolved by realizing that the Poisson steady state generalizes to arbitrary mRNA lifetime distributions. A mapping between mRNA dynamics and queueing theory highlights an identifiability problem: a measured Poisson steady state is consistent with a large variety of microscopic models. Here, I provide a rigorous and intuitive explanation for the universality of the Poisson steady state. I show that the mRNA birth-death process and its complex decay variants all take the form of the familiar Poisson law of rare events, under a nonlinear rescaling of time. As a corollary, not only steady-states but also transients are Poisson distributed. Deviations from the Poisson form occur only under two conditions, promoter fluctuations leading to transcriptional bursts or nonindependent degradation of mRNA molecules. These results place severe limits on the power of single-cell experiments to probe microscopic mechanisms, and they highlight the need for single-molecule measurements. Copyright © 2016 The Authors. Published by Elsevier Inc. All rights reserved.

Irreversible Local Markov Chains with Rapid Convergence towards Equilibrium

Science.gov (United States)

Kapfer, Sebastian C.; Krauth, Werner

2017-12-01

We study the continuous one-dimensional hard-sphere model and present irreversible local Markov chains that mix on faster time scales than the reversible heat bath or Metropolis algorithms. The mixing time scales appear to fall into two distinct universality classes, both faster than for reversible local Markov chains. The event-chain algorithm, the infinitesimal limit of one of these Markov chains, belongs to the class presenting the fastest decay. For the lattice-gas limit of the hard-sphere model, reversible local Markov chains correspond to the symmetric simple exclusion process (SEP) with periodic boundary conditions. The two universality classes for irreversible Markov chains are realized by the totally asymmetric SEP (TASEP), and by a faster variant (lifted TASEP) that we propose here. We discuss how our irreversible hard-sphere Markov chains generalize to arbitrary repulsive pair interactions and carry over to higher dimensions through the concept of lifted Markov chains and the recently introduced factorized Metropolis acceptance rule.

A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments

International Nuclear Information System (INIS)

Fisicaro, G.; Goedecker, S.; Genovese, L.; Andreussi, O.; Marzari, N.

2016-01-01

The computational study of chemical reactions in complex, wet environments is critical for applications in many fields. It is often essential to study chemical reactions in the presence of applied electrochemical potentials, taking into account the non-trivial electrostatic screening coming from the solvent and the electrolytes. As a consequence, the electrostatic potential has to be found by solving the generalized Poisson and the Poisson-Boltzmann equations for neutral and ionic solutions, respectively. In the present work, solvers for both problems have been developed. A preconditioned conjugate gradient method has been implemented for the solution of the generalized Poisson equation and the linear regime of the Poisson-Boltzmann, allowing to solve iteratively the minimization problem with some ten iterations of the ordinary Poisson equation solver. In addition, a self-consistent procedure enables us to solve the non-linear Poisson-Boltzmann problem. Both solvers exhibit very high accuracy and parallel efficiency and allow for the treatment of periodic, free, and slab boundary conditions. The solver has been integrated into the BigDFT and Quantum-ESPRESSO electronic-structure packages and will be released as an independent program, suitable for integration in other codes

A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments.

Science.gov (United States)

Fisicaro, G; Genovese, L; Andreussi, O; Marzari, N; Goedecker, S

2016-01-07

The computational study of chemical reactions in complex, wet environments is critical for applications in many fields. It is often essential to study chemical reactions in the presence of applied electrochemical potentials, taking into account the non-trivial electrostatic screening coming from the solvent and the electrolytes. As a consequence, the electrostatic potential has to be found by solving the generalized Poisson and the Poisson-Boltzmann equations for neutral and ionic solutions, respectively. In the present work, solvers for both problems have been developed. A preconditioned conjugate gradient method has been implemented for the solution of the generalized Poisson equation and the linear regime of the Poisson-Boltzmann, allowing to solve iteratively the minimization problem with some ten iterations of the ordinary Poisson equation solver. In addition, a self-consistent procedure enables us to solve the non-linear Poisson-Boltzmann problem. Both solvers exhibit very high accuracy and parallel efficiency and allow for the treatment of periodic, free, and slab boundary conditions. The solver has been integrated into the BigDFT and Quantum-ESPRESSO electronic-structure packages and will be released as an independent program, suitable for integration in other codes.

A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments

Energy Technology Data Exchange (ETDEWEB)

Fisicaro, G., E-mail: giuseppe.fisicaro@unibas.ch; Goedecker, S. [Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel (Switzerland); Genovese, L. [University of Grenoble Alpes, CEA, INAC-SP2M, L-Sim, F-38000 Grenoble (France); Andreussi, O. [Institute of Computational Science, Università della Svizzera Italiana, Via Giuseppe Buffi 13, CH-6904 Lugano (Switzerland); Theory and Simulations of Materials (THEOS) and National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, Station 12, CH-1015 Lausanne (Switzerland); Marzari, N. [Theory and Simulations of Materials (THEOS) and National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, Station 12, CH-1015 Lausanne (Switzerland)

2016-01-07

The computational study of chemical reactions in complex, wet environments is critical for applications in many fields. It is often essential to study chemical reactions in the presence of applied electrochemical potentials, taking into account the non-trivial electrostatic screening coming from the solvent and the electrolytes. As a consequence, the electrostatic potential has to be found by solving the generalized Poisson and the Poisson-Boltzmann equations for neutral and ionic solutions, respectively. In the present work, solvers for both problems have been developed. A preconditioned conjugate gradient method has been implemented for the solution of the generalized Poisson equation and the linear regime of the Poisson-Boltzmann, allowing to solve iteratively the minimization problem with some ten iterations of the ordinary Poisson equation solver. In addition, a self-consistent procedure enables us to solve the non-linear Poisson-Boltzmann problem. Both solvers exhibit very high accuracy and parallel efficiency and allow for the treatment of periodic, free, and slab boundary conditions. The solver has been integrated into the BigDFT and Quantum-ESPRESSO electronic-structure packages and will be released as an independent program, suitable for integration in other codes.

Estimation with Right-Censored Observations Under A Semi-Markov Model.

Science.gov (United States)

Zhao, Lihui; Hu, X Joan

2013-06-01

The semi-Markov process often provides a better framework than the classical Markov process for the analysis of events with multiple states. The purpose of this paper is twofold. First, we show that in the presence of right censoring, when the right end-point of the support of the censoring time is strictly less than the right end-point of the support of the semi-Markov kernel, the transition probability of the semi-Markov process is nonidentifiable, and the estimators proposed in the literature are inconsistent in general. We derive the set of all attainable values for the transition probability based on the censored data, and we propose a nonparametric inference procedure for the transition probability using this set. Second, the conventional approach to constructing confidence bands is not applicable for the semi-Markov kernel and the sojourn time distribution. We propose new perturbation resampling methods to construct these confidence bands. Different weights and transformations are explored in the construction. We use simulation to examine our proposals and illustrate them with hospitalization data from a recent cancer survivor study.

Generalized Boolean logic Driven Markov Processes: A powerful modeling framework for Model-Based Safety Analysis of dynamic repairable and reconfigurable systems

International Nuclear Information System (INIS)

Piriou, Pierre-Yves; Faure, Jean-Marc; Lesage, Jean-Jacques

2017-01-01

This paper presents a modeling framework that permits to describe in an integrated manner the structure of the critical system to analyze, by using an enriched fault tree, the dysfunctional behavior of its components, by means of Markov processes, and the reconfiguration strategies that have been planned to ensure safety and availability, with Moore machines. This framework has been developed from BDMP (Boolean logic Driven Markov Processes), a previous framework for dynamic repairable systems. First, the contribution is motivated by pinpointing the limitations of BDMP to model complex reconfiguration strategies and the failures of the control of these strategies. The syntax and semantics of GBDMP (Generalized Boolean logic Driven Markov Processes) are then formally defined; in particular, an algorithm to analyze the dynamic behavior of a GBDMP model is developed. The modeling capabilities of this framework are illustrated on three representative examples. Last, qualitative and quantitative analysis of GDBMP models highlight the benefits of the approach.

Lindley frailty model for a class of compound Poisson processes

Science.gov (United States)

Kadilar, Gamze Özel; Ata, Nihal

2013-10-01

The Lindley distribution gain importance in survival analysis for the similarity of exponential distribution and allowance for the different shapes of hazard function. Frailty models provide an alternative to proportional hazards model where misspecified or omitted covariates are described by an unobservable random variable. Despite of the distribution of the frailty is generally assumed to be continuous, it is appropriate to consider discrete frailty distributions In some circumstances. In this paper, frailty models with discrete compound Poisson process for the Lindley distributed failure time are introduced. Survival functions are derived and maximum likelihood estimation procedures for the parameters are studied. Then, the fit of the models to the earthquake data set of Turkey are examined.

Radio pulsar glitches as a state-dependent Poisson process

Science.gov (United States)

Fulgenzi, W.; Melatos, A.; Hughes, B. D.

2017-10-01

Gross-Pitaevskii simulations of vortex avalanches in a neutron star superfluid are limited computationally to ≲102 vortices and ≲102 avalanches, making it hard to study the long-term statistics of radio pulsar glitches in realistically sized systems. Here, an idealized, mean-field model of the observed Gross-Pitaevskii dynamics is presented, in which vortex unpinning is approximated as a state-dependent, compound Poisson process in a single random variable, the spatially averaged crust-superfluid lag. Both the lag-dependent Poisson rate and the conditional distribution of avalanche-driven lag decrements are inputs into the model, which is solved numerically (via Monte Carlo simulations) and analytically (via a master equation). The output statistics are controlled by two dimensionless free parameters: α, the glitch rate at a reference lag, multiplied by the critical lag for unpinning, divided by the spin-down rate; and β, the minimum fraction of the lag that can be restored by a glitch. The system evolves naturally to a self-regulated stationary state, whose properties are determined by α/αc(β), where αc(β) ≈ β-1/2 is a transition value. In the regime α ≳ αc(β), one recovers qualitatively the power-law size and exponential waiting-time distributions observed in many radio pulsars and Gross-Pitaevskii simulations. For α ≪ αc(β), the size and waiting-time distributions are both power-law-like, and a correlation emerges between size and waiting time until the next glitch, contrary to what is observed in most pulsars. Comparisons with astrophysical data are restricted by the small sample sizes available at present, with ≤35 events observed per pulsar.

Nuclide transport of decay chain in the fractured rock medium: a model using continuous time Markov process

International Nuclear Information System (INIS)

Younmyoung Lee; Kunjai Lee

1995-01-01

A model using continuous time Markov process for nuclide transport of decay chain of arbitrary length in the fractured rock medium has been developed. Considering the fracture in the rock matrix as a finite number of compartments, the transition probability for nuclide from the transition intensity between and out of the compartments is represented utilizing Chapman-Kolmogorov equation, with which the expectation and the variance of nuclide distribution for the fractured rock medium could be obtained. A comparison between continuous time Markov process model and available analytical solutions for the nuclide transport of three decay chains without rock matrix diffusion has been made showing comparatively good agreement. Fittings with experimental breakthrough curves obtained with nonsorbing materials such as NaLS and uranine in the artificial fractured rock are also made. (author)

Projected metastable Markov processes and their estimation with observable operator models

International Nuclear Information System (INIS)

Wu, Hao; Prinz, Jan-Hendrik; Noé, Frank

2015-01-01

The determination of kinetics of high-dimensional dynamical systems, such as macromolecules, polymers, or spin systems, is a difficult and generally unsolved problem — both in simulation, where the optimal reaction coordinate(s) are generally unknown and are difficult to compute, and in experimental measurements, where only specific coordinates are observable. Markov models, or Markov state models, are widely used but suffer from the fact that the dynamics on a coarsely discretized state spaced are no longer Markovian, even if the dynamics in the full phase space are. The recently proposed projected Markov models (PMMs) are a formulation that provides a description of the kinetics on a low-dimensional projection without making the Markovianity assumption. However, as yet no general way of estimating PMMs from data has been available. Here, we show that the observed dynamics of a PMM can be exactly described by an observable operator model (OOM) and derive a PMM estimator based on the OOM learning

Unobserved heterogeneity in the power law nonhomogeneous Poisson process

International Nuclear Information System (INIS)

Asfaw, Zeytu Gashaw; Lindqvist, Bo Henry

2015-01-01

A study of possible consequences of heterogeneity in the failure intensity of repairable systems is presented. The basic model studied is the nonhomogeneous Poisson process with power law intensity function. When several similar systems are under observation, the assumption that the corresponding processes are independent and identically distributed is often questionable. In practice there may be an unobserved heterogeneity among the systems. The heterogeneity is modeled by introduction of unobserved gamma distributed frailties. The relevant likelihood function is derived, and maximum likelihood estimation is illustrated. In a simulation study we then compare results when using a power law model without taking into account heterogeneity, with the corresponding results obtained when the heterogeneity is accounted for. A motivating data example is also given. - Highlights: • Consequences of overlooking heterogeneity in similar repairable systems are studied. • Likelihood functions are established for power law NHPP w/ and w/o heterogeneity. • ML estimators for parameters of power law NHPP with heterogeneity are derived. • A simulation study shows the effects of heterogeneity and its ignorance in models

Modelagem da gestão de estoques de peças de reposição através de cadeias de Markov A model for spare parts stock management using Markov chains

Directory of Open Access Journals (Sweden)

Antonio Vinicius Pimpão Gomes

2008-04-01

Full Text Available Nessa pesquisa é apresentada uma abordagem para gestão de estoques de peças de reposição com base em cadeias de Markov. É feita uma comparação com a simulação convencional, a fim de validar esta abordagem, bem como é apresentada uma heurística para determinação dos parâmetros da política (S, s de gestão de estoques, dado um conjunto de itens de custo (falta, excesso e ressuprimento e de demanda com distribuição Poisson. A análise dos gráficos desses itens de custo em função dos parâmetros da política (S, s fornece os trade-offs básicos para a formulação da heurística.In this study, we propose a model for a management stock system of spare parts using Markov chains. We compare this method with a conventional simulation showing that both methods are equivalent. In addition, we propose heuristics to find the system parameters based on the properties of Markov Chains and graphics related to the costs implied in the stock management of spare parts.

Correlations in Output and Overflow Traffic Processes in Simple Queues

Directory of Open Access Journals (Sweden)

Don McNickle

2007-01-01

Full Text Available We consider some simple Markov and Erlang queues with limited storage space. Although the departure processes from some such systems are known to be Poisson, they actually consist of the superposition of two complex correlated processes, the overflow process and the output process. We measure the cross-correlation between the counting processes for these two processes. It turns out that this can be positive, negative, or even zero (without implying independence. The models suggest some general principles on how big these correlations are, and when they are important. This may suggest when renewal or moment approximations to similar processes will be successful, and when they will not.

