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.

Molecular characterization of the Hepatitis B virus genotypes in Colombia: A Bayesian inference on the genotype F

Hepatitis B is a worldwide health problem affecting about 2 billion people and more than 350 million are chronic carriers of the virus. Nine HBV genotypes (A to I) have been described. The geographical distribution of HBV genotypes is not completely understood due to the limited number of samples from some parts of the world. One such example is Colombia, in which few studies have described the HBV genotypes. In this study, we characterized HBV genotypes in 143 HBsAg-positive volunteer blood donors from Colombia. A fragment of 1306 bp partially comprising HBsAg and the DNA polymerase coding regions (S/POL) was amplified and sequenced. Bayesian phylogenetic analyses were conducted using the Markov Chain Monte Carlo (MCMC) approach to obtain the maximum clade credibility (MCC) tree using BEAST v.1.5.3. Of all samples, 68 were positive and 52 were successfully sequenced. Genotype F was the most prevalent in this population (77%) - subgenotypes F3 (75%) and Fib (2%). Genotype G (7.7%) and subgenotype A2 (15.3%) were also found. Genotype G sequence analysis suggests distinct introductions of this genotype in the country. Furthermore, we estimated the time of the most recent common ancestor (TMRCA) for each HBV/F subgenotype and also for Colombian F3 sequences using two different datasets: (i) 77 sequences comprising 1306 bp of S/POL region and (ii) 283 sequences comprising 681 bp of S/POL region. We also used two other previously estimated evolutionary rates: (i) 2.60 x 10(-4) s/s/y and (ii) 1.5 x 10(-5) s/s/y. Here we report the HBV genotypes circulating in Colombia and estimated the TMRCA for the four different subgenotypes of genotype F. (C) 2010 Elsevier B.V. All rights reserved.

A Bayesian approach to fuzzy hypotheses testing for the estimation of optimal age for vaccination against measles

Fuzzy Bayesian tests were performed to evaluate whether the mother`s seroprevalence and children`s seroconversion to measles vaccine could be considered as ""high"" or ""low"". The results of the tests were aggregated into a fuzzy rule-based model structure, which would allow an expert to influence the model results. The linguistic model was developed considering four input variables. As the model output, we obtain the recommended age-specific vaccine coverage. The inputs of the fuzzy rules are fuzzy sets and the outputs are constant functions, performing the simplest Takagi-Sugeno-Kang model. This fuzzy approach is compared to a classical one, where the classical Bayes test was performed. Although the fuzzy and classical performances were similar, the fuzzy approach was more detailed and revealed important differences. In addition to taking into account subjective information in the form of fuzzy hypotheses it can be intuitively grasped by the decision maker. Finally, we show that the Bayesian test of fuzzy hypotheses is an interesting approach from the theoretical point of view, in the sense that it combines two complementary areas of investigation, normally seen as competitive. (C) 2007 IMACS. Published by 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.

Diffuse liver disease classification from ultrasound surface characterization, clinical and laboratorial data

In this work liver contour is semi-automatically segmented and quantified in order to help the identification and diagnosis of diffuse liver disease. The features extracted from the liver contour are jointly used with clinical and laboratorial data in the staging process. The classification results of a support vector machine, a Bayesian and a k-nearest neighbor classifier are compared. A population of 88 patients at five different stages of diffuse liver disease and a leave-one-out cross-validation strategy are used in the classification process. The best results are obtained using the k-nearest neighbor classifier, with an overall accuracy of 80.68%. The good performance of the proposed method shows a reliable indicator that can improve the information in the staging of diffuse liver disease.

Fatty liver characterization and classification by ultrasound

Steatosis, also known as fatty liver, corresponds to an abnormal retention of lipids within the hepatic cells and reflects an impairment of the normal processes of synthesis and elimination of fat. Several causes may lead to this condition, namely obesity, diabetes, or alcoholism. In this paper an automatic classification algorithm is proposed for the diagnosis of the liver steatosis from ultrasound images. The features are selected in order to catch the same characteristics used by the physicians in the diagnosis of the disease based on visual inspection of the ultrasound images. The algorithm, designed in a Bayesian framework, computes two images: i) a despeckled one, containing the anatomic and echogenic information of the liver, and ii) an image containing only the speckle used to compute the textural features. These images are computed from the estimated RF signal generated by the ultrasound probe where the dynamic range compression performed by the equipment is taken into account. A Bayes classifier, trained with data manually classified by expert clinicians and used as ground truth, reaches an overall accuracy of 95% and a 100% of sensitivity. The main novelties of the method are the estimations of the RF and speckle images which make it possible to accurately compute textural features of the liver parenchyma relevant for the diagnosis.

Fatty liver automatic diagnosis from ultrasound images

In this paper an automatic classification algorithm is proposed for the diagnosis of the liver steatosis, also known as, fatty liver, from ultrasound images. The features, automatically extracted from the ultrasound images used by the classifier, are basically the ones used by the physicians in the diagnosis of the disease based on visual inspection of the ultrasound images. The main novelty of the method is the utilization of the speckle noise that corrupts the ultrasound images to compute textural features of the liver parenchyma relevant for the diagnosis. The algorithm uses the Bayesian framework to compute a noiseless image, containing anatomic and echogenic information of the liver and a second image containing only the speckle noise used to compute the textural features. The classification results, with the Bayes classifier using manually classified data as ground truth show that the automatic classifier reaches an accuracy of 95% and a 100% of sensitivity.