Identifiability and Comparison of Estimation Methods on Weibull Mixture Models

In this article, the finite mixture model of Weibull distributions is studied, the identifiability of the model with m components is proven, and the parameter estimators for the case of two components resulted by several algorithms are compared. The parameter estimators are obtained with maximum likelihood performing calculations with different algorithms: expectation-maximization (EM), Fisher scoring, backfitting, optimization of k-nearest neighbor approach, and random walk algorithm using Monte Carlo simulation. The Akaike information criterion and the log-likelihood value are used to compare models. In general, the proposed random walk algorithm shows better performance in mean square error and bias. Finally, the results are applied to electronic component lifetime data.     

Spatio-temporal Trend Analysis of Spring Arrival Data for Migratory Birds

There is increasing interest in spatio-temporal analysis of environmental and ecological responses to changes in the climate due to the recent concerns about climate change. In this work, we propose a spatio-temporal modeling framework for analyzing environmental and ecological data while accounting for spatial and temporal structure, as well as climate effects. As an example, we consider data on bird migration in the United States and analyze the spring arrival dates of Purple Martins between historical data (1905–1940) from the North American Bird Phenology Program and recent data (2001–2010) from the Purple Martin Conservation Association. The proposed approach allows researchers to compare mean arrival dates while accounting for spatial and temporal variability. Our results for Purple Martins showed statistically significant earlier spring arrivals in parts of United States over the recent years. The proposed approach provides a useful tool for statistical analysis of spatio-temporal data related to studies of climate change.     

Minimal Markov Basis for Tests of Main Effect Models for 2p-1 Fractional Factorial Designs of Resolution p

We consider conditional exact tests of factor effects in design of experiments for discrete response variables. Similarly to the analysis of contingency tables, Markov chain Monte Carlo methods can be used to perform exact tests, especially when large-sample approximations of the null distributions are poor and the enumeration of the conditional sample space is infeasible. In order to construct a connected Markov chain over the appropriate sample space, one approach is to compute a Markov basis. Theoretically, a Markov basis can be characterized as a generator of a well-specified toric ideal in a polynomial ring and is computed by computational algebraic software. However, the computation of a Markov basis sometimes becomes infeasible, even for problems of moderate sizes. In the present article, we obtain the closed-form expression of minimal Markov bases for the main effect models of 2^{p ? 1} fractional factorial designs of resolution p.     

Estimation in large cross random-effect models by data augmentation

Estimation in mixed linear models is, in general, computationally demanding, since applied problems may involve extensive data sets and large numbers of random effects. Existing computer algorithms are slow and/or require large amounts of memory. These problems are compounded in generalized linear mixed models for categorical data, since even approximate methods involve fitting of a linear mixed model within steps of an iteratively reweighted least squares algorithm. Only in models in which the random effects are hierarchically nested can the computations for fitting these models to large data sets be carried out rapidly. We describe a data augmentation approach to these computational difficulties in which we repeatedly fit an overlapping series of submodels, incorporating the missing terms in each submodel as 'offsets'. The submodels are chosen so that they have a nested random-effect structure, thus allowing maximum exploitation of the computational efficiency which is available in this case. Examples of the use of the algorithm for both metric and discrete responses are discussed, all calculations being carried out using macros within the MLwiN program.     

On convergence of the EM algorithmand the Gibbs sampler

In this article we investigate the relationship between the EM algorithm and the Gibbs sampler. We show that the approximate rate of convergence of the Gibbs sampler by Gaussian approximation is equal to that of the corresponding EM-type algorithm. This helps in implementing either of the algorithms as improvement strategies for one algorithm can be directly transported to the other. In particular, by running the EM algorithm we know approximately how many iterations are needed for convergence of the Gibbs sampler. We also obtain a result that under certain conditions, the EM algorithm used for finding the maximum likelihood estimates can be slower to converge than the corresponding Gibbs sampler for Bayesian inference. We illustrate our results in a number of realistic examples all based on the generalized linear mixed models.     