Accelerated decomposition techniques for large discounted Markov decision processes

Science.gov (United States)

Larach, Abdelhadi; Chafik, S.; Daoui, C.

2017-12-01

Many hierarchical techniques to solve large Markov decision processes (MDPs) are based on the partition of the state space into strongly connected components (SCCs) that can be classified into some levels. In each level, smaller problems named restricted MDPs are solved, and then these partial solutions are combined to obtain the global solution. In this paper, we first propose a novel algorithm, which is a variant of Tarjan's algorithm that simultaneously finds the SCCs and their belonging levels. Second, a new definition of the restricted MDPs is presented to ameliorate some hierarchical solutions in discounted MDPs using value iteration (VI) algorithm based on a list of state-action successors. Finally, a robotic motion-planning example and the experiment results are presented to illustrate the benefit of the proposed decomposition algorithms.

Monitoring Poisson observations using combined applications of Shewhart and EWMA charts

Science.gov (United States)

Abujiya, Mu'azu Ramat

2017-11-01

The Shewhart and exponentially weighted moving average (EWMA) charts for nonconformities are the most widely used procedures of choice for monitoring Poisson observations in modern industries. Individually, the Shewhart EWMA charts are only sensitive to large and small shifts, respectively. To enhance the detection abilities of the two schemes in monitoring all kinds of shifts in Poisson count data, this study examines the performance of combined applications of the Shewhart, and EWMA Poisson control charts. Furthermore, the study proposes modifications based on well-structured statistical data collection technique, ranked set sampling (RSS), to detect shifts in the mean of a Poisson process more quickly. The relative performance of the proposed Shewhart-EWMA Poisson location charts is evaluated in terms of the average run length (ARL), standard deviation of the run length (SDRL), median run length (MRL), average ratio ARL (ARARL), average extra quadratic loss (AEQL) and performance comparison index (PCI). Consequently, all the new Poisson control charts based on RSS method are generally more superior than most of the existing schemes for monitoring Poisson processes. The use of these combined Shewhart-EWMA Poisson charts is illustrated with an example to demonstrate the practical implementation of the design procedure.

Bayesian inference for Markov jump processes with informative observations.

Science.gov (United States)

Golightly, Andrew; Wilkinson, Darren J

2015-04-01

In this paper we consider the problem of parameter inference for Markov jump process (MJP) representations of stochastic kinetic models. Since transition probabilities are intractable for most processes of interest yet forward simulation is straightforward, Bayesian inference typically proceeds through computationally intensive methods such as (particle) MCMC. Such methods ostensibly require the ability to simulate trajectories from the conditioned jump process. When observations are highly informative, use of the forward simulator is likely to be inefficient and may even preclude an exact (simulation based) analysis. We therefore propose three methods for improving the efficiency of simulating conditioned jump processes. A conditioned hazard is derived based on an approximation to the jump process, and used to generate end-point conditioned trajectories for use inside an importance sampling algorithm. We also adapt a recently proposed sequential Monte Carlo scheme to our problem. Essentially, trajectories are reweighted at a set of intermediate time points, with more weight assigned to trajectories that are consistent with the next observation. We consider two implementations of this approach, based on two continuous approximations of the MJP. We compare these constructs for a simple tractable jump process before using them to perform inference for a Lotka-Volterra system. The best performing construct is used to infer the parameters governing a simple model of motility regulation in Bacillus subtilis.

A study on the stochastic model for nuclide transport in the fractured porous rock using continuous time Markov process

International Nuclear Information System (INIS)

Lee, Youn Myoung

1995-02-01

As a newly approaching model, a stochastic model using continuous time Markov process for nuclide decay chain transport of arbitrary length in the fractured porous rock medium has been proposed, by which the need for solving a set of partial differential equations corresponding to various sets of side conditions can be avoided. Once the single planar fracture in the rock matrix is represented by a series of finite number of compartments having region wise constant parameter values in them, the medium is continuous in view of various processes associated with nuclide transport but discrete in medium space and such geologic system is assumed to have Markov property, since the Markov process requires that only the present value of the time dependent random variable be known to determine the future value of random variable, nuclide transport in the medium can then be modeled as a continuous time Markov process. Processes that are involved in nuclide transport are advective transport due to groundwater flow, diffusion into the rock matrix, adsorption onto the wall of the fracture and within the pores in the rock matrix, and radioactive decay chain. The transition probabilities for nuclide from the transition intensities between and out of the compartments are represented utilizing Chapman-Kolmogorov equation, through which the expectation and the variance of nuclide distribution for each compartment or the fractured rock medium can be obtained. Some comparisons between Markov process model developed in this work and available analytical solutions for one-dimensional layered porous medium, fractured medium with rock matrix diffusion, and porous medium considering three member nuclide decay chain without rock matrix diffusion have been made showing comparatively good agreement for all cases. To verify the model developed in this work another comparative study was also made by fitting the experimental data obtained with NaLS and uranine running in the artificial fractured

Detection of Text Lines of Handwritten Arabic Manuscripts using Markov Decision Processes

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Youssef Boulid

2016-09-01

Full Text Available In a character recognition systems, the segmentation phase is critical since the accuracy of the recognition depend strongly on it. In this paper we present an approach based on Markov Decision Processes to extract text lines from binary images of Arabic handwritten documents. The proposed approach detects the connected components belonging to the same line by making use of knowledge about features and arrangement of those components. The initial results show that the system is promising for extracting Arabic handwritten lines.

Singular Poisson tensors

International Nuclear Information System (INIS)

Littlejohn, R.G.

1982-01-01

The Hamiltonian structures discovered by Morrison and Greene for various fluid equations were obtained by guessing a Hamiltonian and a suitable Poisson bracket formula, expressed in terms of noncanonical (but physical) coordinates. In general, such a procedure for obtaining a Hamiltonian system does not produce a Hamiltonian phase space in the usual sense (a symplectic manifold), but rather a family of symplectic manifolds. To state the matter in terms of a system with a finite number of degrees of freedom, the family of symplectic manifolds is parametrized by a set of Casimir functions, which are characterized by having vanishing Poisson brackets with all other functions. The number of independent Casimir functions is the corank of the Poisson tensor J/sup ij/, the components of which are the Poisson brackets of the coordinates among themselves. Thus, these Casimir functions exist only when the Poisson tensor is singular

Nambu–Poisson gauge theory

Energy Technology Data Exchange (ETDEWEB)

Jurčo, Branislav, E-mail: jurco@karlin.mff.cuni.cz [Charles University in Prague, Faculty of Mathematics and Physics, Mathematical Institute, Prague 186 75 (Czech Republic); Schupp, Peter, E-mail: p.schupp@jacobs-university.de [Jacobs University Bremen, 28759 Bremen (Germany); Vysoký, Jan, E-mail: vysokjan@fjfi.cvut.cz [Jacobs University Bremen, 28759 Bremen (Germany); Czech Technical University in Prague, Faculty of Nuclear Sciences and Physical Engineering, Prague 115 19 (Czech Republic)

2014-06-02

We generalize noncommutative gauge theory using Nambu–Poisson structures to obtain a new type of gauge theory with higher brackets and gauge fields. The approach is based on covariant coordinates and higher versions of the Seiberg–Witten map. We construct a covariant Nambu–Poisson gauge theory action, give its first order expansion in the Nambu–Poisson tensor and relate it to a Nambu–Poisson matrix model.

Nambu–Poisson gauge theory

International Nuclear Information System (INIS)

Jurčo, Branislav; Schupp, Peter; Vysoký, Jan

2014-01-01

We generalize noncommutative gauge theory using Nambu–Poisson structures to obtain a new type of gauge theory with higher brackets and gauge fields. The approach is based on covariant coordinates and higher versions of the Seiberg–Witten map. We construct a covariant Nambu–Poisson gauge theory action, give its first order expansion in the Nambu–Poisson tensor and relate it to a Nambu–Poisson matrix model.

A hierarchical Markov decision process modeling feeding and marketing decisions of growing pigs

DEFF Research Database (Denmark)

Pourmoayed, Reza; Nielsen, Lars Relund; Kristensen, Anders Ringgaard

2016-01-01

Feeding is the most important cost in the production of growing pigs and has a direct impact on the marketing decisions, growth and the final quality of the meat. In this paper, we address the sequential decision problem of when to change the feed-mix within a finisher pig pen and when to pick pigs...... for marketing. We formulate a hierarchical Markov decision process with three levels representing the decision process. The model considers decisions related to feeding and marketing and finds the optimal decision given the current state of the pen. The state of the system is based on information from on...

XMRF: an R package to fit Markov Networks to high-throughput genetics data.

Science.gov (United States)

Wan, Ying-Wooi; Allen, Genevera I; Baker, Yulia; Yang, Eunho; Ravikumar, Pradeep; Anderson, Matthew; Liu, Zhandong

2016-08-26

Technological advances in medicine have led to a rapid proliferation of high-throughput "omics" data. Tools to mine this data and discover disrupted disease networks are needed as they hold the key to understanding complicated interactions between genes, mutations and aberrations, and epi-genetic markers. We developed an R software package, XMRF, that can be used to fit Markov Networks to various types of high-throughput genomics data. Encoding the models and estimation techniques of the recently proposed exponential family Markov Random Fields (Yang et al., 2012), our software can be used to learn genetic networks from RNA-sequencing data (counts via Poisson graphical models), mutation and copy number variation data (categorical via Ising models), and methylation data (continuous via Gaussian graphical models). XMRF is the only tool that allows network structure learning using the native distribution of the data instead of the standard Gaussian. Moreover, the parallelization feature of the implemented algorithms computes the large-scale biological networks efficiently. XMRF is available from CRAN and Github ( https://github.com/zhandong/XMRF ).

Network Traffic Monitoring Using Poisson Dynamic Linear Models

Energy Technology Data Exchange (ETDEWEB)

Merl, D. M. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

2011-05-09

In this article, we discuss an approach for network forensics using a class of nonstationary Poisson processes with embedded dynamic linear models. As a modeling strategy, the Poisson DLM (PoDLM) provides a very flexible framework for specifying structured effects that may influence the evolution of the underlying Poisson rate parameter, including diurnal and weekly usage patterns. We develop a novel particle learning algorithm for online smoothing and prediction for the PoDLM, and demonstrate the suitability of the approach to real-time deployment settings via a new application to computer network traffic monitoring.

Transient Properties of Probability Distribution for a Markov Process with Size-dependent Additive Noise

Science.gov (United States)

Yamada, Yuhei; Yamazaki, Yoshihiro

2018-04-01

This study considered a stochastic model for cluster growth in a Markov process with a cluster size dependent additive noise. According to this model, the probability distribution of the cluster size transiently becomes an exponential or a log-normal distribution depending on the initial condition of the growth. In this letter, a master equation is obtained for this model, and derivation of the distributions is discussed.

Perbandingan Regresi Binomial Negatif dan Regresi Conway-Maxwell-Poisson dalam Mengatasi Overdispersi pada Regresi Poisson

Directory of Open Access Journals (Sweden)

Lusi Eka Afri

2017-03-01

Full Text Available Regresi Binomial Negatif dan regresi Conway-Maxwell-Poisson merupakan solusi untuk mengatasi overdispersi pada regresi Poisson. Kedua model tersebut merupakan perluasan dari model regresi Poisson. Menurut Hinde dan Demetrio (2007, terdapat beberapa kemungkinan terjadi overdispersi pada regresi Poisson yaitu keragaman hasil pengamatan keragaman individu sebagai komponen yang tidak dijelaskan oleh model, korelasi antar respon individu, terjadinya pengelompokan dalam populasi dan peubah teramati yang dihilangkan. Akibatnya dapat menyebabkan pendugaan galat baku yang terlalu rendah dan akan menghasilkan pendugaan parameter yang bias ke bawah (underestimate. Penelitian ini bertujuan untuk membandingan model Regresi Binomial Negatif dan model regresi Conway-Maxwell-Poisson (COM-Poisson dalam mengatasi overdispersi pada data distribusi Poisson berdasarkan statistik uji devians. Data yang digunakan dalam penelitian ini terdiri dari dua sumber data yaitu data simulasi dan data kasus terapan. Data simulasi yang digunakan diperoleh dengan membangkitkan data berdistribusi Poisson yang mengandung overdispersi dengan menggunakan bahasa pemrograman R berdasarkan karakteristik data berupa , peluang munculnya nilai nol (p serta ukuran sampel (n. Data dibangkitkan berguna untuk mendapatkan estimasi koefisien parameter pada regresi binomial negatif dan COM-Poisson.   Kata Kunci: overdispersi, regresi binomial negatif, regresi Conway-Maxwell-Poisson Negative binomial regression and Conway-Maxwell-Poisson regression could be used to overcome over dispersion on Poisson regression. Both models are the extension of Poisson regression model. According to Hinde and Demetrio (2007, there will be some over dispersion on Poisson regression: observed variance in individual variance cannot be described by a model, correlation among individual response, and the population group and the observed variables are eliminated. Consequently, this can lead to low standard error

Prescription-induced jump distributions in multiplicative Poisson processes.

Science.gov (United States)

Suweis, Samir; Porporato, Amilcare; Rinaldo, Andrea; Maritan, Amos

2011-06-01

Generalized Langevin equations (GLE) with multiplicative white Poisson noise pose the usual prescription dilemma leading to different evolution equations (master equations) for the probability distribution. Contrary to the case of multiplicative Gaussian white noise, the Stratonovich prescription does not correspond to the well-known midpoint (or any other intermediate) prescription. By introducing an inertial term in the GLE, we show that the Itô and Stratonovich prescriptions naturally arise depending on two time scales, one induced by the inertial term and the other determined by the jump event. We also show that, when the multiplicative noise is linear in the random variable, one prescription can be made equivalent to the other by a suitable transformation in the jump probability distribution. We apply these results to a recently proposed stochastic model describing the dynamics of primary soil salinization, in which the salt mass balance within the soil root zone requires the analysis of different prescriptions arising from the resulting stochastic differential equation forced by multiplicative white Poisson noise, the features of which are tailored to the characters of the daily precipitation. A method is finally suggested to infer the most appropriate prescription from the data.

