Multivariate Markov chain models have previously been proposed in for studying dependent multiple categorical data sequences. For a given multivariate Markov chain model, an important problem is to study its joint stationary distribution. In this paper, we use two techniques to present some perturbation bounds for the joint stationary distribution vector of a multivariate Markov chain with s ca...

Planning for supply water demands (drinkable and irrigation water demands) is a necessary problem. For this purpose, three subjects must be considered (optimization of water supply systems such as volume of reservoir dams, optimization of released water from reservoir and prediction of next droughts). For optimization of volume of reservoir dams, yield model is applied. Reliability of yield mod...

Graphical Markov models use graphs ei ther undirected directed or mixed to rep resent possible dependences among statis tical variables Applications of undirected graphs UDGs include models for spatial de pendence and image analysis while acyclic directed graphs ADGs which are espe cially convenient for statistical analysis arise in such elds as genetics and psychomet rics and as models for exp...

Hidden Markov models (HMMs) are a class of stochastic models that have proven to be powerful tools for the analysis of molecular sequence data. A hidden Markov model can be viewed as a black box that generates sequences of observations. The unobservable internal state of the box is stochastic and is determined by a finite state Markov chain. The observable output is stochastic with distribution...

Obtaining information about particle dispersion in a room is crucial in reducing the risk of infectious disease transmission among occupants. This study developed a Markov chain model for quickly obtaining the information on the basis of a steady-state flow field calculated by computational fluid dynamics. When solving the particle transport equations, the Markov chain model does not require it...

Bayesian networks are a popular representation of asymmetric (for example causal) relationships between random variables. Markov random fields (MRFs) are a complementary model of symmetric relationships used in computer vision, spatial modeling, and social and gene expression networks. A chain graph model under the Lauritzen-Wermuth-Frydenberg interpretation (hereafter a chain graph model) gene...

Production and prediction of land-use/land cover changes (LULCC) map are among the significant issues regarding input of many environmental and hydrological models. Among various introduced methods, similarity-weighted instance-based machine learning algorithm (SimWeight) and Markov-chain with lower complexity and proper performnce are frequently used. The main aim of this study is utilizing Si...

We present a Markov chain Monte Carlo (MCMC) method for generating Markov chains using Markov bases for conditional independence models for a fourway contingency table. We then describe a Markov basis characterized by Markov properties associated with a given conditional independence model and show how to use the Markov basis to generate random tables of a Markov chain. The estimates of exact p...

Six topologies of dynamic Bayesian Networks are evaluated for predicting the future user events: (1) Markov Chain of order 1, (2) Hidden Markov Model, (3) autoregressive Hidden Markov Model, (4) factorial Hidden Markov Model, (5) simple hierarchical Hidden Markov Model and (6) tree structured Hidden Markov Model. Goal of the investigation is to evaluate, which of these models has the best fit f...

The following chapter can be understood as one sort of brief introduction to the history and basics of the Hidden Markov Models. Hidden Markov Models (HMMs) are learnable finite stochastic automates. Nowadays, they are considered as a specific form of dynamic Bayesian networks. Dynamic Bayesian networks are based on the theory of Bayes (Bayes & Price, 1763). A Hidden Markov Model consists of tw...