A Bayesian nonparametric Markovian model for non-stationary time series

Stationary time series models built from parametric distributions are, in general, limited in scope due to the assumptions imposed on the residual distribution and autoregression relationship. We present a modeling approach for univariate time series data, which makes no assumptions of stationarity, and can accommodate complex dynamics and capture non-standard distributions. The model for the transition density arises from the conditional distribution implied by a Bayesian nonparametric mixture of bivariate normals. This results in a flexible autoregressive form for the conditional transition density, defining a time-homogeneous, non-stationary Markovian model for real-valued data indexed in discrete time. To obtain a computationally tractable algorithm for posterior inference, we utilize a square-root-free Cholesky decomposition of the mixture kernel covariance matrix. Results from simulated data suggest that the model is able to recover challenging transition densities and non-linear dynamic relationships. We also illustrate the model on time intervals between eruptions of the Old Faithful geyser. Extensions to accommodate higher order structure and to develop a state-space model are also discussed.     

Hierarchical Bayesian modeling of marked non-homogeneous Poisson processes with finite mixtures and inclusion of covariate information

We investigate marked non-homogeneous Poisson processes using finite mixtures of bivariate normal components to model the spatial intensity function. We employ a Bayesian hierarchical framework for estimation of the parameters in the model, and propose an approach for including covariate information in this context. The methodology is exemplified through an application involving modeling of and inference for tornado occurrences.     

The effect of parameter estimation on the performance of one-sided Shewhart control charts for zero-inflated processes

ABSTRACT

Zero-inflated probability models are used to model count data that have an excessive number of zeros. Shewhart-type control charts have been proposed for the monitoring of zero-inflated processes. Usually their performance is evaluated under the assumption of known process parameters. However, in practice, their values are rarely known and they have to be estimated from an in-control historical Phase I sample. In the present paper, we investigate the performance of Shewhart-type control charts for zero-inflated processes with estimated parameters and propose practical guidelines for the statistical design of the examined charts, when the size of the preliminary sample is predetermined.     

Discriminating membrane proteins using the joint distribution of length sums of success and failure runs

Discriminating integral membrane proteins from water-soluble ones, has been over the past decades an important goal for computational molecular biology. A major drawback of methods appeared in the literature, is that most of the authors tried to solve the problem using machine learning techniques. Specifically, most of the proposed methods require an appropriate dataset for training, and consequently the results depend heavily on the suitability of the dataset, itself. Motivated by these facts, in this paper we develop a formal discrimination procedure that is based on appropriate theoretical observations on the sequence of hydrophobic and polar residues along the protein sequence and on the exact distribution of a two dimensional runs-related statistic defined on the same sequence. Specifically, for setting up our discrimination procedure, we study thoroughly the exact distribution of a bivariate random variable, which accumulates the exact lengths of both success and failure runs of at least a specific length in a sequence of Bernoulli trials. To investigate the properties of this bivariate random variable, we use the Markov chain embedding technique. Finally, we apply the new procedure to a well-defined dataset of proteins.     

Modelling stochastic order in the analysis of receiver operating characteristic data: Bayesian non-parametric approaches

Summary.  The evaluation of the performance of a continuous diagnostic measure is a commonly encountered task in medical research. We develop Bayesian non-parametric models that use Dirichlet process mixtures and mixtures of Polya trees for the analysis of continuous serologic data. The modelling approach differs from traditional approaches to the analysis of receiver operating characteristic curve data in that it incorporates a stochastic ordering constraint for the distributions of serologic values for the infected and non-infected populations. Biologically such a constraint is virtually always feasible because serologic values from infected individuals tend to be higher than those for non-infected individuals. The models proposed provide data-driven inferences for the infected and non-infected population distributions, and for the receiver operating characteristic curve and corresponding area under the curve. We illustrate and compare the predictive performance of the Dirichlet process mixture and mixture of Polya trees approaches by using serologic data for Johne's disease in dairy cattle.     

Multiple phase neighborhood Search—GRASP based on Lagrangean relaxation, random backtracking Lin–Kernighan and path relinking for the TSP

In this paper, a new modified version of Greedy Randomized Adaptive Search Procedure (GRASP), called Multiple Phase Neighborhood Search—GRASP (MPNS-GRASP), is proposed for the solution of the Traveling Salesman Problem. In this method, some procedures have been included to the classical GRASP algorithm in order to improve its performance and to cope with the major disadvantage of GRASP which is that it does not have a stopping criterion that will prevent the algorithm from spending time in iterations that give minor, if any, improvement in the solution. Thus, in MPNS-GRASP a stopping criterion based on Lagrangean Relaxation and Subgradient Optimization is proposed. Also, a different way for expanding the neighborhood search is used based on a new strategy, the Circle Restricted Local Search Moves strategy. A new variant of the Lin-Kernighan algorithm, called Random Backtracking Lin-Kernighan that helps the algorithm to diversify the search in non-promising regions of the search space is used in the Expanding Neighborhood Search phase of the algorithm. Finally, a Path Relinking Strategy is used in order to explore trajectories between elite solutions. The proposed algorithm is tested on numerous benchmark problems from TSPLIB with very satisfactory results.     

Discussion of paper “nonparametric Bayesian inference in applications” by Peter Müller,Fernando A. Quintana and Garritt L. Page

This is an invited discussion of review paper “Nonparametric Bayesian Inference in Applications” by Peter Müller, Fernando A. Quintana and Garritt L. Page.     

Bayesian Procrustes analysis with applications to hydrology

In this paper, we introduce Procrustes analysis in a Bayesian framework, by treating the classic Procrustes regression equation from a Bayesian perspective, while modeling shapes in two dimensions. The Bayesian approach allows us to compute point estimates and credible sets for the full Procrustes fit parameters. The methods are illustrated through an application to radar data from short-term weather forecasts (nowcasts), a very important problem in hydrology and meteorology.     

A Unified Approach to Prior and Loss Robustness

ABSTRACT

We introduce a new statistical framework in order to study Bayesian loss robustness under classes of priors distributions, thus unifying both concepts of robustness. We propose measures that capture variation with respect to both prior selection and selection of loss function and explore general properties of these measures. We illustrate the approach for the continuous exponential family. Robustness in this context is studied first with respect to prior selection where we consider several classes of priors for the parameter of interest, including unimodal and symmetric and unimodal with positive support. After prior variation has been measured we investigate robustness to loss function, using Hellinger and Linex (Linear Exponential) classes of loss functions. The methods are applied to standard examples.     

Testing the Fit of Gamma Distributions Using the Empirical Moment Generating Function

ABSTRACT

This article presents goodness-of-fit tests for two and three-parameter gamma distributions that are based on minimum quadratic forms of standardized logarithmic differences of values of the moment generating function and its empirical counterpart. The test statistics can be computed without reliance to special functions and have asymptotic chi-squared distributions. Monte Carlo simulations are used to compare the proposed test for the two-parameter gamma distribution with goodness-of-fit tests employing empirical distribution function or spacing statistics. Two data sets are used to illustrate the various tests.