Prescription-induced jump distributions in multiplicative Poisson processes

Science.gov (United States)

Suweis, Samir; Porporato, Amilcare; Rinaldo, Andrea; Maritan, Amos

2011-06-01

Generalized Langevin equations (GLE) with multiplicative white Poisson noise pose the usual prescription dilemma leading to different evolution equations (master equations) for the probability distribution. Contrary to the case of multiplicative Gaussian white noise, the Stratonovich prescription does not correspond to the well-known midpoint (or any other intermediate) prescription. By introducing an inertial term in the GLE, we show that the Itô and Stratonovich prescriptions naturally arise depending on two time scales, one induced by the inertial term and the other determined by the jump event. We also show that, when the multiplicative noise is linear in the random variable, one prescription can be made equivalent to the other by a suitable transformation in the jump probability distribution. We apply these results to a recently proposed stochastic model describing the dynamics of primary soil salinization, in which the salt mass balance within the soil root zone requires the analysis of different prescriptions arising from the resulting stochastic differential equation forced by multiplicative white Poisson noise, the features of which are tailored to the characters of the daily precipitation. A method is finally suggested to infer the most appropriate prescription from the data.

Impulsive Control for Continuous-Time Markov Decision Processes: A Linear Programming Approach

Energy Technology Data Exchange (ETDEWEB)

Dufour, F., E-mail: dufour@math.u-bordeaux1.fr [Bordeaux INP, IMB, UMR CNRS 5251 (France); Piunovskiy, A. B., E-mail: piunov@liv.ac.uk [University of Liverpool, Department of Mathematical Sciences (United Kingdom)

2016-08-15

In this paper, we investigate an optimization problem for continuous-time Markov decision processes with both impulsive and continuous controls. We consider the so-called constrained problem where the objective of the controller is to minimize a total expected discounted optimality criterion associated with a cost rate function while keeping other performance criteria of the same form, but associated with different cost rate functions, below some given bounds. Our model allows multiple impulses at the same time moment. The main objective of this work is to study the associated linear program defined on a space of measures including the occupation measures of the controlled process and to provide sufficient conditions to ensure the existence of an optimal control.

An integral equation approach to the interval reliability of systems modelled by finite semi-Markov processes

International Nuclear Information System (INIS)

Csenki, A.

1995-01-01

The interval reliability for a repairable system which alternates between working and repair periods is defined as the probability of the system being functional throughout a given time interval. In this paper, a set of integral equations is derived for this dependability measure, under the assumption that the system is modelled by an irreducible finite semi-Markov process. The result is applied to the semi-Markov model of a two-unit system with sequential preventive maintenance. The method used for the numerical solution of the resulting system of integral equations is a two-point trapezoidal rule. The system of implementation is the matrix computation package MATLAB on the Apple Macintosh SE/30. The numerical results are discussed and compared with those from simulation

Wind Farm Reliability Modelling Using Bayesian Networks and Semi-Markov Processes

Directory of Open Access Journals (Sweden)

Robert Adam Sobolewski

2015-09-01

Full Text Available Technical reliability plays an important role among factors affecting the power output of a wind farm. The reliability is determined by an internal collection grid topology and reliability of its electrical components, e.g. generators, transformers, cables, switch breakers, protective relays, and busbars. A wind farm reliability’s quantitative measure can be the probability distribution of combinations of operating and failed states of the farm’s wind turbines. The operating state of a wind turbine is its ability to generate power and to transfer it to an external power grid, which means the availability of the wind turbine and other equipment necessary for the power transfer to the external grid. This measure can be used for quantitative analysis of the impact of various wind farm topologies and the reliability of individual farm components on the farm reliability, and for determining the expected farm output power with consideration of the reliability. This knowledge may be useful in an analysis of power generation reliability in power systems. The paper presents probabilistic models that quantify the wind farm reliability taking into account the above-mentioned technical factors. To formulate the reliability models Bayesian networks and semi-Markov processes were used. Using Bayesian networks the wind farm structural reliability was mapped, as well as quantitative characteristics describing equipment reliability. To determine the characteristics semi-Markov processes were used. The paper presents an example calculation of: (i probability distribution of the combination of both operating and failed states of four wind turbines included in the wind farm, and (ii expected wind farm output power with consideration of its reliability.

Recursive smoothers for hidden discrete-time Markov chains

Directory of Open Access Journals (Sweden)

Lakhdar Aggoun

2005-01-01

Full Text Available We consider a discrete-time Markov chain observed through another Markov chain. The proposed model extends models discussed by Elliott et al. (1995. We propose improved recursive formulae to update smoothed estimates of processes related to the model. These recursive estimates are used to update the parameter of the model via the expectation maximization (EM algorithm.

Transportation and concentration inequalities for bifurcating Markov chains

DEFF Research Database (Denmark)

Penda, S. Valère Bitseki; Escobar-Bach, Mikael; Guillin, Arnaud

2017-01-01

We investigate the transportation inequality for bifurcating Markov chains which are a class of processes indexed by a regular binary tree. Fitting well models like cell growth when each individual gives birth to exactly two offsprings, we use transportation inequalities to provide useful...... concentration inequalities.We also study deviation inequalities for the empirical means under relaxed assumptions on the Wasserstein contraction for the Markov kernels. Applications to bifurcating nonlinear autoregressive processes are considered for point-wise estimates of the non-linear autoregressive...

Quantum fields and Poisson processes: Interaction of a cut-off boson field with a quantum particle

International Nuclear Information System (INIS)

Bertrand, J.; Rideau, G.; Gaveau, B.

1985-01-01

The solution of the Schroedinger equation for a boson field interacting with a quantum particle is written as an expectation on a Poisson process counting the variations of the boson-occupation numbers for each momentum. An energy cut-off is needed for the expectation to be meaningful. (orig.)

Constructing Dynamic Event Trees from Markov Models

International Nuclear Information System (INIS)

Paolo Bucci; Jason Kirschenbaum; Tunc Aldemir; Curtis Smith; Ted Wood

2006-01-01

In the probabilistic risk assessment (PRA) of process plants, Markov models can be used to model accurately the complex dynamic interactions between plant physical process variables (e.g., temperature, pressure, etc.) and the instrumentation and control system that monitors and manages the process. One limitation of this approach that has prevented its use in nuclear power plant PRAs is the difficulty of integrating the results of a Markov analysis into an existing PRA. In this paper, we explore a new approach to the generation of failure scenarios and their compilation into dynamic event trees from a Markov model of the system. These event trees can be integrated into an existing PRA using software tools such as SAPHIRE. To implement our approach, we first construct a discrete-time Markov chain modeling the system of interest by: (a) partitioning the process variable state space into magnitude intervals (cells), (b) using analytical equations or a system simulator to determine the transition probabilities between the cells through the cell-to-cell mapping technique, and, (c) using given failure/repair data for all the components of interest. The Markov transition matrix thus generated can be thought of as a process model describing the stochastic dynamic behavior of the finite-state system. We can therefore search the state space starting from a set of initial states to explore all possible paths to failure (scenarios) with associated probabilities. We can also construct event trees of arbitrary depth by tracing paths from a chosen initiating event and recording the following events while keeping track of the probabilities associated with each branch in the tree. As an example of our approach, we use the simple level control system often used as benchmark in the literature with one process variable (liquid level in a tank), and three control units: a drain unit and two supply units. Each unit includes a separate level sensor to observe the liquid level in the tank

The impulse cutoff an entropy functional measure on trajectories of Markov diffusion process integrating in information path functional

OpenAIRE

Lerner, Vladimir S.

2012-01-01

The impulses, cutting entropy functional (EF) measure on trajectories Markov diffusion process, integrate information path functional (IPF) composing discrete information Bits extracted from observing random process. Each cut brings memory of the cutting entropy, which provides both reduction of the process entropy and discrete unit of the cutting entropy a Bit. Consequently, information is memorized entropy cutting in random observations which process interactions. The origin of information ...

Almost Poisson integration of rigid body systems

International Nuclear Information System (INIS)

Austin, M.A.; Krishnaprasad, P.S.; Li-Sheng Wang

1993-01-01

In this paper we discuss the numerical integration of Lie-Poisson systems using the mid-point rule. Since such systems result from the reduction of hamiltonian systems with symmetry by lie group actions, we also present examples of reconstruction rules for the full dynamics. A primary motivation is to preserve in the integration process, various conserved quantities of the original dynamics. A main result of this paper is an O(h 3 ) error estimate for the Lie-Poisson structure, where h is the integration step-size. We note that Lie-Poisson systems appear naturally in many areas of physical science and engineering, including theoretical mechanics of fluids and plasmas, satellite dynamics, and polarization dynamics. In the present paper we consider a series of progressively complicated examples related to rigid body systems. We also consider a dissipative example associated to a Lie-Poisson system. The behavior of the mid-point rule and an associated reconstruction rule is numerically explored. 24 refs., 9 figs

Variance to mean ratio, R(t), for poisson processes on phylogenetic trees.

Science.gov (United States)

Goldman, N

1994-09-01

The ratio of expected variance to mean, R(t), of numbers of DNA base substitutions for contemporary sequences related by a "star" phylogeny is widely seen as a measure of the adherence of the sequences' evolution to a Poisson process with a molecular clock, as predicted by the "neutral theory" of molecular evolution under certain conditions. A number of estimators of R(t) have been proposed, all predicted to have mean 1 and distributions based on the chi 2. Various genes have previously been analyzed and found to have values of R(t) far in excess of 1, calling into question important aspects of the neutral theory. In this paper, I use Monte Carlo simulation to show that the previously suggested means and distributions of estimators of R(t) are highly inaccurate. The analysis is applied to star phylogenies and to general phylogenetic trees, and well-known gene sequences are reanalyzed. For star phylogenies the results show that Kimura's estimators ("The Neutral Theory of Molecular Evolution," Cambridge Univ. Press, Cambridge, 1983) are unsatisfactory for statistical testing of R(t), but confirm the accuracy of Bulmer's correction factor (Genetics 123: 615-619, 1989). For all three nonstar phylogenies studied, attained values of all three estimators of R(t), although larger than 1, are within their true confidence limits under simple Poisson process models. This shows that lineage effects can be responsible for high estimates of R(t), restoring some limited confidence in the molecular clock and showing that the distinction between lineage and molecular clock effects is vital.(ABSTRACT TRUNCATED AT 250 WORDS)

Markov Random Fields on Triangle Meshes

DEFF Research Database (Denmark)

Andersen, Vedrana; Aanæs, Henrik; Bærentzen, Jakob Andreas

2010-01-01

In this paper we propose a novel anisotropic smoothing scheme based on Markov Random Fields (MRF). Our scheme is formulated as two coupled processes. A vertex process is used to smooth the mesh by displacing the vertices according to a MRF smoothness prior, while an independent edge process label...

Modeling treatment of ischemic heart disease with partially observable Markov decision processes.

Science.gov (United States)

Hauskrecht, M; Fraser, H

1998-01-01

Diagnosis of a disease and its treatment are not separate, one-shot activities. Instead they are very often dependent and interleaved over time, mostly due to uncertainty about the underlying disease, uncertainty associated with the response of a patient to the treatment and varying cost of different diagnostic (investigative) and treatment procedures. The framework of Partially observable Markov decision processes (POMDPs) developed and used in operations research, control theory and artificial intelligence communities is particularly suitable for modeling such a complex decision process. In the paper, we show how the POMDP framework could be used to model and solve the problem of the management of patients with ischemic heart disease, and point out modeling advantages of the framework over standard decision formalisms.

Planning treatment of ischemic heart disease with partially observable Markov decision processes.

Science.gov (United States)

Hauskrecht, M; Fraser, H

2000-03-01

Diagnosis of a disease and its treatment are not separate, one-shot activities. Instead, they are very often dependent and interleaved over time. This is mostly due to uncertainty about the underlying disease, uncertainty associated with the response of a patient to the treatment and varying cost of different diagnostic (investigative) and treatment procedures. The framework of partially observable Markov decision processes (POMDPs) developed and used in the operations research, control theory and artificial intelligence communities is particularly suitable for modeling such a complex decision process. In this paper, we show how the POMDP framework can be used to model and solve the problem of the management of patients with ischemic heart disease (IHD), and demonstrate the modeling advantages of the framework over standard decision formalisms.

Markov bridges, bisection and variance reduction

DEFF Research Database (Denmark)

Asmussen, Søren; Hobolth, Asger

. In this paper we firstly consider the problem of generating sample paths from a continuous-time Markov chain conditioned on the endpoints using a new algorithm based on the idea of bisection. Secondly we study the potential of the bisection algorithm for variance reduction. In particular, examples are presented......Time-continuous Markov jump processes is a popular modelling tool in disciplines ranging from computational finance and operations research to human genetics and genomics. The data is often sampled at discrete points in time, and it can be useful to simulate sample paths between the datapoints...

Efficient rare-event simulation for multiple jump events in regularly varying random walks and compound Poisson processes

NARCIS (Netherlands)

B. Chen (Bohan); J. Blanchet; C.H. Rhee (Chang-Han); A.P. Zwart (Bert)

2017-01-01

textabstractWe propose a class of strongly efficient rare event simulation estimators for random walks and compound Poisson processes with a regularly varying increment/jump-size distribution in a general large deviations regime. Our estimator is based on an importance sampling strategy that hinges

A note on optimal (s,S) and (R,nQ) policies under a stuttering Poisson demand process

DEFF Research Database (Denmark)

Larsen, Christian

2015-01-01

In this note, a new efficient algorithm is proposed to find an optimal (s, S) replenishment policy for inventory systems with continuous reviews and where the demand follows a stuttering Poisson process (the compound element is geometrically distributed). We also derive three upper bounds...

Monte Carlo methods for the reliability analysis of Markov systems

International Nuclear Information System (INIS)

Buslik, A.J.

1985-01-01

This paper presents Monte Carlo methods for the reliability analysis of Markov systems. Markov models are useful in treating dependencies between components. The present paper shows how the adjoint Monte Carlo method for the continuous time Markov process can be derived from the method for the discrete-time Markov process by a limiting process. The straightforward extensions to the treatment of mean unavailability (over a time interval) are given. System unavailabilities can also be estimated; this is done by making the system failed states absorbing, and not permitting repair from them. A forward Monte Carlo method is presented in which the weighting functions are related to the adjoint function. In particular, if the exact adjoint function is known then weighting factors can be constructed such that the exact answer can be obtained with a single Monte Carlo trial. Of course, if the exact adjoint function is known, there is no need to perform the Monte Carlo calculation. However, the formulation is useful since it gives insight into choices of the weight factors which will reduce the variance of the estimator

Composable Markov Building Blocks

NARCIS (Netherlands)

Evers, S.; Fokkinga, M.M.; Apers, Peter M.G.; Prade, H.; Subrahmanian, V.S.

