Poisson-Driven Stationary Markov Models

ABSTRACT

We propose a simple yet powerful method to construct strictly stationary Markovian models with given but arbitrary invariant distributions. The idea is based on a Poisson-type transform modulating the dependence structure in the model. An appealing feature of our approach is the possibility to control the underlying transition probabilities and, therefore, incorporate them within standard estimation methods. Given the resulting representation of the transition density, a Gibbs sampler algorithm based on the slice method is proposed and implemented. In the discrete-time case, special attention is placed to the class of generalized inverse Gaussian distributions. In the continuous case, we first provide a brief treatment of the class of gamma distributions, and then extend it to cover other invariant distributions, such as the generalized extreme value class. The proposed approach and estimation algorithm are illustrated with real financial datasets. Supplementary materials for this article are available online.     

Analysis of structural equation models with exact and stochastic constraints using a bayesian approach

In this paper, multisample analyses of exactand stochastic constraints with identified structural equation models are investigated using a Bayesian approach. Asymptotic properties of the estimates are developed and a multiplier method is employed to obtain the solution. A numerical example is also included as an illustration.     

Aggregate Consumer Behavior and Household Equivalence Scales

This article presents estimates of household equivalence scales, broken down by demographic characteristics, of U.S. households. Separate estimates are given by family size, age of head, region, race, and urban versus rural residence. Commodity-specific scales are presented for five separate commodity groups—energy, food, consumer goods, capital services, and other services. The estimates are obtained from an econometric model of aggregate consumer behavior. The parameters of this model are estimated by combining aggregate time series and individual cross-section data.     

Bayesian analysis of longitudinal ordered data with flexible random effects using McMC: application to diabetic macular Edema data

In the analysis of correlated ordered data, mixed-effect models are frequently used to control the subject heterogeneity effects. A common assumption in fitting these models is the normality of random effects. In many cases, this is unrealistic, making the estimation results unreliable. This paper considers several flexible models for random effects and investigates their properties in the model fitting. We adopt a proportional odds logistic regression model and incorporate the skewed version of the normal, Student's t and slash distributions for the effects. Stochastic representations for various flexible distributions are proposed afterwards based on the mixing strategy approach. This reduces the computational burden being performed by the McMC technique. Furthermore, this paper addresses the identifiability restrictions and suggests a procedure to handle this issue. We analyze a real data set taken from an ophthalmic clinical trial. Model selection is performed by suitable Bayesian model selection criteria.     

Exact Multivariate Permutation Tests for Fixed Effects in Mixed-Models

A test for the fixed effect in mixed-models is proposed. It is based on permutation strategy and is exact. The testing approach presented is very general and the class of models covered is very broad.

Multivariate responses with different type of variables (e.g., continuous, categorical, and ranks) are usually tested with separated models and the overall test are usually reached through Bonferroni-like combinations, i.e., without taking into account the joint distribution of the test statistics. On the contrary, in this approach the joint distribution is immediately obtained and the dependence among tests is taken into account in the overall test. The methods are implemented in the R package flip, freely available on CRAN.     

Exact computation of minimum sample size for estimation of binomial parameters

It is indicated by some researchers in the literature that it might be difficult to exactly determine the minimum sample size for the estimation of a binomial parameter with prescribed margin of error and confidence level. In this paper, we investigate such a very old but also extremely important problem and demonstrate that the difficulty for obtaining the exact solution is not insurmountable. Unlike the classical approximate sample size method based on the central limit theorem, we develop a new approach for computing the minimum sample size that does not require any approximation. Moreover, our approach overcomes the conservatism of existing rigorous sample size methods derived from Bernoulli's theorem or Chernoff-Hoeffding bound.Our computational machinery consists of two essential ingredients. First, we prove that the minimum of coverage probability with respect to a binomial parameter bounded in an interval is attained at a discrete set of finite many values of the binomial parameter. This allows for reducing infinite many evaluations of coverage probability to finite many evaluations. Second, a recursive bounding technique is developed to further improve the efficiency of computation.     

A hierarchical eigenmodel for pooled covariance estimation

Summary.  Although the covariance matrices corresponding to different populations are unlikely to be exactly equal they can still exhibit a high degree of similarity. For example, some pairs of variables may be positively correlated across most groups, whereas the correlation between other pairs may be consistently negative. In such cases much of the similarity across covariance matrices can be described by similarities in their principal axes, which are the axes that are defined by the eigenvectors of the covariance matrices. Estimating the degree of across-population eigenvector heterogeneity can be helpful for a variety of estimation tasks. For example, eigenvector matrices can be pooled to form a central set of principal axes and, to the extent that the axes are similar, covariance estimates for populations having small sample sizes can be stabilized by shrinking their principal axes towards the across-population centre. To this end, the paper develops a hierarchical model and estimation procedure for pooling principal axes across several populations. The model for the across-group heterogeneity is based on a matrix-valued antipodally symmetric Bingham distribution that can flexibly describe notions of 'centre' and 'spread' for a population of orthogonal matrices.     

Bayesian and approximate bayesian solutions to simultaneous estimation of multiple dynamic processes

In this paper we motivate solutions to simultaneous estimation of multiple dynamic processes in situations where the correspondence between the set of measurements and the set of processes is uncertain and thus special modelling is required to accomodate the unclassified data. We derive the optimal Bayesian solution for non linear processes which turns out to be very computationally complicated, and then suggest a quasi Bayes approximation which removes the complication due to the uncertain measurement-process correspondence. Numerical illustrations are provided for the linear case.     

Computing some bayes estimates for the mean of a normal distribution

For sampling from a normal population with unknown mean, two families of prior densities for the mean are discussed. The corresponding posterior densities are found. A data analyst may choose a prior from these families to represent prior beliefs and then compute the corresponding Bayes estimator, using the techniques discussed.