Bayesian approximations in randomized response model

Practical Bayesian inference depends upon detailed examination of posterior distribution. When the prior and likelihood are conjugate, this is easily carried out; however, in general, one must resort to numerical approximation. In this paper, our aim is to solve, using MAPLE, the Bayesian paradigm, for a very special data collecting procedure, known as the randomized-response technique. This allows researchers to obtain sensitive information while guaranteeing privacy to respondents. This approach intends to reduce false responses on sensitive questions. Exact methods and approximations will be compared from the accuracy point of view as well as for the computational effort.

Robust Bayesian analysis of heavy-tailed stochastic volatility models using scale mixtures of normal distributions

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Phylogenetic Relationships in Eleocharis (Cyperaceae): C-4 Photosynthesis Origins and Patterns of Diversification in the Spikerushes

Eleocharis (Cyperaceae) is a morphologically and physiologically diverse lineage of 250 + species with a cosmopolitan distribution. We here explore phylogenetic relationships in this lineage using maximum parsimony and Bayesian inference analyses of nrDNA ITS and cpDNA trnC-ycf6 and ycf6-psbM sequence data with the goals of comparing our phylogenetic hypotheses to previous classifications, morphological variation, and photosynthetic pathway variation. Our results suggest that in Eleocharis C, photosynthesis has been derived at least three times, with several cases of possible reversion to C-3-like or intermediate pathways and several additional origins of C-3-C-4 intermediate photosynthetic pathways, as inferred by carbon isotope ratio measurements. Many classification units currently recognized in Eleocharis are not monophyletic, however, E. subgenus Limnochloa and E. subgenus Scirpidium are monophyletic. Other classification units largely corresponding to clades include E. subgenus Zinserlingia, E. subseries Chaetariae, and E. series Maculosae. Problems with species circumscription and morphological variation in several groups are discussed in light of the phylogeny, particularly in the context of species membership of seven focal clades found in the analyses.

Bayesian L-optimal exact design of experiments for biological kinetic models

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Genetic parameters by Bayesian inference for dual purpose Jaffarabadi buffaloes

Knowledge of genetic parameters is essential for improved reproductive management and increased yield. Quantitative analysis of genetic parameters is lacking for many breeds of buffaloes. This article provides the first estimate of genetic parameters for dual purpose (meat and milk) Brazilian Jaffarabadi buffaloes, using Bayesian inference. Data on milk yield (MY), lactation length (LL), weight at 205 days (W205) and 365 (W365) days of age, and average daily gain (ADG) from 205 to 365 days of age were collected in two herds. Bivariate analyses (using the program MTGSAM) were performed with the Gibbs sampler to obtain estimates of variance and covariance. Average lactation milk yield and lactation length were 1 620.2 +/- 450.9 kg and 257.6 +/- 46.8 days, respectively, and the mean values for weight traits (kg) were 181.6 +/- 63.3 (W205), 298.04 +/- 116.1 (W365), and 0.73 +/- 0.35 (ADG). Heritability estimates (modes) were 0.16 for MY, 0.10 for LL, 0.43 for W205, 0.48 for W365 and 0.32 for ADG. There was a high genetic correlation (0.96) between milk yield and lactation length and very high genetic correlations (0.99) between the three growth traits. Our data suggest that both milk production and growth traits have clear potential for yield improvement through direct selection in this dual purpose breed. The selection for weight at an early age would be successful and selection for MY can be performed in the first lactation.

Bayesian outlier analysis in binary regression

We propose alternative approaches to analyze residuals in binary regression models based on random effect components. Our preferred model does not depend upon any tuning parameter, being completely automatic. Although the focus is mainly on accommodation of outliers, the proposed methodology is also able to detect them. Our approach consists of evaluating the posterior distribution of random effects included in the linear predictor. The evaluation of the posterior distributions of interest involves cumbersome integration, which is easily dealt with through stochastic simulation methods. We also discuss different specifications of prior distributions for the random effects. The potential of these strategies is compared in a real data set. The main finding is that the inclusion of extra variability accommodates the outliers, improving the adjustment of the model substantially, besides correctly indicating the possible outliers.

Bayesian estimation of generalized exponential distribution under noninformative priors

The generalized exponential distribution, proposed by Gupta and Kundu (1999), is a good alternative to standard lifetime distributions as exponential, Weibull or gamma. Several authors have considered the problem of Bayesian estimation of the parameters of generalized exponential distribution, assuming independent gamma priors and other informative priors. In this paper, we consider a Bayesian analysis of the generalized exponential distribution by assuming the conventional non-informative prior distributions, as Jeffreys and reference prior, to estimate the parameters. These priors are compared with independent gamma priors for both parameters. The comparison is carried out by examining the frequentist coverage probabilities of Bayesian credible intervals. We shown that maximal data information prior implies in an improper posterior distribution for the parameters of a generalized exponential distribution. It is also shown that the choice of a parameter of interest is very important for the reference prior. The different choices lead to different reference priors in this case. Numerical inference is illustrated for the parameters by considering data set of different sizes and using MCMC (Markov Chain Monte Carlo) methods.

Molecular phylogeny of the New World Dipsadidae (Serpentes: Colubroidea): a reappraisal

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Genetic correlations between categorical morphological traits in Nelore cattle by applying Bayesian analysis under a threshold animal model

P>In this study, Bayesian analysis under a threshold animal model was used to estimate genetic correlations between morphological traits (body structure, finishing precocity and muscling) in Nelore cattle evaluated at weaning and yearling. Visual scores obtained from 7651 Nelore cattle at weaning and from 4155 animals at yearling, belonging to the Brazilian Nelore Program, were used. Genetic parameters for the morphological traits were estimated by two-trait Bayesian analysis under a threshold animal model. The genetic correlations between the morphological traits evaluated at two ages of the animal (weaning and yearling) were positive and high for body structure (0.91), finishing precocity (0.96) and muscling (0.94). These results indicate that the traits are mainly determined by the same set of genes of additive action and that direct selection at weaning will also result in genetic progress for the same traits at yearling. Thus, selection of the best genotypes during only one phase of life of the animal is suggested. However, genetic differences between morphological traits were better detected during the growth phase to yearling. Direct selection for body structure, finishing precocity and muscling at only one age, preferentially at yearling, is recommended as genetic differences between traits can be detected at this age.

The Poisson-exponential distribution: a Bayesian approach

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

STOMACH CONTENTS ANALYSIS of WHITE MARLIN (TETRAPTURUS ALBIDUS) CAUGHT OFF SOUTHERN and SOUTHEASTERN BRAZIL: A BAYESIAN ANALYSIS.

This study proposes to ascertain the importance of each alimentary category in the Tetrapturus albidus diet composition, as well as to propose the use of the Bayesian approach for analysis of these data. The stomachs were collected during fishing cruises carried out by the Santos-SP longliner from July 2007 to June 2008. For Bayesian model formulation, each alimentary item was clustered in four food categories as: teleost, cephalopod, crustaceans, and others. To estimate the proportion of each food category, the multinomial model with Dirichlet conjugate prior distribution was used. After the stomach contents analysis, 133 food items were identified, which belonged to 9 taxa. The most important food category is constituted by cephalopod molluscs, followed by teleost fishes. The food category comprised of crustaceans presents a low contribution and in this case it could be considered to be an accidental food item. The Bayesian approach means a distinct view in relation to traditional methods, as it permits one to incorporate information obtained from the literature. It should be useful to analyse great top predators, which are usually caught in small numbers.

MOLECULAR PHYLOGENY of THE GENUS KUMANOA (BATRACHOSPERMALES, RHODOPHYTA)

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)