2007-01-01

In situations where disjunct parts of the same process are described by their own first-order Markov models and only one model applies at a time (activity in one model coincides with non-activity in the other models), these models can be joined together into one. Under certain conditions, nearly all

Fast and Accurate Poisson Denoising With Trainable Nonlinear Diffusion.

Science.gov (United States)

Feng, Wensen; Qiao, Peng; Chen, Yunjin; Wensen Feng; Peng Qiao; Yunjin Chen; Feng, Wensen; Chen, Yunjin; Qiao, Peng

2018-06-01

The degradation of the acquired signal by Poisson noise is a common problem for various imaging applications, such as medical imaging, night vision, and microscopy. Up to now, many state-of-the-art Poisson denoising techniques mainly concentrate on achieving utmost performance, with little consideration for the computation efficiency. Therefore, in this paper we aim to propose an efficient Poisson denoising model with both high computational efficiency and recovery quality. To this end, we exploit the newly developed trainable nonlinear reaction diffusion (TNRD) model which has proven an extremely fast image restoration approach with performance surpassing recent state-of-the-arts. However, the straightforward direct gradient descent employed in the original TNRD-based denoising task is not applicable in this paper. To solve this problem, we resort to the proximal gradient descent method. We retrain the model parameters, including the linear filters and influence functions by taking into account the Poisson noise statistics, and end up with a well-trained nonlinear diffusion model specialized for Poisson denoising. The trained model provides strongly competitive results against state-of-the-art approaches, meanwhile bearing the properties of simple structure and high efficiency. Furthermore, our proposed model comes along with an additional advantage, that the diffusion process is well-suited for parallel computation on graphics processing units (GPUs). For images of size , our GPU implementation takes less than 0.1 s to produce state-of-the-art Poisson denoising performance.

An open Markov chain scheme model for a credit consumption portfolio fed by ARIMA and SARMA processes

Science.gov (United States)

Esquível, Manuel L.; Fernandes, José Moniz; Guerreiro, Gracinda R.

2016-06-01

We introduce a schematic formalism for the time evolution of a random population entering some set of classes and such that each member of the population evolves among these classes according to a scheme based on a Markov chain model. We consider that the flow of incoming members is modeled by a time series and we detail the time series structure of the elements in each of the classes. We present a practical application to data from a credit portfolio of a Cape Verdian bank; after modeling the entering population in two different ways - namely as an ARIMA process and as a deterministic sigmoid type trend plus a SARMA process for the residues - we simulate the behavior of the population and compare the results. We get that the second method is more accurate in describing the behavior of the populations when compared to the observed values in a direct simulation of the Markov chain.

On a Poisson homogeneous space of bilinear forms with a Poisson-Lie action

Science.gov (United States)

Chekhov, L. O.; Mazzocco, M.

2017-12-01

Let \\mathscr A be the space of bilinear forms on C^N with defining matrices A endowed with a quadratic Poisson structure of reflection equation type. The paper begins with a short description of previous studies of the structure, and then this structure is extended to systems of bilinear forms whose dynamics is governed by the natural action A\\mapsto B ABT} of the {GL}_N Poisson-Lie group on \\mathscr A. A classification is given of all possible quadratic brackets on (B, A)\\in {GL}_N× \\mathscr A preserving the Poisson property of the action, thus endowing \\mathscr A with the structure of a Poisson homogeneous space. Besides the product Poisson structure on {GL}_N× \\mathscr A, there are two other (mutually dual) structures, which (unlike the product Poisson structure) admit reductions by the Dirac procedure to a space of bilinear forms with block upper triangular defining matrices. Further generalisations of this construction are considered, to triples (B,C, A)\\in {GL}_N× {GL}_N× \\mathscr A with the Poisson action A\\mapsto B ACT}, and it is shown that \\mathscr A then acquires the structure of a Poisson symmetric space. Generalisations to chains of transformations and to the quantum and quantum affine algebras are investigated, as well as the relations between constructions of Poisson symmetric spaces and the Poisson groupoid. Bibliography: 30 titles.

Confluence reduction for Markov automata

NARCIS (Netherlands)

Timmer, Mark; van de Pol, Jan Cornelis; Stoelinga, Mariëlle Ida Antoinette

Markov automata are a novel formalism for specifying systems exhibiting nondeterminism, probabilistic choices and Markovian rates. Recently, the process algebra MAPA was introduced to efficiently model such systems. As always, the state space explosion threatens the analysability of the models

Confluence Reduction for Markov Automata

NARCIS (Netherlands)

Timmer, Mark; van de Pol, Jan Cornelis; Stoelinga, Mariëlle Ida Antoinette; Braberman, Victor; Fribourg, Laurent

Markov automata are a novel formalism for specifying systems exhibiting nondeterminism, probabilistic choices and Markovian rates. Recently, the process algebra MAPA was introduced to efficiently model such systems. As always, the state space explosion threatens the analysability of the models

Homogeneous Poisson structures

International Nuclear Information System (INIS)

Shafei Deh Abad, A.; Malek, F.

1993-09-01

We provide an algebraic definition for Schouten product and give a decomposition for any homogenenous Poisson structure in any n-dimensional vector space. A large class of n-homogeneous Poisson structures in R k is also characterized. (author). 4 refs

Composable Markov Building Blocks

NARCIS (Netherlands)

Evers, S.; Fokkinga, M.M.; Apers, Peter M.G.

2007-01-01

In situations where disjunct parts of the same process are described by their own first-order Markov models, these models can be joined together under the constraint that there can only be one activity at a time, i.e. the activities of one model coincide with non-activity in the other models. Under

Understanding poisson regression.

Science.gov (United States)

Hayat, Matthew J; Higgins, Melinda

2014-04-01

Nurse investigators often collect study data in the form of counts. Traditional methods of data analysis have historically approached analysis of count data either as if the count data were continuous and normally distributed or with dichotomization of the counts into the categories of occurred or did not occur. These outdated methods for analyzing count data have been replaced with more appropriate statistical methods that make use of the Poisson probability distribution, which is useful for analyzing count data. The purpose of this article is to provide an overview of the Poisson distribution and its use in Poisson regression. Assumption violations for the standard Poisson regression model are addressed with alternative approaches, including addition of an overdispersion parameter or negative binomial regression. An illustrative example is presented with an application from the ENSPIRE study, and regression modeling of comorbidity data is included for illustrative purposes. Copyright 2014, SLACK Incorporated.

Multi-state reliability for pump group in system based on UGF and semi-Markov process

International Nuclear Information System (INIS)

Shang Yanlong; Cai Qi; Zhao Xinwen; Chen Ling

2012-01-01

In this paper, multi-state reliability value of pump group in nuclear power system is obtained by the combination method of the universal generating function (UGF) and Semi-Markov process. UGF arithmetic model of multi-state system reliability is studied, and the performance state probability expression of multi-state component is derived using semi-Markov theory. A quantificational model is defined to express the performance rate of the system and component. Different availability results by multi-state and binary state analysis method are compared under the condition whether the performance rate can satisfy the demanded value, and the mean value of system instantaneous output performance is also obtained. It shows that this combination method is an effective and feasible one which can quantify the effect of the partial failure on the system reliability, and the result of multi-state system reliability by this method deduces the modesty of the reliability value obtained by binary reliability analysis method. (authors)

Students' Progress throughout Examination Process as a Markov Chain

Science.gov (United States)

Hlavatý, Robert; Dömeová, Ludmila

2014-01-01

The paper is focused on students of Mathematical methods in economics at the Czech university of life sciences (CULS) in Prague. The idea is to create a model of students' progress throughout the whole course using the Markov chain approach. Each student has to go through various stages of the course requirements where his success depends on the…

Modifications to POISSON

International Nuclear Information System (INIS)

Harwood, L.H.

1981-01-01

At MSU we have used the POISSON family of programs extensively for magnetic field calculations. In the presently super-saturated computer situation, reducing the run time for the program is imperative. Thus, a series of modifications have been made to POISSON to speed up convergence. Two of the modifications aim at having the first guess solution as close as possible to the final solution. The other two aim at increasing the convergence rate. In this discussion, a working knowledge of POISSON is assumed. The amount of new code and expected time saving for each modification is discussed

A Markov decision model for optimising economic production lot size ...

African Journals Online (AJOL)

Adopting such a Markov decision process approach, the states of a Markov chain represent possible states of demand. The decision of whether or not to produce additional inventory units is made using dynamic programming. This approach demonstrates the existence of an optimal state-dependent EPL size, and produces ...

Periodic Poisson Solver for Particle Tracking

International Nuclear Information System (INIS)

Dohlus, M.; Henning, C.

2015-05-01

A method is described to solve the Poisson problem for a three dimensional source distribution that is periodic into one direction. Perpendicular to the direction of periodicity a free space (or open) boundary is realized. In beam physics, this approach allows to calculate the space charge field of a continualized charged particle distribution with periodic pattern. The method is based on a particle mesh approach with equidistant grid and fast convolution with a Green's function. The periodic approach uses only one period of the source distribution, but a periodic extension of the Green's function. The approach is numerically efficient and allows the investigation of periodic- and pseudo-periodic structures with period lengths that are small compared to the source dimensions, for instance of laser modulated beams or of the evolution of micro bunch structures. Applications for laser modulated beams are given.

Predictions and implications of a poisson process model to describe corrosion of transuranic waste drums

International Nuclear Information System (INIS)

Lyon, B.F.; Holmes, J.A.; Wilbert, K.A.

1995-01-01

A risk assessment methodology is described in this paper to compare risks associated with immediate or near-term retrieval of transuranic (TRU) waste drums from bermed storage versus delayed retrieval. Assuming a Poisson process adequately describes corrosion, significant breaching of drums is expected to begin at - 15 and 24 yr for pitting and general corrosion, respectively. Because of this breaching, more risk will be incurred by delayed than by immediate retrieval

Non-equal-time Poisson brackets

OpenAIRE

Nikolic, H.

1998-01-01

The standard definition of the Poisson brackets is generalized to the non-equal-time Poisson brackets. Their relationship to the equal-time Poisson brackets, as well as to the equal- and non-equal-time commutators, is discussed.

Critically Important Object Security System Element Model

Directory of Open Access Journals (Sweden)

I. V. Khomyackov

2012-03-01

Full Text Available A stochastic model of critically important object security system element has been developed. The model includes mathematical description of the security system element properties and external influences. The state evolution of the security system element is described by the semi-Markov process with finite states number, the semi-Markov matrix and the initial semi-Markov process states probabilities distribution. External influences are set with the intensity of the Poisson thread.

Branes in Poisson sigma models

International Nuclear Information System (INIS)

Falceto, Fernando

2010-01-01

In this review we discuss possible boundary conditions (branes) for the Poisson sigma model. We show how to carry out the perturbative quantization in the presence of a general pre-Poisson brane and how this is related to the deformation quantization of Poisson structures. We conclude with an open problem: the perturbative quantization of the system when the boundary has several connected components and we use a different pre-Poisson brane in every component.

On using continuoas Markov processes for unit service life evaluation taking as an example the RBMK-1000 gate-regulating valve

International Nuclear Information System (INIS)

Klemin, A.I.; Emel'yanov, V.S.; Rabchun, A.V.

1984-01-01

A technique is sugfested for estimating service life indices of equipment based on describing the process of the equipment ageing by continuous Markov diffusion process. It is noted that a number of problems on estimating durability indices of products is reduced to problems of estimating characteristics of the time of the first attainment of the preset boundary (boundaries) by a random process describing the ageing of a product. The methods of statistic estimation of the drift and diffusion coefficient in the continuous Markov diffusion process are considered formulae for their point and interval estimates are presented. A special description is given for a case of a stationary process and determining in this case mathematical expectation and dispersion of the time of the first attainment of a boundary (boundaries). The method of numerical simulation of the diffusion process with constant drift and diffusion coefficients is also described; results obtained on the basis of such a simulation are discussed. An example of using the suggested technique for quantitative estimate of the service life for the RBMK-1000 gate-regulating value is given

Extended Poisson Exponential Distribution

Directory of Open Access Journals (Sweden)

Anum Fatima

2015-09-01

Full Text Available A new mixture of Modified Exponential (ME and Poisson distribution has been introduced in this paper. Taking the Maximum of Modified Exponential random variable when the sample size follows a zero truncated Poisson distribution we have derived the new distribution, named as Extended Poisson Exponential distribution. This distribution possesses increasing and decreasing failure rates. The Poisson-Exponential, Modified Exponential and Exponential distributions are special cases of this distribution. We have also investigated some mathematical properties of the distribution along with Information entropies and Order statistics of the distribution. The estimation of parameters has been obtained using the Maximum Likelihood Estimation procedure. Finally we have illustrated a real data application of our distribution.

Exact solution for the Poisson field in a semi-infinite strip.

Science.gov (United States)

Cohen, Yossi; Rothman, Daniel H

2017-04-01

The Poisson equation is associated with many physical processes. Yet exact analytic solutions for the two-dimensional Poisson field are scarce. Here we derive an analytic solution for the Poisson equation with constant forcing in a semi-infinite strip. We provide a method that can be used to solve the field in other intricate geometries. We show that the Poisson flux reveals an inverse square-root singularity at a tip of a slit, and identify a characteristic length scale in which a small perturbation, in a form of a new slit, is screened by the field. We suggest that this length scale expresses itself as a characteristic spacing between tips in real Poisson networks that grow in response to fluxes at tips.

Estimation of Poisson noise in spatial domain

Science.gov (United States)

Švihlík, Jan; Fliegel, Karel; Vítek, Stanislav; Kukal, Jaromír.; Krbcová, Zuzana

2017-09-01

This paper deals with modeling of astronomical images in the spatial domain. We consider astronomical light images contaminated by the dark current which is modeled by Poisson random process. Dark frame image maps the thermally generated charge of the CCD sensor. In this paper, we solve the problem of an addition of two Poisson random variables. At first, the noise analysis of images obtained from the astronomical camera is performed. It allows estimating parameters of the Poisson probability mass functions in every pixel of the acquired dark frame. Then the resulting distributions of the light image can be found. If the distributions of the light image pixels are identified, then the denoising algorithm can be applied. The performance of the Bayesian approach in the spatial domain is compared with the direct approach based on the method of moments and the dark frame subtraction.

