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.

Comparative phylogeography of three rainforest-restricted lizards from mid-east Queensland

Several small isolates of rainforest situated on the central eastern coast of Australia are home to a rich herpetofauna, including four endemic species of leaftail geckos (Phyllurus spp.) and two skinks (Eulamprus spp.). To examine the extent and geographic pattern of historical subdivision among isolates, we assayed mtDNA variation in two species endemic to rainforests of this region (Phyllurus ossa and Eulamprus amplus) and, for comparison, a more widespread and less specialised lizard, Carlia rhomboidalis. There is a clear genetic signature of historical changes in population size and distribution in P. ossa that is consistent with Pleistocene (or earlier) rainforest contraction and subsequent expansion. Although more pronounced in the gecko, phylogeographic structure was congruent between E. amplus and P. ossa. In contrast to the saxicolous, rainforest-restricted P. ossa and E. amplus, the rainforest-generalist species, C. rhomboidalis, does not display strong geographic population structure. The differences in genetic population structure exhibited by the three species are consistent with species-specific differences in ecology.

Comparative phylogeography of two open forest frogs from eastern Australia

We investigated the phylogeography of two closely related Australian frog species from open forest habitats, Limnodynastes tasmaniensis and L. peronii, using mitochondrial ND4 sequence data. Comparison of our results with previous work on Litoria fallax allowed us to test the generality of phylogeographic patterns among non-rainforest anurans along the east coast of Australia. In general, there was no strong evidence for congruence between overall patterns of genetic structure in the three species. However, phylogenetic breaks congruent with the position of the Burdekin Gap were detected at some level in all species. As previously noted for closed forest taxa, this area of dry habitat appears to have been an important influence on the evolution of several open forest taxa. There were broad geographic similarities in the phylogenetic structuring of southern populations of L. peronii and L. tasmaniensis. Contrarily, although the McPherson Range has previously been noted to coincide geographically with a major mtDNA phylogenetic break in Litoria fallax this pattern is not apparent in L. peronii or L. tasmaniensis. It appears that major phylogeographic splits within L. peronii and L. tasmaniensis may predate the Quaternary. We conclude that phylogeographies of open forest frogs are complex and more difficult to predict than for rainforest taxa, mainly due to an absence of palaeomodels for historical distributions of non-rainforest habitats. (C) 2001 The Linnean Society of London.

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.

Reconciling paleodistribution models and comparative phylogeography in the Wet Tropics rainforest land snail Gnarosophia bellendenkerensis (Brazier 1875)

Comparative phylogeography has proved useful for investigating biological responses to past climate change and is strongest when combined with extrinsic hypotheses derived from the fossil record or geology. However, the rarity of species with sufficient, spatially explicit fossil evidence restricts the application of this method. Here, we develop an alternative approach in which spatial models of predicted species distributions under serial paleoclimates are compared with a molecular phylogeography, in this case for a snail endemic to the rainforests of North Queensland, Australia. We also compare the phylogeography of the snail to those from several endemic vertebrates and use consilience across all of these approaches to enhance biogeographical inference for this rainforest fauna. The snail mtDNA phylogeography is consistent with predictions from paleoclimate modeling in relation to the location and size of climatic refugia through the late Pleistocene-Holocene and broad patterns of extinction and recolonization. There is general agreement between quantitative estimates of population expansion from sequence data (using likelihood and coalescent methods) vs. distributional modeling. The snail phylogeography represents a composite of both common and idiosyncratic patterns seen among vertebrates, reflecting the geographically finer scale of persistence and subdivision in the snail. In general, this multifaceted approach, combining spatially explicit paleoclimatological models and comparative phylogeography, provides a powerful approach to locating historical refugia and understanding species' responses to them.

Phylogeography of the pipefish, Urocampus carinirostris, suggests secondary intergradation of ancient lineages

We assayed the pattern of mitoehondrial DNA evolution in the live bearing, seagrass specialist pipefish, Urocampus carinirostris, in eastern Australia. These life history attributes were predicted to result in strong phylogeographic structure in U. carinirostris. Phylogenetic analysis of cytochrome b sequences detected two monophyletic mtDNA clades that differed by 8.69% sequence divergence - a large level of intraspecific divergence for a marine fish. The geographical distribution of clades was non-random and resembled clinal secondary intergradation over a 130-km stretch of coastline. Contrary to phylogeographic predictions, this large phylogeographic break does not occur across a traditionally recognised biogeographic boundary. Analyses of historical demography suggested that individuals belonging to the most widespread clade underwent a population expansion from a small refuge population during the Pleistocene.

The phylogeography and connectivity of the latitudinally widespread scleractinian coral Plesiastrea versipora in the Western Pacific

Whereas terrestrial animal populations might show genetic connectivity within a continent, marine species, such as hermatypic corals, may have connectivity stretching to all corners of the planet. We quantified the genetic variability within and among populations of the widespread scleractinian coral, Plesiastrea versipora along the eastern Australian seaboard (4145 km) and the Ryukyu Archipelago (Japan, 681 km) using sequences of internal transcribed spacers (ITS1-2) from ribosomal DNA. Geographic patterns in genetic variability were deduced from a nested clade analysis (NCA) performed on a parsimony network haplotype. This analysis allowed the establishment of geographical associations in the distribution of haplotypes within the network cladogram, therefore allowing us to deduce phylogeographical patterns based under models of restricted gene flow, fragmentation and range expansion. No significant structure was found among Ryukyu Archipelago populations. The lack of an association between the positions of haplotypes in the cladogram with geographical location of these populations may be accounted for by a high level of gene flow of P. versipora within this region, probably due to the strong Kuroshio Current. In contrast, strong geographical associations were apparent among populations of P. versipora along the south-east coast of Australia. This pattern of restricted genetic connectivity among populations of P. versipora on the eastern seaboard of Australia seems to be associated with the present surface ocean current (the East Australian Current) on this side of the south-western Pacific Ocean.

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.