Bayesian Estimation of the Regression Model with Autocorrelated Errors Under Contamination

In this article, the Bayesian analysis of the regression model with errors terms generated by a first-order autoregressive model is considered. Our aim is to study the effect of two kinds of contamination of this model via the posterior distribution of the regression parameter.     

Assessment of Catastrophic Risk Using Bayesian Network Constructed from Domain Knowledge and Spatial Data

Prediction of natural disasters and their consequences is difficult due to the uncertainties and complexity of multiple related factors. This article explores the use of domain knowledge and spatial data to construct a Bayesian network (BN) that facilitates the integration of multiple factors and quantification of uncertainties within a consistent system for assessment of catastrophic risk. A BN is chosen due to its advantages such as merging multiple source data and domain knowledge in a consistent system, learning from the data set, inference with missing data, and support of decision making. A key advantage of our methodology is the combination of domain knowledge and learning from the data to construct a robust network. To improve the assessment, we employ spatial data analysis and data mining to extend the training data set, select risk factors, and fine‐tune the network. Another major advantage of our methodology is the integration of an optimal discretizer, informative feature selector, learners, search strategies for local topologies, and Bayesian model averaging. These techniques all contribute to a robust prediction of risk probability of natural disasters. In the flood disaster's study, our methodology achieved a better probability of detection of high risk, a better precision, and a better ROC area compared with other methods, using both cross‐validation and prediction of catastrophic risk based on historic data. Our results suggest that BN is a good alternative for risk assessment and as a decision tool in the management of catastrophic risk.     

Bayesian autoregressive spectral analysis

The article describes an operational Bayesian approach to making inferences for the spectral density function for univariate autoregressive processes and for the AR operator of multivariate autoregressive processes. The derivation of the approach is described. Numerical examples, including the Wolfer Sunspot numbers, are used to demonstrate the practical usefulness of the approach.     

Bayesian discrete latent spatial modeling of crack initiation in orthopaedic hip replacement bone cement

In this paper, we propose a spatial model for the initiation of cracks in the bone cement of hip replacement specimens. The failure of hip replacements can be attributed mainly to damage accumulation, consisting of crack initiation and growth, occurring in the cement mantle that interlocks the hip prosthesis and the femur bone. Since crack initiation is an important factor in determining the lifetime of a replacement, the understanding of the reasons for crack initiation is vital in attempting to prolong the life of the hip replacement. The data consist of crack location coordinates from five laboratory experimental models, together with stress measurements. It is known that stress plays a major role in the initiation of cracks, and it is also known that other unmeasurable factors such as air bubbles (pores) in the cement mantle are also influential. We propose an identity-link spatial Poisson regression model for the counts of cracks in discrete regions of the cement, incorporating both the measured (stress), and through a latent process, any unmeasured factors (possibly pores) that may be influential. All analysis is carried out in a Bayesian framework, allowing for the inclusion of prior information obtained from engineers, and parameter estimation for the model is done via Markov chain Monte Carlo techniques.     

Efficiency determinants in retail stores: a Bayesian framework

This paper analyzes the impact of vertical integration, age, geographic expansion, and low price strategy on the cost efficiency of retail stores. We test our hypotheses using the innovative Bayesian frontier methodology. The data involve a sample of Spanish retail stores that operate in a highly competitive and dynamic environment. From the results, it is clear that cost efficiency is higher for stores that have: longer years in business, stronger geographical presence, and lower price offerings. Vertical integration, on the other hand, is negatively related to efficiency. Further discussions of these findings and related managerial implications are provided in the paper.     

Geometric sample size determination in Bayesian analysis

The problem of sample size determination in the context of Bayesian analysis is considered. For the familiar and practically important parameter of a geometric distribution with a beta prior, three different Bayesian approaches based on the highest posterior density intervals are discussed. A computer program handles all computational complexities and is available upon request.     

A Bayesian model for estimating the malaria transition probabilities considering individuals lost to follow-up

It is known that patients may cease participating in a longitudinal study and become lost to follow-up. The objective of this article is to present a Bayesian model to estimate the malaria transition probabilities considering individuals lost to follow-up. We consider a homogeneous population, and it is assumed that the considered period of time is small enough to avoid two or more transitions from one state of health to another. The proposed model is based on a Gibbs sampling algorithm that uses information of lost to follow-up at the end of the longitudinal study. To simulate the unknown number of individuals with positive and negative states of malaria at the end of the study and lost to follow-up, two latent variables were introduced in the model. We used a real data set and a simulated data to illustrate the application of the methodology. The proposed model showed a good fit to these data sets, and the algorithm did not show problems of convergence or lack of identifiability. We conclude that the proposed model is a good alternative to estimate probabilities of transitions from one state of health to the other in studies with low adherence to follow-up.     

Limited information bayesian analysis of a structural coefficient in a simultaneous equations system

An analytical expression is obtained for the marginal posterior density for a structural coefficient in a simultaneous equations system based on a limited information Bayesian analysis. A con- ditional posterior density is obtained given reduced form para- meters. This conditional posterior density is in univariate student t form. Numerical examples suggest that the conditional density hasa tighter distribution around the posterior mean than the unconditional density when the correlation between the endo- genous variables and the structural error term is high.     

Data-driven tests of uniformity on product manifolds

Data-driven versions of Sobolev tests of uniformity on compact Riemannian manifolds are reviewed and their large-sample asymptotic properties are given. A variant which is suitable for product manifolds is introduced. Data-driven goodness-of-fit tests of multivariate distributions are derived from data-driven tests of uniformity on tori.