HMM filtering and parameter estimation of an electricity spot price model

International Nuclear Information System (INIS)

Erlwein, Christina; Benth, Fred Espen; Mamon, Rogemar

2010-01-01

In this paper we develop a model for electricity spot price dynamics. The spot price is assumed to follow an exponential Ornstein-Uhlenbeck (OU) process with an added compound Poisson process. In this way, the model allows for mean-reversion and possible jumps. All parameters are modulated by a hidden Markov chain in discrete time. They are able to switch between different economic regimes representing the interaction of various factors. Through the application of reference probability technique, adaptive filters are derived, which in turn, provide optimal estimates for the state of the Markov chain and related quantities of the observation process. The EM algorithm is applied to find optimal estimates of the model parameters in terms of the recursive filters. We implement this self-calibrating model on a deseasonalised series of daily spot electricity prices from the Nordic exchange Nord Pool. On the basis of one-step ahead forecasts, we found that the model is able to capture the empirical characteristics of Nord Pool spot prices. (author)

Analyzing hospitalization data: potential limitations of Poisson regression.

Science.gov (United States)

Weaver, Colin G; Ravani, Pietro; Oliver, Matthew J; Austin, Peter C; Quinn, Robert R

2015-08-01

Poisson regression is commonly used to analyze hospitalization data when outcomes are expressed as counts (e.g. number of days in hospital). However, data often violate the assumptions on which Poisson regression is based. More appropriate extensions of this model, while available, are rarely used. We compared hospitalization data between 206 patients treated with hemodialysis (HD) and 107 treated with peritoneal dialysis (PD) using Poisson regression and compared results from standard Poisson regression with those obtained using three other approaches for modeling count data: negative binomial (NB) regression, zero-inflated Poisson (ZIP) regression and zero-inflated negative binomial (ZINB) regression. We examined the appropriateness of each model and compared the results obtained with each approach. During a mean 1.9 years of follow-up, 183 of 313 patients (58%) were never hospitalized (indicating an excess of 'zeros'). The data also displayed overdispersion (variance greater than mean), violating another assumption of the Poisson model. Using four criteria, we determined that the NB and ZINB models performed best. According to these two models, patients treated with HD experienced similar hospitalization rates as those receiving PD {NB rate ratio (RR): 1.04 [bootstrapped 95% confidence interval (CI): 0.49-2.20]; ZINB summary RR: 1.21 (bootstrapped 95% CI 0.60-2.46)}. Poisson and ZIP models fit the data poorly and had much larger point estimates than the NB and ZINB models [Poisson RR: 1.93 (bootstrapped 95% CI 0.88-4.23); ZIP summary RR: 1.84 (bootstrapped 95% CI 0.88-3.84)]. We found substantially different results when modeling hospitalization data, depending on the approach used. Our results argue strongly for a sound model selection process and improved reporting around statistical methods used for modeling count data. © The Author 2015. Published by Oxford University Press on behalf of ERA-EDTA. All rights reserved.

Benchmarking of a Markov multizone model of contaminant transport.

Science.gov (United States)

Jones, Rachael M; Nicas, Mark

2014-10-01

A Markov chain model previously applied to the simulation of advection and diffusion process of gaseous contaminants is extended to three-dimensional transport of particulates in indoor environments. The model framework and assumptions are described. The performance of the Markov model is benchmarked against simple conventional models of contaminant transport. The Markov model is able to replicate elutriation predictions of particle deposition with distance from a point source, and the stirred settling of respirable particles. Comparisons with turbulent eddy diffusion models indicate that the Markov model exhibits numerical diffusion in the first seconds after release, but over time accurately predicts mean lateral dispersion. The Markov model exhibits some instability with grid length aspect when turbulence is incorporated by way of the turbulent diffusion coefficient, and advection is present. However, the magnitude of prediction error may be tolerable for some applications and can be avoided by incorporating turbulence by way of fluctuating velocity (e.g. turbulence intensity). © The Author 2014. Published by Oxford University Press on behalf of the British Occupational Hygiene Society.

Wick calculus on spaces of generalized functions of compound poisson white noise

Science.gov (United States)

Lytvynov, Eugene W.; Rebenko, Alexei L.; Shchepan'ur, Gennadi V.

1997-04-01

We derive white noise calculus for a compound Poisson process. Namely, we consider, on the Schwartz space of tempered distributions, S', a measure of compound Poisson white noise, μcp, and construct a whole scale of standard nuclear triples ( Scp) - x ⊃ L2cp) ≡ L2( S', dμcp) ⊃( Scpx, x≥ 0, which are obtained as images under some isomorphism of the corresponding triples centred at a Fock space. It turns out that the most interesting case is x = 1, when our triple coincides with the triple that is constructed by using a system of Appell polynomials in the framework of non-Gaussian biorthogonal analysis. Our special attention is paid to the Wick calculus of the Poisson field, or the quantum compound Poisson white noise process in other terms, which is the family of operators acting from ( Scp) 1 into ( Scp) 1 as multiplication by the compound Poisson white noise ω( t).

Complete synchronization of the global coupled dynamical network induced by Poisson noises.

Science.gov (United States)

Guo, Qing; Wan, Fangyi

2017-01-01

The different Poisson noise-induced complete synchronization of the global coupled dynamical network is investigated. Based on the stability theory of stochastic differential equations driven by Poisson process, we can prove that Poisson noises can induce synchronization and sufficient conditions are established to achieve complete synchronization with probability 1. Furthermore, numerical examples are provided to show the agreement between theoretical and numerical analysis.

The Logic of Adaptive Behavior - Knowledge Representation and Algorithms for the Markov Decision Process Framework in First-Order Domains

NARCIS (Netherlands)

van Otterlo, M.

2008-01-01

Learning and reasoning in large, structured, probabilistic worlds is at the heart of artificial intelligence. Markov decision processes have become the de facto standard in modeling and solving sequential decision making problems under uncertainty. Many efficient reinforcement learning and dynamic

On (co)homology of Frobenius Poisson algebras

OpenAIRE

Zhu, Can; Van Oystaeyen, Fred; ZHANG, Yinhuo

2014-01-01

In this paper, we study Poisson (co)homology of a Frobenius Poisson algebra. More precisely, we show that there exists a duality between Poisson homology and Poisson cohomology of Frobenius Poisson algebras, similar to that between Hochschild homology and Hochschild cohomology of Frobenius algebras. Then we use the non-degenerate bilinear form on a unimodular Frobenius Poisson algebra to construct a Batalin-Vilkovisky structure on the Poisson cohomology ring making it into a Batalin-Vilkovisk...

A Novel Analytical Model for Network-on-Chip using Semi-Markov Process

Directory of Open Access Journals (Sweden)

WANG, J.

2011-02-01

Full Text Available Network-on-Chip (NoC communication architecture is proposed to resolve the bottleneck of Multi-processor communication in a single chip. In this paper, a performance analytical model using Semi-Markov Process (SMP is presented to obtain the NoC performance. More precisely, given the related parameters, SMP is used to describe the behavior of each channel and the header flit routing time on each channel can be calculated by analyzing the SMP. Then, the average packet latency in NoC can be calculated. The accuracy of our model is illustrated through simulation. Indeed, the experimental results show that the proposed model can be used to obtain NoC performance and it performs better than the state-of-art models. Therefore, our model can be used as a useful tool to guide the NoC design process.

Non-stationary Markov chains

OpenAIRE

Mallak, Saed

1996-01-01

Ankara : Department of Mathematics and Institute of Engineering and Sciences of Bilkent University, 1996. Thesis (Master's) -- Bilkent University, 1996. Includes bibliographical references leaves leaf 29 In thi.s work, we studierl the Ergodicilv of Non-Stationary .Markov chains. We gave several e.xainples with different cases. We proved that given a sec[uence of Markov chains such that the limit of this sec|uence is an Ergodic Markov chain, then the limit of the combination ...

FIND: difFerential chromatin INteractions Detection using a spatial Poisson process.

Science.gov (United States)

Djekidel, Mohamed Nadhir; Chen, Yang; Zhang, Michael Q

2018-02-12

Polymer-based simulations and experimental studies indicate the existence of a spatial dependency between the adjacent DNA fibers involved in the formation of chromatin loops. However, the existing strategies for detecting differential chromatin interactions assume that the interacting segments are spatially independent from the other segments nearby. To resolve this issue, we developed a new computational method, FIND, which considers the local spatial dependency between interacting loci. FIND uses a spatial Poisson process to detect differential chromatin interactions that show a significant difference in their interaction frequency and the interaction frequency of their neighbors. Simulation and biological data analysis show that FIND outperforms the widely used count-based methods and has a better signal-to-noise ratio. © 2018 Djekidel et al.; Published by Cold Spring Harbor Laboratory Press.

Normal forms in Poisson geometry

NARCIS (Netherlands)

Marcut, I.T.

2013-01-01

The structure of Poisson manifolds is highly nontrivial even locally. The first important result in this direction is Conn's linearization theorem around fixed points. One of the main results of this thesis (Theorem 2) is a normal form theorem in Poisson geometry, which is the Poisson-geometric

Control Design for Untimed Petri Nets Using Markov Decision Processes

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Cherki Daoui

2017-01-01

Full Text Available Design of control sequences for discrete event systems (DESs has been presented modelled by untimed Petri nets (PNs. PNs are well-known mathematical and graphical models that are widely used to describe distributed DESs, including choices, synchronizations and parallelisms. The domains of application include, but are not restricted to, manufacturing systems, computer science and transportation networks. We are motivated by the observation that such systems need to plan their production or services. The paper is more particularly concerned with control issues in uncertain environments when unexpected events occur or when control errors disturb the behaviour of the system. To deal with such uncertainties, a new approach based on discrete time Markov decision processes (MDPs has been proposed that associates the modelling power of PNs with the planning power of MDPs. Finally, the simulation results illustrate the benefit of our method from the computational point of view. (original abstract

Error-Rate Bounds for Coded PPM on a Poisson Channel

Science.gov (United States)

Moision, Bruce; Hamkins, Jon

2009-01-01

Equations for computing tight bounds on error rates for coded pulse-position modulation (PPM) on a Poisson channel at high signal-to-noise ratio have been derived. These equations and elements of the underlying theory are expected to be especially useful in designing codes for PPM optical communication systems. The equations and the underlying theory apply, more specifically, to a case in which a) At the transmitter, a linear outer code is concatenated with an inner code that includes an accumulator and a bit-to-PPM-symbol mapping (see figure) [this concatenation is known in the art as "accumulate-PPM" (abbreviated "APPM")]; b) The transmitted signal propagates on a memoryless binary-input Poisson channel; and c) At the receiver, near-maximum-likelihood (ML) decoding is effected through an iterative process. Such a coding/modulation/decoding scheme is a variation on the concept of turbo codes, which have complex structures, such that an exact analytical expression for the performance of a particular code is intractable. However, techniques for accurately estimating the performances of turbo codes have been developed. The performance of a typical turbo code includes (1) a "waterfall" region consisting of a steep decrease of error rate with increasing signal-to-noise ratio (SNR) at low to moderate SNR, and (2) an "error floor" region with a less steep decrease of error rate with increasing SNR at moderate to high SNR. The techniques used heretofore for estimating performance in the waterfall region have differed from those used for estimating performance in the error-floor region. For coded PPM, prior to the present derivations, equations for accurate prediction of the performance of coded PPM at high SNR did not exist, so that it was necessary to resort to time-consuming simulations in order to make such predictions. The present derivation makes it unnecessary to perform such time-consuming simulations.

An Approach of Diagnosis Based On The Hidden Markov Chains Model

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Karim Bouamrane

2008-07-01

Full Text Available Diagnosis is a key element in industrial system maintenance process performance. A diagnosis tool is proposed allowing the maintenance operators capitalizing on the knowledge of their trade and subdividing it for better performance improvement and intervention effectiveness within the maintenance process service. The Tool is based on the Markov Chain Model and more precisely the Hidden Markov Chains (HMC which has the system failures determination advantage, taking into account the causal relations, stochastic context modeling of their dynamics and providing a relevant diagnosis help by their ability of dubious information use. Since the FMEA method is a well adapted artificial intelligence field, the modeling with Markov Chains is carried out with its assistance. Recently, a dynamic programming recursive algorithm, called 'Viterbi Algorithm', is being used in the Hidden Markov Chains field. This algorithm provides as input to the HMC a set of system observed effects and generates at exit the various causes having caused the loss from one or several system functions.

Operations and support cost modeling using Markov chains

Science.gov (United States)

Unal, Resit

1989-01-01

Systems for future missions will be selected with life cycle costs (LCC) as a primary evaluation criterion. This reflects the current realization that only systems which are considered affordable will be built in the future due to the national budget constaints. Such an environment calls for innovative cost modeling techniques which address all of the phases a space system goes through during its life cycle, namely: design and development, fabrication, operations and support; and retirement. A significant portion of the LCC for reusable systems are generated during the operations and support phase (OS). Typically, OS costs can account for 60 to 80 percent of the total LCC. Clearly, OS costs are wholly determined or at least strongly influenced by decisions made during the design and development phases of the project. As a result OS costs need to be considered and estimated early in the conceptual phase. To be effective, an OS cost estimating model needs to account for actual instead of ideal processes by associating cost elements with probabilities. One approach that may be suitable for OS cost modeling is the use of the Markov Chain Process. Markov chains are an important method of probabilistic analysis for operations research analysts but they are rarely used for life cycle cost analysis. This research effort evaluates the use of Markov Chains in LCC analysis by developing OS cost model for a hypothetical reusable space transportation vehicle (HSTV) and suggests further uses of the Markov Chain process as a design-aid tool.

Sieve estimation in a Markov illness-death process under dual censoring.

Science.gov (United States)

Boruvka, Audrey; Cook, Richard J

2016-04-01

Semiparametric methods are well established for the analysis of a progressive Markov illness-death process observed up to a noninformative right censoring time. However, often the intermediate and terminal events are censored in different ways, leading to a dual censoring scheme. In such settings, unbiased estimation of the cumulative transition intensity functions cannot be achieved without some degree of smoothing. To overcome this problem, we develop a sieve maximum likelihood approach for inference on the hazard ratio. A simulation study shows that the sieve estimator offers improved finite-sample performance over common imputation-based alternatives and is robust to some forms of dependent censoring. The proposed method is illustrated using data from cancer trials. © The Author 2015. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

Combining experimental and simulation data of molecular processes via augmented Markov models.

