Bayesian analysis of the error correction model

This paper presents a method for estimating the posterior probability density of the cointegrating rank of a multivariate error correction model. A second contribution is the careful elicitation of the prior for the cointegrating vectors derived from a prior on the cointegrating space. This prior obtains naturally from treating the cointegrating space as the parameter of interest in inference and overcomes problems previously encountered in Bayesian cointegration analysis. Using this new prior and Laplace approximation, an estimator for the posterior probability of the rank is given. The approach performs well compared with information criteria in Monte Carlo experiments. (C) 2003 Elsevier B.V. All rights reserved.

A Comparison of Bayesian and Sampling Theory Inferences in a Probit Model

HE PROBIT MODEL IS A POPULAR DEVICE for explaining binary choice decisions in econometrics. It has been used to describe choices such as labor force participation, travel mode, home ownership, and type of education. These and many more examples can be found in papers by Amemiya (1981) and Maddala (1983). Given the contribution of economics towards explaining such choices, and given the nature of data that are collected, prior information on the relationship between a choice probability and several explanatory variables frequently exists. Bayesian inference is a convenient vehicle for including such prior information. Given the increasing popularity of Bayesian inference it is useful to ask whether inferences from a probit model are sensitive to a choice between Bayesian and sampling theory techniques. Of interest is the sensitivity of inference on coefficients, probabilities, and elasticities. We consider these issues in a model designed to explain choice between fixed and variable interest rate mortgages. Two Bayesian priors are employed: a uniform prior on the coefficients, designed to be noninformative for the coefficients, and an inequality restricted prior on the signs of the coefficients. We often know, a priori, whether increasing the value of a particular explanatory variable will have a positive or negative effect on a choice probability. This knowledge can be captured by using a prior probability density function (pdf) that is truncated to be positive or negative. Thus, three sets of results are compared:those from maximum likelihood (ML) estimation, those from Bayesian estimation with an unrestricted uniform prior on the coefficients, and those from Bayesian estimation with a uniform prior truncated to accommodate inequality restrictions on the coefficients.

Bayesian feedback versus Markovian feedback in a two-level atom

We compare two different approaches to the control of the dynamics of a continuously monitored open quantum system. The first is Markovian feedback, as introduced in quantum optics by Wiseman and Milburn [Phys. Rev. Lett. 70, 548 (1993)]. The second is feedback based on an estimate of the system state, developed recently by Doherty and Jacobs [Phys. Rev. A 60, 2700 (1999)]. Here we choose to call it, for brevity, Bayesian feedback. For systems with nonlinear dynamics, we expect these two methods of feedback control to give markedly different results. The simplest possible nonlinear system is a driven and damped two-level atom, so we choose this as our model system. The monitoring is taken to be homodyne detection of the atomic fluorescence, and the control is by modulating the driving. The aim of the feedback in both cases is to stabilize the internal state of the atom as close as possible to an arbitrarily chosen pure state, in the presence of inefficient detection and other forms of decoherence. Our results (obtained without recourse to stochastic simulations) prove that Bayesian feedback is never inferior, and is usually superior, to Markovian feedback. However, it would be far more difficult to implement than Markovian feedback and it loses its superiority when obvious simplifying approximations are made. It is thus not clear which form of feedback would be better in the face of inevitable experimental imperfections.

Fitting genetic models to twin data with binary and ordered categorical responses: A comparison of structural equation modelling and Bayesian hierarchical models

We compare Bayesian methodology utilizing free-ware BUGS (Bayesian Inference Using Gibbs Sampling) with the traditional structural equation modelling approach based on another free-ware package, Mx. Dichotomous and ordinal (three category) twin data were simulated according to different additive genetic and common environment models for phenotypic variation. Practical issues are discussed in using Gibbs sampling as implemented by BUGS to fit subject-specific Bayesian generalized linear models, where the components of variation may be estimated directly. The simulation study (based on 2000 twin pairs) indicated that there is a consistent advantage in using the Bayesian method to detect a correct model under certain specifications of additive genetics and common environmental effects. For binary data, both methods had difficulty in detecting the correct model when the additive genetic effect was low (between 10 and 20%) or of moderate range (between 20 and 40%). Furthermore, neither method could adequately detect a correct model that included a modest common environmental effect (20%) even when the additive genetic effect was large (50%). Power was significantly improved with ordinal data for most scenarios, except for the case of low heritability under a true ACE model. We illustrate and compare both methods using data from 1239 twin pairs over the age of 50 years, who were registered with the Australian National Health and Medical Research Council Twin Registry (ATR) and presented symptoms associated with osteoarthritis occurring in joints of the hand.

