Markov basis for statistical model of contingency tables gives a useful tool for performing the conditional test of the model via Markov chain Monte Carlo method. In this paper we derive explicit forms of Markov bases for change point models and block diagonal effect models, which are typical block-wise effect models of two-way contingency tables, and perform conditional tests with some real da...

The Bayesian approach to hierarchical linear models has many advantages when compared with likelihood-based methods. Initially, the clear advantage has been with robust inference in small sample settings. But more recent approaches to Bayesian computations, based on Markov Chain Monte Carlo (MCMC) simulation, have vastly improved the viability of Bayesian models in practice. Many of the newer a...

The paper presents a quick and simpli ed aggregation method for a large class of Markov chain functionals based on the concept of stochastic complementation. Aggregation results in a reduction in the number of Markov states by grouping them into a smaller number of aggregated states, thereby producing a considerable saving on computational complexity associated with maximum likelihood parameter...

The paper examines the application of semi-Markov models to the phenomenon of earthquakes in Tehran province. Generally, earthquakes are not independent of each other, and time and place of earthquakes are related to previous earthquakes; moreover, the time between earthquakes affects the pattern of their occurrence; thus, this occurrence can be likened to semi-Markov models. ...

Bayesian statistics is becoming an important statistical tool for practitioners to deal with analysis of complex data and complicated statistical models. The impact of Bayesian analysis in combination with Markov Chain Monte Carlo (MCMC) technology is realized optimally in the domain of applications. The ecological data could be a storehouse of natural history and experimental data is used to a...

In this paper, we introduce a Bayesian analysis for non-homogeneous Poisson process in software reliability models. Posterior summaries of interest are obtained using Markov chain Monte Carlo methods. We compare the results obtained from using conjugate and reference priors. Model selection based on the prequential conditional predictive ordinates is developed.

In this paper, we obtain the Rényi entropy rate for irreducible-aperiodic Markov chains with countable state space, using the theory of countable nonnegative matrices. We also obtain the bound for the rate of Rényi entropy of an irreducible Markov chain. Finally, we show that the bound for the Rényi entropy rate is the Shannon entropy rate.

Markov chains are fundamental tools used throughout the sciences and engineering; the design and analysis of Markov Chains has been a focus of theoretical computer science for the last 20 years. A Markov Chain takes a random walk in a large state space Ω, converging to a target stationary distribution π over Ω. The number of steps needed for the random walk to have distribution close to π is th...

This paper presents the analysis of a renewal input  finite buffer queue wherein the customers can decide either to  join the queue with a probability or balk. The service process is Markovian service process ($MSP$) governed  by an underlying $m$-state Markov chain. Employing the supplementary  variable and imbedded Markov chain techniques,   the steady-state system length distributions at pre...

A Bayesian uncertainty analysis of 12 parameters of the Bern2.5D climate model is presented. This includes an extensive sensitivity study with respect to the major statistical assumptions. Special attention is given to the parameter representing climate sensitivity. Using the framework of robust Bayesian analysis, the authors first define a nonparametric set of prior distributions for climate s...