Science.gov (United States)

Olsson, Simon; Wu, Hao; Paul, Fabian; Clementi, Cecilia; Noé, Frank

2017-08-01

Accurate mechanistic description of structural changes in biomolecules is an increasingly important topic in structural and chemical biology. Markov models have emerged as a powerful way to approximate the molecular kinetics of large biomolecules while keeping full structural resolution in a divide-and-conquer fashion. However, the accuracy of these models is limited by that of the force fields used to generate the underlying molecular dynamics (MD) simulation data. Whereas the quality of classical MD force fields has improved significantly in recent years, remaining errors in the Boltzmann weights are still on the order of a few [Formula: see text], which may lead to significant discrepancies when comparing to experimentally measured rates or state populations. Here we take the view that simulations using a sufficiently good force-field sample conformations that are valid but have inaccurate weights, yet these weights may be made accurate by incorporating experimental data a posteriori. To do so, we propose augmented Markov models (AMMs), an approach that combines concepts from probability theory and information theory to consistently treat systematic force-field error and statistical errors in simulation and experiment. Our results demonstrate that AMMs can reconcile conflicting results for protein mechanisms obtained by different force fields and correct for a wide range of stationary and dynamical observables even when only equilibrium measurements are incorporated into the estimation process. This approach constitutes a unique avenue to combine experiment and computation into integrative models of biomolecular structure and dynamics.

A twisted generalization of Novikov-Poisson algebras

OpenAIRE

Yau, Donald

2010-01-01

Hom-Novikov-Poisson algebras, which are twisted generalizations of Novikov-Poisson algebras, are studied. Hom-Novikov-Poisson algebras are shown to be closed under tensor products and several kinds of twistings. Necessary and sufficient conditions are given under which Hom-Novikov-Poisson algebras give rise to Hom-Poisson algebras.

Poisson hierarchy of discrete strings

International Nuclear Information System (INIS)

Ioannidou, Theodora; Niemi, Antti J.

2016-01-01

The Poisson geometry of a discrete string in three dimensional Euclidean space is investigated. For this the Frenet frames are converted into a spinorial representation, the discrete spinor Frenet equation is interpreted in terms of a transfer matrix formalism, and Poisson brackets are introduced in terms of the spinor components. The construction is then generalised, in a self-similar manner, into an infinite hierarchy of Poisson algebras. As an example, the classical Virasoro (Witt) algebra that determines reparametrisation diffeomorphism along a continuous string, is identified as a particular sub-algebra, in the hierarchy of the discrete string Poisson algebra. - Highlights: • Witt (classical Virasoro) algebra is derived in the case of discrete string. • Infinite dimensional hierarchy of Poisson bracket algebras is constructed for discrete strings. • Spinor representation of discrete Frenet equations is developed.

Poisson hierarchy of discrete strings

Energy Technology Data Exchange (ETDEWEB)

Ioannidou, Theodora, E-mail: ti3@auth.gr [Faculty of Civil Engineering, School of Engineering, Aristotle University of Thessaloniki, 54249, Thessaloniki (Greece); Niemi, Antti J., E-mail: Antti.Niemi@physics.uu.se [Department of Physics and Astronomy, Uppsala University, P.O. Box 803, S-75108, Uppsala (Sweden); Laboratoire de Mathematiques et Physique Theorique CNRS UMR 6083, Fédération Denis Poisson, Université de Tours, Parc de Grandmont, F37200, Tours (France); Department of Physics, Beijing Institute of Technology, Haidian District, Beijing 100081 (China)

2016-01-28

The Poisson geometry of a discrete string in three dimensional Euclidean space is investigated. For this the Frenet frames are converted into a spinorial representation, the discrete spinor Frenet equation is interpreted in terms of a transfer matrix formalism, and Poisson brackets are introduced in terms of the spinor components. The construction is then generalised, in a self-similar manner, into an infinite hierarchy of Poisson algebras. As an example, the classical Virasoro (Witt) algebra that determines reparametrisation diffeomorphism along a continuous string, is identified as a particular sub-algebra, in the hierarchy of the discrete string Poisson algebra. - Highlights: • Witt (classical Virasoro) algebra is derived in the case of discrete string. • Infinite dimensional hierarchy of Poisson bracket algebras is constructed for discrete strings. • Spinor representation of discrete Frenet equations is developed.

Criterion of Semi-Markov Dependent Risk Model

Institute of Scientific and Technical Information of China (English)

Xiao Yun MO; Xiang Qun YANG

2014-01-01

A rigorous definition of semi-Markov dependent risk model is given. This model is a generalization of the Markov dependent risk model. A criterion and necessary conditions of semi-Markov dependent risk model are obtained. The results clarify relations between elements among semi-Markov dependent risk model more clear and are applicable for Markov dependent risk model.

A comparison between Poisson and zero-inflated Poisson regression models with an application to number of black spots in Corriedale sheep

Directory of Open Access Journals (Sweden)

Rodrigues-Motta Mariana

2008-07-01

Full Text Available Abstract Dark spots in the fleece area are often associated with dark fibres in wool, which limits its competitiveness with other textile fibres. Field data from a sheep experiment in Uruguay revealed an excess number of zeros for dark spots. We compared the performance of four Poisson and zero-inflated Poisson (ZIP models under four simulation scenarios. All models performed reasonably well under the same scenario for which the data were simulated. The deviance information criterion favoured a Poisson model with residual, while the ZIP model with a residual gave estimates closer to their true values under all simulation scenarios. Both Poisson and ZIP models with an error term at the regression level performed better than their counterparts without such an error. Field data from Corriedale sheep were analysed with Poisson and ZIP models with residuals. Parameter estimates were similar for both models. Although the posterior distribution of the sire variance was skewed due to a small number of rams in the dataset, the median of this variance suggested a scope for genetic selection. The main environmental factor was the age of the sheep at shearing. In summary, age related processes seem to drive the number of dark spots in this breed of sheep.

The second order extended Kalman filter and Markov nonlinear filter for data processing in interferometric systems

International Nuclear Information System (INIS)

Ermolaev, P; Volynsky, M

2014-01-01

Recurrent stochastic data processing algorithms using representation of interferometric signal as output of a dynamic system, which state is described by vector of parameters, in some cases are more effective, compared with conventional algorithms. Interferometric signals depend on phase nonlinearly. Consequently it is expedient to apply algorithms of nonlinear stochastic filtering, such as Kalman type filters. An application of the second order extended Kalman filter and Markov nonlinear filter that allows to minimize estimation error is described. Experimental results of signals processing are illustrated. Comparison of the algorithms is presented and discussed.

Use of Poisson spatiotemporal regression models for the Brazilian Amazon Forest: malaria count data

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Jorge Alberto Achcar

2011-12-01

Full Text Available INTRODUCTION: Malaria is a serious problem in the Brazilian Amazon region, and the detection of possible risk factors could be of great interest for public health authorities. The objective of this article was to investigate the association between environmental variables and the yearly registers of malaria in the Amazon region using Bayesian spatiotemporal methods. METHODS: We used Poisson spatiotemporal regression models to analyze the Brazilian Amazon forest malaria count for the period from 1999 to 2008. In this study, we included some covariates that could be important in the yearly prediction of malaria, such as deforestation rate. We obtained the inferences using a Bayesian approach and Markov Chain Monte Carlo (MCMC methods to simulate samples for the joint posterior distribution of interest. The discrimination of different models was also discussed. RESULTS: The model proposed here suggests that deforestation rate, the number of inhabitants per km², and the human development index (HDI are important in the prediction of malaria cases. CONCLUSIONS: It is possible to conclude that human development, population growth, deforestation, and their associated ecological alterations are conducive to increasing malaria risk. We conclude that the use of Poisson regression models that capture the spatial and temporal effects under the Bayesian paradigm is a good strategy for modeling malaria counts.

Use of Poisson spatiotemporal regression models for the Brazilian Amazon Forest: malaria count data.

Science.gov (United States)

Achcar, Jorge Alberto; Martinez, Edson Zangiacomi; Souza, Aparecida Doniseti Pires de; Tachibana, Vilma Mayumi; Flores, Edilson Ferreira

2011-01-01

Malaria is a serious problem in the Brazilian Amazon region, and the detection of possible risk factors could be of great interest for public health authorities. The objective of this article was to investigate the association between environmental variables and the yearly registers of malaria in the Amazon region using bayesian spatiotemporal methods. We used Poisson spatiotemporal regression models to analyze the Brazilian Amazon forest malaria count for the period from 1999 to 2008. In this study, we included some covariates that could be important in the yearly prediction of malaria, such as deforestation rate. We obtained the inferences using a bayesian approach and Markov Chain Monte Carlo (MCMC) methods to simulate samples for the joint posterior distribution of interest. The discrimination of different models was also discussed. The model proposed here suggests that deforestation rate, the number of inhabitants per km², and the human development index (HDI) are important in the prediction of malaria cases. It is possible to conclude that human development, population growth, deforestation, and their associated ecological alterations are conducive to increasing malaria risk. We conclude that the use of Poisson regression models that capture the spatial and temporal effects under the bayesian paradigm is a good strategy for modeling malaria counts.

Gap processing for adaptive maximal poisson-disk sampling

KAUST Repository

Yan, Dongming; Wonka, Peter

2013-01-01

In this article, we study the generation of maximal Poisson-disk sets with varying radii. First, we present a geometric analysis of gaps in such disk sets. This analysis is the basis for maximal and adaptive sampling in Euclidean space and on manifolds. Second, we propose efficient algorithms and data structures to detect gaps and update gaps when disks are inserted, deleted, moved, or when their radii are changed.We build on the concepts of regular triangulations and the power diagram. Third, we show how our analysis contributes to the state-of-the-art in surface remeshing. © 2013 ACM.

Gap processing for adaptive maximal poisson-disk sampling

KAUST Repository

Yan, Dongming

2013-10-17

In this article, we study the generation of maximal Poisson-disk sets with varying radii. First, we present a geometric analysis of gaps in such disk sets. This analysis is the basis for maximal and adaptive sampling in Euclidean space and on manifolds. Second, we propose efficient algorithms and data structures to detect gaps and update gaps when disks are inserted, deleted, moved, or when their radii are changed.We build on the concepts of regular triangulations and the power diagram. Third, we show how our analysis contributes to the state-of-the-art in surface remeshing. © 2013 ACM.

Numerical construction of the p(fold) (committor) reaction coordinate for a Markov process.

Science.gov (United States)

Krivov, Sergei V

2011-10-06

To simplify the description of a complex multidimensional dynamical process, one often projects it onto a single reaction coordinate. In protein folding studies, the folding probability p(fold) is an optimal reaction coordinate which preserves many important properties of the dynamics. The construction of the coordinate is difficult. Here, an efficient numerical approach to construct the p(fold) reaction coordinate for a Markov process (satisfying the detailed balance) is described. The coordinate is obtained by optimizing parameters of a chosen functional form to make a generalized cut-based free energy profile the highest. The approach is illustrated by constructing the p(fold) reaction coordinate for the equilibrium folding simulation of FIP35 protein reported by Shaw et al. (Science 2010, 330, 341-346). © 2011 American Chemical Society

Quantization of the Poisson SU(2) and its Poisson homogeneous space - the 2-sphere

International Nuclear Information System (INIS)

Sheu, A.J.L.

1991-01-01

We show that deformation quantizations of the Poisson structures on the Poisson Lie group SU(2) and its homogeneous space, the 2-sphere, are compatible with Woronowicz's deformation quantization of SU(2)'s group structure and Podles' deformation quantization of 2-sphere's homogeneous structure, respectively. So in a certain sense the multiplicativity of the Lie Poisson structure on SU(2) at the classical level is preserved under quantization. (orig.)

Cumulative Poisson Distribution Program

Science.gov (United States)

Bowerman, Paul N.; Scheuer, Ernest M.; Nolty, Robert

1990-01-01

Overflow and underflow in sums prevented. Cumulative Poisson Distribution Program, CUMPOIS, one of two computer programs that make calculations involving cumulative Poisson distributions. Both programs, CUMPOIS (NPO-17714) and NEWTPOIS (NPO-17715), used independently of one another. CUMPOIS determines cumulative Poisson distribution, used to evaluate cumulative distribution function (cdf) for gamma distributions with integer shape parameters and cdf for X (sup2) distributions with even degrees of freedom. Used by statisticians and others concerned with probabilities of independent events occurring over specific units of time, area, or volume. Written in C.

Tomography of images with poisson miose: pre-processing of projections

International Nuclear Information System (INIS)

Furuie, S.S.

1989-01-01

This work present an alternative approach in order to reconstruct images with low signal to noise ratio. Basically it consist of smoothing projections taking into account that the noise is Poisson. These filtered projections are used to reconstruct the original image, applying direct Fourier method. This approach is compared with convolution back projection and EM (Expectation-Maximization). (author) [pt

Dirichlet forms methods for Poisson point measures and Lévy processes with emphasis on the creation-annihilation techniques

CERN Document Server

Bouleau, Nicolas

2015-01-01

A simplified approach to Malliavin calculus adapted to Poisson random measures is developed and applied in this book. Called the “lent particle method” it is based on perturbation of the position of particles. Poisson random measures describe phenomena involving random jumps (for instance in mathematical finance) or the random distribution of particles (as in statistical physics). Thanks to the theory of Dirichlet forms, the authors develop a mathematical tool for a quite general class of random Poisson measures and significantly simplify computations of Malliavin matrices of Poisson functionals. The method gives rise to a new explicit calculus that they illustrate on various examples: it consists in adding a particle and then removing it after computing the gradient. Using this method, one can establish absolute continuity of Poisson functionals such as Lévy areas, solutions of SDEs driven by Poisson measure and, by iteration, obtain regularity of laws. The authors also give applications to error calcul...

Markov chain modelling of pitting corrosion in underground pipelines

Energy Technology Data Exchange (ETDEWEB)

Caleyo, F. [Departamento de Ingenieri' a Metalurgica, ESIQIE, IPN, UPALM Edif. 7, Zacatenco, Mexico D. F. 07738 (Mexico)], E-mail: fcaleyo@gmail.com; Velazquez, J.C. [Departamento de Ingenieri' a Metalurgica, ESIQIE, IPN, UPALM Edif. 7, Zacatenco, Mexico D. F. 07738 (Mexico); Valor, A. [Facultad de Fisica, Universidad de La Habana, San Lazaro y L, Vedado, 10400 La Habana (Cuba); Hallen, J.M. [Departamento de Ingenieri' a Metalurgica, ESIQIE, IPN, UPALM Edif. 7, Zacatenco, Mexico D. F. 07738 (Mexico)

2009-09-15

A continuous-time, non-homogenous linear growth (pure birth) Markov process has been used to model external pitting corrosion in underground pipelines. The closed form solution of Kolmogorov's forward equations for this type of Markov process is used to describe the transition probability function in a discrete pit depth space. The identification of the transition probability function can be achieved by correlating the stochastic pit depth mean with the deterministic mean obtained experimentally. Monte-Carlo simulations previously reported have been used to predict the time evolution of the mean value of the pit depth distribution for different soil textural classes. The simulated distributions have been used to create an empirical Markov chain-based stochastic model for predicting the evolution of pitting corrosion depth and rate distributions from the observed properties of the soil. The proposed model has also been applied to pitting corrosion data from pipeline repeated in-line inspections and laboratory immersion experiments.

