Construction of a Markov Chain with Given Stationary Distribution

Given a rational, finite probability vector, a Markov chain is constructed having the given vector as its stationary distribution.     

Approximate Bayesian Computation for Exponential Random Graph Models for Large Social Networks

We consider the issue of sampling from the posterior distribution of exponential random graph (ERG) models and other statistical models with intractable normalizing constants. Existing methods based on exact sampling are either infeasible or require very long computing time. We study a class of approximate Markov chain Monte Carlo (MCMC) sampling schemes that deal with this issue. We also develop a new Metropolis–Hastings kernel to sample sparse large networks from ERG models. We illustrate the proposed methods on several examples.     

Chain pooling model selection for two-level fixed effects factorial experiments

As many as three iterated statistical model deletion procedures are considered for an experiment.Population model coeff cients were chosen to simulate a saturated 2⁴experiment having an unfavorable distribution of parameter values.Using random number studies, three model selection strategies were developed, namely, (1) a strategy to be used in anticipation of large coefficients of variation (neighborhood of 65 percent), (2) strategy to be used in anticipation of small coefficients of variation (4 percent or less), and (3) a security regret strategy to be used in the absence of such prior knowledge     

Long memory stochastic volatility : A bayesian approach

We propose a simulation-based Bayesian approach to the analysis of long memory stochastic volatility models, stationary and nonstationary. The main tool used to reduce the likelihood function to a tractable form is an approximate state-space representation of the model, A data set of stock market returns is analyzed with the proposed method. The approach taken here allows a quantitative assessment of the empirical evidence in favor of the stationarity, or nonstationarity, of the instantaneous volatility of the data.     

Clear Effects in the 2 n−p Combined Design

The technique of semifolding is used to develop the 2 ^n?p designs. Based on the initial analysis, some factors may be more important than others. In other words, the results from analyzing the original experiment may suggest a specific set of effects to be de-aliased. On the other hand, some previously acquired information might be available for specific factors. In these cases, one may desire to isolate the main effects of these factors and each of their two-factor interactions in the experiments. Four rules that are presented in this article can systematically isolate effects of potential interest, which should serve well for researchers in all disciplines. The combined design, by semifolding, provides estimates of the interactions that involve specific factors so that the alias chains of the two-factor interactions can be broken.     

The analysis of some biological data

This paper considers the building of stochastic models and the related analysis of discrete data in two biological problems, The first arises from the reproduction of yeast cells, while the secondis concerned with the aggregation of nucleoli. Galton-Watson and aggregation models are constructed for the respective processes and their goodness of fit to the data tested     

Local efficiency of moment estimators in beta-binomial model

In this paper, the beta-binomial model is introduced as a Markov chain. It is shown that the correlated binomial model of Kupper and Haseman (1978) is identical to the additive binomial model of AItham(1978) and both are a first order approximation of the beta-binomial model. For small γ, the local efficiency of the moment estimators for the mean ρ and the extra-binomial variation γ is examined analytically. It is shown that, locally, the moment estimator for p is efficient up to the second order of y. Exact formulae for the relative efficiency are obtained for both the cases with γ known and unknown. Generalization to the unequal sample size case is also carried out. In particular, the gain in efficiency by using the quasi-likelihood estimator instead of the ratio estimator for p is studied when γ is known. These results are in agreement with the Monte Carlo results of Kleinman(1973) and Crowder(1985).     

Bayesian,MLE, and GMM Estimation of a Spot Rate Model

ABSTRACT

We develop Markov chain Monte Carlo algorithms for estimating the parameters of the short-term interest rate model. Using Monte Carlo experiments we compare the Bayes estimators with the maximum likelihood and generalized method of moments estimators. We estimate the model using the Japanese overnight call rate data.     

Quotas on runs of successes and failures in a multi-state markov chain

For the time-homogeneous multi-state Markov chain {X_n,n≧0} with states labeled as "0" (success) and "f"(failure), f=1,2,… the waiting time problems to be discussed arise by setting quotas on runs of success and failures. Some particular cases are considered.     

The Modeling and Seasonal Adjustment of Weekly Observations

Several important economic time series are recorded on a particular day every week. Seasonal adjustment of such series is difficult because the number of weeks varies between 52 and 53 and the position of the recording day changes from year to year. In addition certain festivals, most notably Easter, take place at different times according to the year. This article presents a solution to problems of this kind by setting up a structural time series model that allows the seasonal pattern to evolve over time and enables trend extraction and seasonal adjustment to be carried out by means of state-space filtering and smoothing algorithms. The method is illustrated with a Bank of England series on the money supply.