A bayesian approach to dynamic tobit models

This paper develops a posterior simulation method for a dynamic Tobit model. The major obstacle rooted in such a problem lies in high dimensional integrals, induced by dependence among censored observations, in the likelihood function. The primary contribution of this study is to develop a practical and efficient sampling scheme for the conditional posterior distributions of the censored (i.e., unobserved) data, so that the Gibbs sampler with the data augmentation algorithm is successfully applied. The substantial differences between this approach and some existing methods are highlighted. The proposed simulation method is investigated by means of a Monte Carlo study and applied to a regression model of Japanese exports of passenger cars to the U.S. subject to a non-tariff trade barrier.     

Stochastic Templates for Aquaculture Images and a Parallel Pattern Detector

A general statistical approach is presented for the identification of objects in digital images, motivated by an application in aquaculture involving underwater images of fish. Using Procrustes analysis, a point distribution model is fitted on a set of training images and used as a prior distribution for the shape of a deformable template. The likelihood of a proposed template is calculated in terms of the response from a feature detector along the boundary of the template. The posterior distribution of template variables is examined by using Markov chain Monte Carlo analysis. A key challenge in the aquaculture application is the variable nature of edges arising from the surface curvature of fish and the low contrast between the foreground and background. Conventional gradient-based edge detection proves inadequate, but a parallel pattern detector copes much better. Results are presented for a fully automated analysis of the database. The strengths and weaknesses of this approach are discussed and future developments are outlined.     

Conditional Prior Proposals in Dynamic Models

ABSTRACT. Dynamic models extend state space models to non-normal observations. This paper suggests a specific hybrid Metropolis–Hastings algorithm as a simple device for Bayesian inference via Markov chain Monte Carlo in dynamic models. Hastings proposals from the (conditional) prior distribution of the unknown, time-varying parameters are used to update the corresponding full conditional distributions. It is shown through simulated examples that the methodology has optimal performance in situations where the prior is relatively strong compared to the likelihood. Typical examples include smoothing priors for categorical data. A specific blocking strategy is proposed to ensure good mixing and convergence properties of the simulated Markov chain. It is also shown that the methodology is easily extended to robust transition models using mixtures of normals. The applicability is illustrated with an analysis of a binomial and a binary time series, known in the literature.     

A Monte Carlo simulation study on partially adaptive estimators of linear regression models

This paper presents a comprehensive comparison of well-known partially adaptive estimators (PAEs) in terms of efficiency in estimating regression parameters. The aim is to identify the best estimators of regression parameters when error terms follow from normal, Laplace, Student's t, normal mixture, lognormal and gamma distribution via the Monte Carlo simulation. In the results of the simulation, efficient PAEs are determined in the case of symmetric leptokurtic and skewed leptokurtic regression error data. Additionally, these estimators are also compared in terms of regression applications. Regarding these applications, using certain standard error estimators, it is shown that PAEs can reduce the standard error of the slope parameter estimate relative to ordinary least squares.     

Missing data techniques for multilevel data: implications of model misspecification

When modeling multilevel data, it is important to accurately represent the interdependence of observations within clusters. Ignoring data clustering may result in parameter misestimation. However, it is not well established to what degree parameter estimates are affected by model misspecification when applying missing data techniques (MDTs) to incomplete multilevel data. We compare the performance of three MDTs with incomplete hierarchical data. We consider the impact of imputation model misspecification on the quality of parameter estimates by employing multiple imputation under assumptions of a normal model (MI/NM) with two-level cross-sectional data when values are missing at random on the dependent variable at rates of 10%, 30%, and 50%. Five criteria are used to compare estimates from MI/NM to estimates from MI assuming a linear mixed model (MI/LMM) and maximum likelihood estimation to the same incomplete data sets. With 10% missing data (MD), techniques performed similarly for fixed-effects estimates, but variance components were biased with MI/NM. Effects of model misspecification worsened at higher rates of MD, with the hierarchical structure of the data markedly underrepresented by biased variance component estimates. MI/LMM and maximum likelihood provided generally accurate and unbiased parameter estimates but performance was negatively affected by increased rates of MD.