Markov chain modelling of pitting corrosion in underground pipelines

International Nuclear Information System (INIS)

Caleyo, F.; Velazquez, J.C.; Valor, A.; Hallen, J.M.

2009-01-01

A continuous-time, non-homogenous linear growth (pure birth) Markov process has been used to model external pitting corrosion in underground pipelines. The closed form solution of Kolmogorov's forward equations for this type of Markov process is used to describe the transition probability function in a discrete pit depth space. The identification of the transition probability function can be achieved by correlating the stochastic pit depth mean with the deterministic mean obtained experimentally. Monte-Carlo simulations previously reported have been used to predict the time evolution of the mean value of the pit depth distribution for different soil textural classes. The simulated distributions have been used to create an empirical Markov chain-based stochastic model for predicting the evolution of pitting corrosion depth and rate distributions from the observed properties of the soil. The proposed model has also been applied to pitting corrosion data from pipeline repeated in-line inspections and laboratory immersion experiments.

The Marginal Distributions of a Crossing Time and Renewal Numbers Related with Two Poisson Processes are as Ph-Distributions

Directory of Open Access Journals (Sweden)

Mir G. H. Talpur

2006-01-01

Full Text Available In this paper we consider, how to find the marginal distributions of crossing time and renewal numbers related with two poisson processes by using probability arguments. The obtained results show that the one-dimension marginal distributions are N+1 order PH-distributions.

Nonlinear Poisson equation for heterogeneous media.

Science.gov (United States)

Hu, Langhua; Wei, Guo-Wei

2012-08-22

The Poisson equation is a widely accepted model for electrostatic analysis. However, the Poisson equation is derived based on electric polarizations in a linear, isotropic, and homogeneous dielectric medium. This article introduces a nonlinear Poisson equation to take into consideration of hyperpolarization effects due to intensive charges and possible nonlinear, anisotropic, and heterogeneous media. Variational principle is utilized to derive the nonlinear Poisson model from an electrostatic energy functional. To apply the proposed nonlinear Poisson equation for the solvation analysis, we also construct a nonpolar solvation energy functional based on the nonlinear Poisson equation by using the geometric measure theory. At a fixed temperature, the proposed nonlinear Poisson theory is extensively validated by the electrostatic analysis of the Kirkwood model and a set of 20 proteins, and the solvation analysis of a set of 17 small molecules whose experimental measurements are also available for a comparison. Moreover, the nonlinear Poisson equation is further applied to the solvation analysis of 21 compounds at different temperatures. Numerical results are compared to theoretical prediction, experimental measurements, and those obtained from other theoretical methods in the literature. A good agreement between our results and experimental data as well as theoretical results suggests that the proposed nonlinear Poisson model is a potentially useful model for electrostatic analysis involving hyperpolarization effects. Copyright © 2012 Biophysical Society. Published by Elsevier Inc. All rights reserved.

An Application of Graph Theory in Markov Chains Reliability Analysis

Directory of Open Access Journals (Sweden)

Pavel Skalny

2014-01-01

Full Text Available The paper presents reliability analysis which was realized for an industrial company. The aim of the paper is to present the usage of discrete time Markov chains and the flow in network approach. Discrete Markov chains a well-known method of stochastic modelling describes the issue. The method is suitable for many systems occurring in practice where we can easily distinguish various amount of states. Markov chains are used to describe transitions between the states of the process. The industrial process is described as a graph network. The maximal flow in the network corresponds to the production. The Ford-Fulkerson algorithm is used to quantify the production for each state. The combination of both methods are utilized to quantify the expected value of the amount of manufactured products for the given time period.

Master equation for She-Leveque scaling and its classification in terms of other Markov models of developed turbulence

Science.gov (United States)

Nickelsen, Daniel

2017-07-01

The statistics of velocity increments in homogeneous and isotropic turbulence exhibit universal features in the limit of infinite Reynolds numbers. After Kolmogorov’s scaling law from 1941, many turbulence models aim for capturing these universal features, some are known to have an equivalent formulation in terms of Markov processes. We derive the Markov process equivalent to the particularly successful scaling law postulated by She and Leveque. The Markov process is a jump process for velocity increments u(r) in scale r in which the jumps occur randomly but with deterministic width in u. From its master equation we establish a prescription to simulate the She-Leveque process and compare it with Kolmogorov scaling. To put the She-Leveque process into the context of other established turbulence models on the Markov level, we derive a diffusion process for u(r) using two properties of the Navier-Stokes equation. This diffusion process already includes Kolmogorov scaling, extended self-similarity and a class of random cascade models. The fluctuation theorem of this Markov process implies a ‘second law’ that puts a loose bound on the multipliers of the random cascade models. This bound explicitly allows for instances of inverse cascades, which are necessary to satisfy the fluctuation theorem. By adding a jump process to the diffusion process, we go beyond Kolmogorov scaling and formulate the most general scaling law for the class of Markov processes having both diffusion and jump parts. This Markov scaling law includes She-Leveque scaling and a scaling law derived by Yakhot.

Tornadoes and related damage costs: statistical modeling with a semi-Markov approach

OpenAIRE

Corini, Chiara; D'Amico, Guglielmo; Petroni, Filippo; Prattico, Flavio; Manca, Raimondo

2015-01-01

We propose a statistical approach to tornadoes modeling for predicting and simulating occurrences of tornadoes and accumulated cost distributions over a time interval. This is achieved by modeling the tornadoes intensity, measured with the Fujita scale, as a stochastic process. Since the Fujita scale divides tornadoes intensity into six states, it is possible to model the tornadoes intensity by using Markov and semi-Markov models. We demonstrate that the semi-Markov approach is able to reprod...

Reliability estimation of semi-Markov systems: a case study

International Nuclear Information System (INIS)

Ouhbi, Brahim; Limnios, Nikolaos

1997-01-01

In this article, we are concerned with the estimation of the reliability and the availability of a turbo-generator rotor using a set of data observed in a real engineering situation provided by Electricite De France (EDF). The rotor is modeled by a semi-Markov process, which is used to estimate the rotor's reliability and availability. To do this, we present a method for estimating the semi-Markov kernel from a censored data

Poisson's ratio of fiber-reinforced composites

Science.gov (United States)

Christiansson, Henrik; Helsing, Johan

1996-05-01

Poisson's ratio flow diagrams, that is, the Poisson's ratio versus the fiber fraction, are obtained numerically for hexagonal arrays of elastic circular fibers in an elastic matrix. High numerical accuracy is achieved through the use of an interface integral equation method. Questions concerning fixed point theorems and the validity of existing asymptotic relations are investigated and partially resolved. Our findings for the transverse effective Poisson's ratio, together with earlier results for random systems by other authors, make it possible to formulate a general statement for Poisson's ratio flow diagrams: For composites with circular fibers and where the phase Poisson's ratios are equal to 1/3, the system with the lowest stiffness ratio has the highest Poisson's ratio. For other choices of the elastic moduli for the phases, no simple statement can be made.

Applying a Markov approach as a Lean Thinking analysis of waste elimination in a Rice Production Process

Directory of Open Access Journals (Sweden)

Eldon Glen Caldwell Marin

2015-01-01

Full Text Available The Markov Chains Model was proposed to analyze stochastic events when recursive cycles occur; for example, when rework in a continuous flow production affects the overall performance. Typically, the analysis of rework and scrap is done through a wasted material cost perspective and not from the perspective of waste capacity that reduces throughput and economic value added (EVA. Also, we can not find many cases of this application in agro-industrial production in Latin America, given the complexity of the calculations and the need for robust applications. This scientific work presents the results of a quasi-experimental research approach in order to explain how to apply DOE methods and Markov analysis in a rice production process located in Central America, evaluating the global effects of a single reduction in rework and scrap in a part of the whole line. The results show that in this case it is possible to evaluate benefits from Global Throughput and EVA perspective and not only from the saving costs perspective, finding a relationship between operational indicators and corporate performance. However, it was found that it is necessary to analyze the markov chains configuration with many rework points, also it is still relevant to take into account the effects on takt time and not only scrap´s costs.

Numerical simulations of piecewise deterministic Markov processes with an application to the stochastic Hodgkin-Huxley model

Science.gov (United States)

Ding, Shaojie; Qian, Min; Qian, Hong; Zhang, Xuejuan

2016-12-01

The stochastic Hodgkin-Huxley model is one of the best-known examples of piecewise deterministic Markov processes (PDMPs), in which the electrical potential across a cell membrane, V(t), is coupled with a mesoscopic Markov jump process representing the stochastic opening and closing of ion channels embedded in the membrane. The rates of the channel kinetics, in turn, are voltage-dependent. Due to this interdependence, an accurate and efficient sampling of the time evolution of the hybrid stochastic systems has been challenging. The current exact simulation methods require solving a voltage-dependent hitting time problem for multiple path-dependent intensity functions with random thresholds. This paper proposes a simulation algorithm that approximates an alternative representation of the exact solution by fitting the log-survival function of the inter-jump dwell time, H(t), with a piecewise linear one. The latter uses interpolation points that are chosen according to the time evolution of the H(t), as the numerical solution to the coupled ordinary differential equations of V(t) and H(t). This computational method can be applied to all PDMPs. Pathwise convergence of the approximated sample trajectories to the exact solution is proven, and error estimates are provided. Comparison with a previous algorithm that is based on piecewise constant approximation is also presented.

Effects of stochastic interest rates in decision making under risk: A Markov decision process model for forest management

Science.gov (United States)

Mo Zhou; Joseph Buongiorno

2011-01-01

Most economic studies of forest decision making under risk assume a fixed interest rate. This paper investigated some implications of this stochastic nature of interest rates. Markov decision process (MDP) models, used previously to integrate stochastic stand growth and prices, can be extended to include variable interest rates as well. This method was applied to...

Modeling dyadic processes using Hidden Markov Models: A time series approach to mother-infant interactions during infant immunization.

Science.gov (United States)

Stifter, Cynthia A; Rovine, Michael

2015-01-01

The focus of the present longitudinal study, to examine mother-infant interaction during the administration of immunizations at two and six months of age, used hidden Markov modeling, a time series approach that produces latent states to describe how mothers and infants work together to bring the infant to a soothed state. Results revealed a 4-state model for the dyadic responses to a two-month inoculation whereas a 6-state model best described the dyadic process at six months. Two of the states at two months and three of the states at six months suggested a progression from high intensity crying to no crying with parents using vestibular and auditory soothing methods. The use of feeding and/or pacifying to soothe the infant characterized one two-month state and two six-month states. These data indicate that with maturation and experience, the mother-infant dyad is becoming more organized around the soothing interaction. Using hidden Markov modeling to describe individual differences, as well as normative processes, is also presented and discussed.

Markov-switching model for nonstationary runoff conditioned on El Nino information

DEFF Research Database (Denmark)

Gelati, Emiliano; Madsen, H.; Rosbjerg, Dan

2010-01-01

We define a Markov-modulated autoregressive model with exogenous input (MARX) to generate runoff scenarios using climatic information. Runoff parameterization is assumed to be conditioned on a hidden climate state following a Markov chain, where state transition probabilities are functions...... of the climatic input. MARX allows stochastic modeling of nonstationary runoff, as runoff anomalies are described by a mixture of autoregressive models with exogenous input, each one corresponding to a climate state. We apply MARX to inflow time series of the Daule Peripa reservoir (Ecuador). El Nino Southern...... Oscillation (ENSO) information is used to condition runoff parameterization. Among the investigated ENSO indexes, the NINO 1+2 sea surface temperature anomalies and the trans-Nino index perform best as predictors. In the perspective of reservoir optimization at various time scales, MARX produces realistic...

Pumped shot noise in adiabatically modulated graphene-based double-barrier structures.

Science.gov (United States)

Zhu, Rui; Lai, Maoli

2011-11-16

Quantum pumping processes are accompanied by considerable quantum noise. Based on the scattering approach, we investigated the pumped shot noise properties in adiabatically modulated graphene-based double-barrier structures. It is found that compared with the Poisson processes, the pumped shot noise is dramatically enhanced where the dc pumped current changes flow direction, which demonstrates the effect of the Klein paradox.

Pumped shot noise in adiabatically modulated graphene-based double-barrier structures

Science.gov (United States)

Zhu, Rui; Lai, Maoli

2011-11-01

Quantum pumping processes are accompanied by considerable quantum noise. Based on the scattering approach, we investigated the pumped shot noise properties in adiabatically modulated graphene-based double-barrier structures. It is found that compared with the Poisson processes, the pumped shot noise is dramatically enhanced where the dc pumped current changes flow direction, which demonstrates the effect of the Klein paradox.

Generalized Markov branching models

OpenAIRE

Li, Junping

2005-01-01

In this thesis, we first considered a modified Markov branching process incorporating both state-independent immigration and resurrection. After establishing the criteria for regularity and uniqueness, explicit expressions for the extinction probability and mean extinction time are presented. The criteria for recurrence and ergodicity are also established. In addition, an explicit expression for the equilibrium distribution is presented.\\ud \\ud We then moved on to investigate the basic proper...

Essentials of stochastic processes

CERN Document Server

Durrett, Richard

2016-01-01

Building upon the previous editions, this textbook is a first course in stochastic processes taken by undergraduate and graduate students (MS and PhD students from math, statistics, economics, computer science, engineering, and finance departments) who have had a course in probability theory. It covers Markov chains in discrete and continuous time, Poisson processes, renewal processes, martingales, and option pricing. One can only learn a subject by seeing it in action, so there are a large number of examples and more than 300 carefully chosen exercises to deepen the reader’s understanding. Drawing from teaching experience and student feedback, there are many new examples and problems with solutions that use TI-83 to eliminate the tedious details of solving linear equations by hand, and the collection of exercises is much improved, with many more biological examples. Originally included in previous editions, material too advanced for this first course in stochastic processes has been eliminated while treatm...

Application of Hidden Markov Models in Biomolecular Simulations.