Are Ichthyosporea animals or fungi? Bayesian phylogenetic analysis of elongation factor 1α of Ichthyophonus irregularis

Ichthyosporea is a recently recognized group of morphologically simple eukaryotes, many of which cause disease in aquatic organisms. Ribosomal RNA sequence analyses place Ichthyosporea near the divergence of the animal and fungal lineages, but do not allow resolution of its exact phylogenetic position. Some of the best evidence for a specific grouping of animals and fungi (Opisthokonta) has come from elongation factor 1alpha, not only phylogenetic analysis of sequences but also the presence or absence of short insertions and deletions. We sequenced the EF-1alpha gene from the ichthyosporean parasite Ichthyophonus irregularis and determined its phylogenetic position using neighbor-joining, parsimony and Bayesian methods. We also sequenced EF-1alpha genes from four chytrids to provide broader representation within fungi. Sequence analyses and the presence of a characteristic 12 amino acid insertion strongly indicate that I. irregularis is a member of Opisthokonta, but do not resolve whether I. irregularis is a specific relative of animals or of fungi. However, the EF-1alpha of I. irregularis exhibits a two amino acid deletion heretofore reported only among fungi. (C) 2003 Elsevier Science (USA). All rights reserved.

Bayesian inferences on the recent island colonization history by the bird Zosterops lateralis lateralis

The founding of new populations by small numbers of colonists has been considered a potentially important mechanism promoting evolutionary change in island populations. Colonizing species, such as members of the avian species complex Zosterops lateralis, have been used to support this idea. A large amount of background information on recent colonization history is available for one Zosterops subspecies, Z. lateralis lateralis, providing the opportunity to reconstruct the population dynamics of its colonization sequence. We used a Bayesian approach to combine historical and demographic information available on Z. l. lateralis with genotypic data from six microsatellite loci, and a rejection algorithm to make simultaneous inferences on the demographic parameters describing the recent colonization history of this subspecies in four southwest Pacific islands. Demographic models assuming mutation–drift equilibrium or a large number of founders were better supported than models assuming founder events for three of four recently colonized island populations. Posterior distributions of demographic parameters supported (i) a large stable effective population size of several thousands individuals with point estimates around 4000–5000; (ii) a founder event of very low intensity with a large effective number of founders around 150–200 individuals for each island in three of four islands, suggesting the colonization of those islands by one flock of large size or several flocks of average size; and (iii) a founder event of higher intensity on Norfolk Island with an effective number of founders around 20 individuals, suggesting colonization by a single flock of moderate size. Our inferences on demographic parameters, especially those on the number of founders, were relatively insensitive to the precise choice of prior distributions for microsatellite mutation processes and demographic parameters, suggesting that our analysis provides a robust description of the recent colonization history of the subspecies.

Analysis of Melanoma Onset: Assessing Familial Aggregation by Using Estimating Equations and Fitting Variance Components via Bayesian Random Effects Models

We investigate whether relative contributions of genetic and shared environmental factors are associated with an increased risk in melanoma. Data from the Queensland Familial Melanoma Project comprising 15,907 subjects arising from 1912 families were analyzed to estimate the additive genetic, common and unique environmental contributions to variation in the age at onset of melanoma. Two complementary approaches for analyzing correlated time-to-onset family data were considered: the generalized estimating equations (GEE) method in which one can estimate relationship-specific dependence simultaneously with regression coefficients that describe the average population response to changing covariates; and a subject-specific Bayesian mixed model in which heterogeneity in regression parameters is explicitly modeled and the different components of variation may be estimated directly. The proportional hazards and Weibull models were utilized, as both produce natural frameworks for estimating relative risks while adjusting for simultaneous effects of other covariates. A simple Markov Chain Monte Carlo method for covariate imputation of missing data was used and the actual implementation of the Bayesian model was based on Gibbs sampling using the free ware package BUGS. In addition, we also used a Bayesian model to investigate the relative contribution of genetic and environmental effects on the expression of naevi and freckles, which are known risk factors for melanoma.