José Galvão Leite

Chironomid species richness in low-order streams in the Brazilian Atlantic Forest: a first approximation through a Bayesian approach

Abstract The Atlantic Forest of Brazil has been identified as a biodiversity hotspot of global significance. We assessed chironomid (Diptera:Chironomidae) taxa richness in 2 vegetation types in this region: the Atlantic Rain Forest and the Atlantic Semi-deciduous Forest. Taxa were collected from 15 low-order streams across multiple habitats. A total of 191 morphospecies were recognized (125 Chironominae, 28 Tanypodinae, and 38 Orthocladiinae). We estimated chironomid richness using a Bayesian statistical approach. Species-richness estimates ranged from 200 (credibility interval, 195–207) to 267 (248–288). These results place low-order streams from Atlantic Forest among the most chironomid speciose areas in the world.

A Bayesian analysis for estimating the number of species in a population using nonhomogeneous Poisson process

We propose a Bayesian approach using nonhomogeneous Poisson process to estimate the number of species of a population. The proposed methodology uses a [pi]-mixture to eliminate the unknown total mean of each species. One contribution of the article is to apply the Metropolis-within-Gibbs algorithm to obtain the marginal posterior distribution of the number of species and the capture mean time.

Bayesian analysis of a correlated binomial model

In this paper a Bayesian approach is applied to the correlated binomial model, CB(n,p,ρ), proposed by Luceno (Comput. Statist. Data Anal. 20 (1995) 511–520). The data augmentation scheme is used in order to overcome the complexity of the mixture likelihood. MCMC methods, including Gibbs sampling and Metropolis within Gibbs, are applied to estimate the posterior marginal for the probability of success p and for the correlation coefficient ρ. The sensitivity of the posterior is studied taking into account several reference priors and it is shown that the posterior characteristics appear not to be influenced by these prior distributions. The article is motivated by a study of plant selection.

Hierarchical Bayesian estimation for the number of species

This paper is concerned with the estimation of the number of species in a population through a fully hierarchical Bayesian model using the Metropolis algorithm. The proposed Bayesian estimator is based on Poisson random variables with means that are distributed according to some prior distributions with unknown hyperparameters. An empirical Bayes approach is considered and compared with the fully Bayesian approach based on biological data.

Bayesian Estimation of the Size of a Closed Population Using Photo-ID Data with Part of the Population Uncatchable

Abstract We develop a Bayesian statistical model for estimating bowhead whale population size from photo-identification data when most of the population is uncatchable. The proposed conditional likelihood function is a product of Darrochs model, formulated as a function of the number of good photos, and a binomial distribution of captured whales given the total number of good photos at each occasion. The full Bayesian model is implemented via adaptive rejection sampling for log concave densities. We apply the model to data from 1985 and 1986 bowhead whale photographic studies and the results compare favorably with the ones obtained in the literature. Also, a comparison with the maximum likelihood procedure with bootstrap simulation is considered using different vague priors for the capture probabilities.

A new long-term lifetime distribution induced by a latent complementary risk framework

In this paper, we proposed a new three-parameter long-term lifetime distribution induced by a latent complementary risk framework with decreasing, increasing and unimodal hazard function, the long-term complementary exponential geometric distribution. The new distribution arises from latent competing risk scenarios, where the lifetime associated scenario, with a particular risk, is not observable, rather we observe only the maximum lifetime value among all risks, and the presence of long-term survival. The properties of the proposed distribution are discussed, including its probability density function and explicit algebraic formulas for its reliability, hazard and quantile functions and order statistics. The parameter estimation is based on the usual maximum-likelihood approach. A simulation study assesses the performance of the estimation procedure. We compare the new distribution with its particular cases, as well as with the long-term Weibull distribution on three real data sets, observing its potential and competitiveness in comparison with some usual long-term lifetime distributions.

On the integrated maximum likelihood estimators for a closed population capture–recapture model with unequal capture probabilities

Nuisance parameter elimination is a central problem in capture–recapture modelling. In this paper, we consider a closed population capture–recapture model which assumes the capture probabilities varies only with the sampling occasions. In this model, the capture probabilities are regarded as nuisance parameters and the unknown number of individuals is the parameter of interest. In order to eliminate the nuisance parameters, the likelihood function is integrated with respect to a weight function (uniform and Jeffreys) of the nuisance parameters resulting in an integrated likelihood function depending only on the population size. For these integrated likelihood functions, analytical expressions for the maximum likelihood estimates are obtained and it is proved that they are always finite and unique. Variance estimates of the proposed estimators are obtained via a parametric bootstrap resampling procedure. The proposed methods are illustrated on a real data set and their frequentist properties are assessed by means of a simulation study.

A Bayesian Approach to Predicting Football Match Outcomes Considering Time Effect Weight

In this chapter we propose a simulation-based method for predicting football match outcomes. We adopt a Bayesian perspective, modeling the number of goals of two opposing teams as a Poisson distribution whose mean is proportional to the relative technical level of opponents. Federation Internationale de Football Association (FIFA) ratings were taken as the measure of technical level of teams saw well as experts’ opinions on the scores of the matches were taken in account to construct the prior distributions of the parameters. Tournament simulations were performed in order to estimate probabilities of winning the tournament assuming different values for the weight attached to the experts’ information and different choices for the sequence of weights attached to the previous observed matches. The methodology is illustrated on the 2010 Football Word Cup.

A generalized negative binomial distribution based on an extended Poisson process

In this article we propose a generalized negative binomial distribution, which is constructed based on an extended Poisson process (a generalization of the homogeneous Poisson process). This distribution is intended to model discrete data with presence of zero-inflation and over-dispersion. For a dataset on animal abundance which presents over-dispersion and a high frequency of zeros, a comparison between our extended distribution and other common distributions used for modeling this kind of data is addressed, supporting the fitting of the proposed model.