Science.gov (United States)

Shukla, Saurabh; Shamsi, Zahra; Moffett, Alexander S; Selvam, Balaji; Shukla, Diwakar

2017-01-01

Hidden Markov models (HMMs) provide a framework to analyze large trajectories of biomolecular simulation datasets. HMMs decompose the conformational space of a biological molecule into finite number of states that interconvert among each other with certain rates. HMMs simplify long timescale trajectories for human comprehension, and allow comparison of simulations with experimental data. In this chapter, we provide an overview of building HMMs for analyzing bimolecular simulation datasets. We demonstrate the procedure for building a Hidden Markov model for Met-enkephalin peptide simulation dataset and compare the timescales of the process.

Detecting Faults By Use Of Hidden Markov Models

Science.gov (United States)

Smyth, Padhraic J.

1995-01-01

Frequency of false alarms reduced. Faults in complicated dynamic system (e.g., antenna-aiming system, telecommunication network, or human heart) detected automatically by method of automated, continuous monitoring. Obtains time-series data by sampling multiple sensor outputs at discrete intervals of t and processes data via algorithm determining whether system in normal or faulty state. Algorithm implements, among other things, hidden first-order temporal Markov model of states of system. Mathematical model of dynamics of system not needed. Present method is "prior" method mentioned in "Improved Hidden-Markov-Model Method of Detecting Faults" (NPO-18982).

Hierarchical Multiple Markov Chain Model for Unsupervised Texture Segmentation

Czech Academy of Sciences Publication Activity Database

Scarpa, G.; Gaetano, R.; Haindl, Michal; Zerubia, J.

2009-01-01

Roč. 18, č. 8 (2009), s. 1830-1843 ISSN 1057-7149 R&D Projects: GA ČR GA102/08/0593 EU Projects: European Commission(XE) 507752 - MUSCLE Institutional research plan: CEZ:AV0Z10750506 Keywords : Classification * texture analysis * segmentation * hierarchical image models * Markov process Subject RIV: BD - Theory of Information Impact factor: 2.848, year: 2009 http://library.utia.cas.cz/separaty/2009/RO/haindl-hierarchical multiple markov chain model for unsupervised texture segmentation.pdf

Flux through a Markov chain

International Nuclear Information System (INIS)

Floriani, Elena; Lima, Ricardo; Ourrad, Ouerdia; Spinelli, Lionel

2016-01-01

Highlights: • The flux through a Markov chain of a conserved quantity (mass) is studied. • Mass is supplied by an external source and ends in the absorbing states of the chain. • Meaningful for modeling open systems whose dynamics has a Markov property. • The analytical expression of mass distribution is given for a constant source. • The expression of mass distribution is given for periodic or random sources. - Abstract: In this paper we study the flux through a finite Markov chain of a quantity, that we will call mass, which moves through the states of the chain according to the Markov transition probabilities. Mass is supplied by an external source and accumulates in the absorbing states of the chain. We believe that studying how this conserved quantity evolves through the transient (non-absorbing) states of the chain could be useful for the modelization of open systems whose dynamics has a Markov property.

Coordination of Conditional Poisson Samples

Directory of Open Access Journals (Sweden)

Grafström Anton

2015-12-01

Full Text Available Sample coordination seeks to maximize or to minimize the overlap of two or more samples. The former is known as positive coordination, and the latter as negative coordination. Positive coordination is mainly used for estimation purposes and to reduce data collection costs. Negative coordination is mainly performed to diminish the response burden of the sampled units. Poisson sampling design with permanent random numbers provides an optimum coordination degree of two or more samples. The size of a Poisson sample is, however, random. Conditional Poisson (CP sampling is a modification of the classical Poisson sampling that produces a fixed-size πps sample. We introduce two methods to coordinate Conditional Poisson samples over time or simultaneously. The first one uses permanent random numbers and the list-sequential implementation of CP sampling. The second method uses a CP sample in the first selection and provides an approximate one in the second selection because the prescribed inclusion probabilities are not respected exactly. The methods are evaluated using the size of the expected sample overlap, and are compared with their competitors using Monte Carlo simulation. The new methods provide a good coordination degree of two samples, close to the performance of Poisson sampling with permanent random numbers.

Compound Poisson Processes and Clustered Damage of Radiation Induced DNA Double Strand Breaks

International Nuclear Information System (INIS)

Gudowska-Nowak, E.; Ritter, S.; Taucher-Scholz, G.; Kraft, G.

2000-01-01

Recent experimental data have demonstrated that DNA damage induced by densely ionizing radiation in mammalian cells is distributed along the DNA molecule in the form of clusters. The principal constituent of DNA damage are double-strand breaks (DSB) which are formed when the breaks occur in both DNA strands and are directly opposite or separated by only a few base pairs. DSBs are believed to be most important lesions produced in chromosomes by radiation; interaction between DSBs can lead to cell killing, mutation or carcinogenesis. The paper discusses a model of clustered DSB formation viewed in terms of compound Poisson process along with the predictive essay of the formalism in application to experimental data. (author)

2nd International Symposium on Semi-Markov Models : Theory and Applications

CERN Document Server

Limnios, Nikolaos

1999-01-01

This book presents a selection of papers presented to the Second Inter­ national Symposium on Semi-Markov Models: Theory and Applications held in Compiegne (France) in December 1998. This international meeting had the same aim as the first one held in Brussels in 1984 : to make, fourteen years later, the state of the art in the field of semi-Markov processes and their applications, bring together researchers in this field and also to stimulate fruitful discussions. The set of the subjects of the papers presented in Compiegne has a lot of similarities with the preceding Symposium; this shows that the main fields of semi-Markov processes are now well established particularly for basic applications in Reliability and Maintenance, Biomedicine, Queue­ ing, Control processes and production. A growing field is the one of insurance and finance but this is not really a surprising fact as the problem of pricing derivative products represents now a crucial problem in economics and finance. For example, stochastic mode...

Tornadoes and related damage costs: statistical modelling with a semi-Markov approach

Directory of Open Access Journals (Sweden)

Guglielmo D’Amico

2016-09-01

Full Text Available We propose a statistical approach to modelling for predicting and simulating occurrences of tornadoes and accumulated cost distributions over a time interval. This is achieved by modelling the tornado intensity, measured with the Fujita scale, as a stochastic process. Since the Fujita scale divides tornado intensity into six states, it is possible to model the tornado intensity by using Markov and semi-Markov models. We demonstrate that the semi-Markov approach is able to reproduce the duration effect that is detected in tornado occurrence. The superiority of the semi-Markov model as compared to the Markov chain model is also affirmed by means of a statistical test of hypothesis. As an application, we compute the expected value and the variance of the costs generated by the tornadoes over a given time interval in a given area. The paper contributes to the literature by demonstrating that semi-Markov models represent an effective tool for physical analysis of tornadoes as well as for the estimation of the economic damages to human things.

Distinguishing Hidden Markov Chains

OpenAIRE

Kiefer, Stefan; Sistla, A. Prasad

2015-01-01

Hidden Markov Chains (HMCs) are commonly used mathematical models of probabilistic systems. They are employed in various fields such as speech recognition, signal processing, and biological sequence analysis. We consider the problem of distinguishing two given HMCs based on an observation sequence that one of the HMCs generates. More precisely, given two HMCs and an observation sequence, a distinguishing algorithm is expected to identify the HMC that generates the observation sequence. Two HM...

Pemodelan Markov Switching Autoregressive

OpenAIRE

Ariyani, Fiqria Devi; Warsito, Budi; Yasin, Hasbi

2014-01-01

Transition from depreciation to appreciation of exchange rate is one of regime switching that ignored by classic time series model, such as ARIMA, ARCH, or GARCH. Therefore, economic variables are modeled by Markov Switching Autoregressive (MSAR) which consider the regime switching. MLE is not applicable to parameters estimation because regime is an unobservable variable. So that filtering and smoothing process are applied to see the regime probabilities of observation. Using this model, tran...

Modeling animal-vehicle collisions using diagonal inflated bivariate Poisson regression.

Science.gov (United States)

Lao, Yunteng; Wu, Yao-Jan; Corey, Jonathan; Wang, Yinhai

2011-01-01

Two types of animal-vehicle collision (AVC) data are commonly adopted for AVC-related risk analysis research: reported AVC data and carcass removal data. One issue with these two data sets is that they were found to have significant discrepancies by previous studies. In order to model these two types of data together and provide a better understanding of highway AVCs, this study adopts a diagonal inflated bivariate Poisson regression method, an inflated version of bivariate Poisson regression model, to fit the reported AVC and carcass removal data sets collected in Washington State during 2002-2006. The diagonal inflated bivariate Poisson model not only can model paired data with correlation, but also handle under- or over-dispersed data sets as well. Compared with three other types of models, double Poisson, bivariate Poisson, and zero-inflated double Poisson, the diagonal inflated bivariate Poisson model demonstrates its capability of fitting two data sets with remarkable overlapping portions resulting from the same stochastic process. Therefore, the diagonal inflated bivariate Poisson model provides researchers a new approach to investigating AVCs from a different perspective involving the three distribution parameters (λ(1), λ(2) and λ(3)). The modeling results show the impacts of traffic elements, geometric design and geographic characteristics on the occurrences of both reported AVC and carcass removal data. It is found that the increase of some associated factors, such as speed limit, annual average daily traffic, and shoulder width, will increase the numbers of reported AVCs and carcass removals. Conversely, the presence of some geometric factors, such as rolling and mountainous terrain, will decrease the number of reported AVCs. Published by Elsevier Ltd.

Bisimulation and Simulation Relations for Markov Chains

NARCIS (Netherlands)

Baier, Christel; Hermanns, H.; Katoen, Joost P.; Wolf, Verena; Aceto, L.; Gordon, A.

2006-01-01

Formal notions of bisimulation and simulation relation play a central role for any kind of process algebra. This short paper sketches the main concepts for bisimulation and simulation relations for probabilistic systems, modelled by discrete- or continuous-time Markov chains.

Confluence reduction for Markov automata (extended version)

NARCIS (Netherlands)

Timmer, Mark; van de Pol, Jan Cornelis; Stoelinga, Mariëlle Ida Antoinette

Markov automata are a novel formalism for specifying systems exhibiting nondeterminism, probabilistic choices and Markovian rates. Recently, the process algebra MAPA was introduced to efficiently model such systems. As always, the state space explosion threatens the analysability of the models

Markov chain of distances between parked cars

International Nuclear Information System (INIS)

Seba, Petr

2008-01-01

We describe the distribution of distances between parked cars as a solution of certain Markov processes and show that its solution is obtained with the help of a distributional fixed point equation. Under certain conditions the process is solved explicitly. The resulting probability density is compared with the actual parking data measured in the city. (fast track communication)

Conditions for the Solvability of the Linear Programming Formulation for Constrained Discounted Markov Decision Processes

Energy Technology Data Exchange (ETDEWEB)

Dufour, F., E-mail: dufour@math.u-bordeaux1.fr [Institut de Mathématiques de Bordeaux, INRIA Bordeaux Sud Ouest, Team: CQFD, and IMB (France); Prieto-Rumeau, T., E-mail: tprieto@ccia.uned.es [UNED, Department of Statistics and Operations Research (Spain)

2016-08-15

We consider a discrete-time constrained discounted Markov decision process (MDP) with Borel state and action spaces, compact action sets, and lower semi-continuous cost functions. We introduce a set of hypotheses related to a positive weight function which allow us to consider cost functions that might not be bounded below by a constant, and which imply the solvability of the linear programming formulation of the constrained MDP. In particular, we establish the existence of a constrained optimal stationary policy. Our results are illustrated with an application to a fishery management problem.

Waiting-time distributions of magnetic discontinuities: Clustering or Poisson process?

International Nuclear Information System (INIS)

Greco, A.; Matthaeus, W. H.; Servidio, S.; Dmitruk, P.

2009-01-01

Using solar wind data from the Advanced Composition Explorer spacecraft, with the support of Hall magnetohydrodynamic simulations, the waiting-time distributions of magnetic discontinuities have been analyzed. A possible phenomenon of clusterization of these discontinuities is studied in detail. We perform a local Poisson's analysis in order to establish if these intermittent events are randomly distributed or not. Possible implications about the nature of solar wind discontinuities are discussed.

Robust Dynamics and Control of a Partially Observed Markov Chain

International Nuclear Information System (INIS)

Elliott, R. J.; Malcolm, W. P.; Moore, J. P.

2007-01-01

In a seminal paper, Martin Clark (Communications Systems and Random Process Theory, Darlington, 1977, pp. 721-734, 1978) showed how the filtered dynamics giving the optimal estimate of a Markov chain observed in Gaussian noise can be expressed using an ordinary differential equation. These results offer substantial benefits in filtering and in control, often simplifying the analysis and an in some settings providing numerical benefits, see, for example Malcolm et al. (J. Appl. Math. Stoch. Anal., 2007, to appear).Clark's method uses a gauge transformation and, in effect, solves the Wonham-Zakai equation using variation of constants. In this article, we consider the optimal control of a partially observed Markov chain. This problem is discussed in Elliott et al. (Hidden Markov Models Estimation and Control, Applications of Mathematics Series, vol. 29, 1995). The innovation in our results is that the robust dynamics of Clark are used to compute forward in time dynamics for a simplified adjoint process. A stochastic minimum principle is established

Nonparametric estimation of the heterogeneity of a random medium using compound Poisson process modeling of wave multiple scattering.

Science.gov (United States)

Le Bihan, Nicolas; Margerin, Ludovic

2009-07-01

In this paper, we present a nonparametric method to estimate the heterogeneity of a random medium from the angular distribution of intensity of waves transmitted through a slab of random material. Our approach is based on the modeling of forward multiple scattering using compound Poisson processes on compact Lie groups. The estimation technique is validated through numerical simulations based on radiative transfer theory.

Non-holonomic dynamics and Poisson geometry

International Nuclear Information System (INIS)

Borisov, A V; Mamaev, I S; Tsiganov, A V

2014-01-01

This is a survey of basic facts presently known about non-linear Poisson structures in the analysis of integrable systems in non-holonomic mechanics. It is shown that by using the theory of Poisson deformations it is possible to reduce various non-holonomic systems to dynamical systems on well-understood phase spaces equipped with linear Lie-Poisson brackets. As a result, not only can different non-holonomic systems be compared, but also fairly advanced methods of Poisson geometry and topology can be used for investigating them. Bibliography: 95 titles

Robust filtering and prediction for systems with embedded finite-state Markov-Chain dynamics

International Nuclear Information System (INIS)

Pate, E.B.

1986-01-01