Species distribution models (SDM) are a key tool in ecology, conservation and management of natural resources. Two key components of the state-ofthe-art SDMs are the description for species distribution response along environmental covariates and the spatial random effect that captures deviations from the distribution patterns explained by environmental covariates. Joint species distribution models (JSDMs) additionally include interspecific correlations which have been shown to improve their descriptive and predictive performance compared to single species models. However, current JSDMs are restricted to hierarchical generalized linear modeling framework. Their limitation is that parametric models have trouble in explaining changes in abundance due, for example, highly nonlinear physical tolerance limits which is particularly important when predicting species distribution in new areas or under scenarios of environmental change. On the other hand, semi-parametric response functions have been shown to improve the predictive performance of SDMs in these tasks in single species models.Here, we propose JSDMs where the responses to environmental covariates are modeled with additive multivariate Gaussian processes coded as linear models of coregionalization. These allow inference for wide range of functional forms and interspecific correlations between the responses. We propose also an efficient approach for inference with Laplace approximation and parameterization of the interspecific covariance matrices on the euclidean space. We demonstrate the benefits of our model with two small scale examples and one real world case study. We use cross-validation to compare the proposed model to analogous semi-parametric single species models and parametric single and joint species models in interpolation and extrapolation tasks. The proposed model outperforms the alternative models in all cases. We also show that the proposed model can be seen as an extension of the current state-of-the-art JSDMs to semi-parametric models.MSC 2010 subject classifications: Primary 60G15, 60K35; secondary 62P12.

RESUMOConsiderando a importância sócio-econômica da região de Presidente Prudente, este estudo teve como objetivo estimar a precipitação pluvial máxima esperada para diferentes níveis de probabilidade e verificar o grau de ajuste dos dados ao modelo Gumbel, com as estimativas dos parâmetros obtidas pelo método de máxima verossimilhança. Pelos resultados, o teste de Kolmogorov-Sminorv (K-S) mostrou que a distribuição Gumbel testada se ajustou com p-valor maior que 0.28 para todos os períodos de tempo considerados, comprovando que a distribuição Gumbel apresenta um bom ajustamento aos dados observados para representar as precipitações pluviais máximas. As estimativas de precipitação obtidas pelo método de máxima verossimilhança são consistentes, conseguindo reproduzir com bastante fidelidade o regime de chuvas da região de Presidente Prudente. Assim, o conhecimento da distribuição da precipitação pluvial máxima mensal e das estimativas das precipitações diárias máximas esperadas, possibilita um planejamento estratégico melhor, minimizando assim o risco de ocorrência de perdas econômicas para essa região. Palavras-Chave: Precipitação máxima, estimador de máxima verossimilhança, distribuição Gumbel, intervalo de confiança. ABSTRACT: STUDY OF THE MAXIMUM ANNUAL PRECIPITATION IN PRESIDENTE PRUDENTEConsidering the socioeconomic importance of Presidente Prudente area, this study aimed at to estimate the maximum pluvial precipitation expected for different levels of probability and to check the fitting degree of the data to the Gumbel model, with the parameter estimation obtained by the maximum likelihood approach. The Kolmogorov-Sminorv (K-S) test showed that the Gumbel distribution has fitted with p-value larger than 0.28 for all of the time periods considered, showing that the Gumbel distribution presents a good fitting to the observed data representing the maximum pluvial precipitations values. The precipitation estimates obtained by the maximum likelihood approach are consistent allowing to reproduce with plenty reliability the rainfall regime for Presidente Prudente region. Therefore, the knowledge of the monthly maximum pluvial precipitation distribution and the expected maximum daily precipitation estimates permits a better strategic planning thus minimizing the risk of economical losses for this region.

Specification of the prior distribution for a Bayesian model is a central part of the Bayesian workflow for data analysis, but it is often difficult even for statistical experts. Prior elicitation transforms domain knowledge of various kinds into well-defined prior distributions, and offers a solution to the prior specification problem, in principle. In practice, however, we are still fairly far from having usable prior elicitation tools that could significantly influence the way we build probabilistic models in academia and industry. We lack elicitation methods that integrate well into the Bayesian workflow and perform elicitation efficiently in terms of costs of time and effort. We even lack a comprehensive theoretical framework for understanding different facets of the prior elicitation problem.Why are we not widely using prior elicitation? We analyze the state of the art by identifying a range of key aspects of prior knowledge elicitation, from properties of the modelling task and the nature of the priors to the form of interaction with the expert. The existing prior elicitation literature is reviewed and categorized in these terms. This allows recognizing under-studied directions in prior elicitation research, finally leading to a proposal of several new avenues to improve prior elicitation methodology.

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In this paper we propose to evaluate and compare Markov chain Monte Carlo (MCMC) methods to estimate the parameters in a generalized extreme value model. We employed the Bayesian approach using traditional Metropolis-Hastings methods, Hamiltonian Monte Carlo (HMC) and Riemann manifold HMC (RMHMC) methods to obtain the approximations to the posterior marginal distributions of interest. Applications to real datasets of maxima illustrate illustrate how HMC can be much more efficient computationally than traditional MCMC and simulation studies are conducted to compare the algorithms in terms of how fast they get close enough to the stationary distribution so as to provide good estimates with a smaller number of iterations.

We propose the Laplace method to derive approximate inference for Gaussian process (GP) regression in the location and scale parameters of the student-t probabilistic model. This allows both mean and variance of data to vary as a function of covariates with the attractive feature that the student-t model has been widely used as a useful tool for robustifying data analysis. The challenge in the approximate inference for the model, lies in the analytical intractability of the posterior distribution and the lack of concavity of the log-likelihood function. We present the natural gradient adaptation for the estimation process which primarily relies on the property that the student-t model naturally has orthogonal parametrization. Due to this particular property of the model the Laplace approximation becomes significantly more robust than the traditional approach using Newton's methods. We also introduce an alternative Laplace approximation by using model's Fisher information matrix. According to experiments this alternative approximation provides very similar posterior approximations and predictive performance to the traditional Laplace approximation with model's Hessian matrix. However, the proposed Laplace-Fisher approximation is faster and more stable to calculate compared to the traditional Laplace approximation. We also compare both of these Laplace approximations with the Markov chain Monte Carlo (MCMC) method. We discuss how our approach can, in general, improve the inference algorithm in cases where the probabilistic model assumed for the data is not log-concave.

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