Complex decision support systems often consist of component modules which, encoding the judgements of panels of domain experts, describe a particular sub-domain of the overall system. Ideally these modules need to be pasted together to provide a comprehensive picture of the whole process. The challenge of building such an integrated system is that, whilst the overall qualitative features are common knowledge to all, the explicit forecasts and their associated uncertainties are only expressed individually by each panel, resulting from its own analysis. The structure of the integrated system therefore needs to facilitate the coherent piecing together of these separate evaluations. If such a system is not available there is a serious danger that this might drive decision makers to incoherent and so
indefensible policy choices. In this talk we first discuss a formal statistical methodology to underpin this integration consisting of sufficient conditions that ensure inference is both coherent and distributed. Under these conditions, the ranking of the available policies will then depend only on a suite of selected outputs of the component modules. Because of this property, we can characterize the inferential routines of an integrated system in a symbolic way and implement these in a computer algebra system. The second part of the talk will explore the possibilities that these symbolic methods offer to enhance the integration of the components. This talk summarizes joint work with J.Q. Smith, M.J. Barons, C. Gorgen and E. Riccomagno.

A ser divulgado.

A ser divulgado.

A atual pandemia de obesidade, de curso explosivo, também no Brasil tende a concentrar-se nos estratos mais pobres da população, e ameaça reverter tendências históricas de aumento da vida média, além de impor custos crescentes ao sistema de saúde. Até o momento não há registro de ações bem sucedidas com impacto populacional, em geral focadas em ações educativas dirigidas a aspectos da dieta e atividade física. Há, portanto, crescente interesse na investigação de fatores que adicionalmente contribuam para a complexa determinação do excesso de peso. Nossos planos academicos para o período vindouro assentam-se em dados de cerca de 4 mil participantes das 4 fases do Estudo Pró-Saúde (EPS: 1999-2015), coorte conduzida entre funcionários de campi universitários no Rio de Janeiro. Será investigado amplo conjunto de fatores potencialmente contribuintes para a obesidade e suas consequências. Dados já coletados, além de parâmetros bioquímicos e genéticos a serem gerados em subamostra,, serão objeto de análises multivariadas transversais e longitudinais entre indicadores de obesidade e características biológicas, comportamentais, contextuais e sociais. Serão apresentadas algumas necessidades sentidas de colaboração com estatísticos!

Several mathematical models for describing the collective behaviour of biological populations (cells, birds, ants …) have been introduced more or less recently. In 1970 and 1971, Evelyn F. Keller and Lee A. Segel proposed two connected models for the chemotactic interaction of amoebae as mediated by acrasin: a macroscopic model describing the behaviour of the local density of cells, concentration of the chemo-attractant etc … in terms of a system of coupled PDE’s, a microscopic one describing the microscopic (individual) behaviour of each cell interacting with the other ones in terms of a random system. In particular the Keller-Segel model describes the possible aggregation of cells depending on the parameters of the system. The macroscopic model has been extensively studied since this time, furnishing many difficult and interesting mathematical problems, and actually the situation is only well understood in two dimensions. The microscopic model has been much less studied. We shall discuss another stochastic microscopic model directly related to the macroscopic one. It is some kind of Mc-Kean Vlasov interacting diffusions model, but with a singular attractive potential (with the opposite sign as in the Dyson Brownian motion introduced in random matrix theory). We shall see how the system feels the critical parameter yielding aggregation. If we have some time, we shall also introduce a stochastic version of the Cucker-Smale model of flocking. Here randomness is introduced to take into account some degree of freedom of each individual, but furnishes a negative answer to flocking. The most common property of these two (as well as others) models is that their properties are almost completel unknown.

(joint work with G. Giacomin)
Disorder relevance is an important question in Statistical Mechanics. It can be formulated as follows: “If the Hamiltonian of model is modified by adding a small random perturbation, does it conserve a phase transition with the same characteristics as that of the pure model.” A mathematical investigation of this matter is of course possible only for models for which the phase transition is rigorously understood in the pure setup, and our work concerns a very simple and tractable model of surfaces in interaction with a defect plane. The surfaces is modeled by the graph of a Gaussian-Free-Field $mathbb Z^d$, $dge 2$, and the interaction is given by an energy reward for each point of the graph whose height is in the interval $[-1,1]$. The system undergoes a wetting transition from a localized phase to a delocalized one, when the mean energy of interaction varies. We investigate the modification of the free-energy curve induced by the introduction of “inhomogeneity” in the interaction. We show that in a certain sense the critical point is left invariant by the presence of homogeneity, but that the localization transition becomes much smoother.

Neste trabalho introduzimos uma nova classe de distribuições multivariadas unimodais motivada pela representação de Khintchine. Inicialmente propomos um modelo univariado cujo suporte cobre todas as distribuições unimodais na reta dos reais. A classe proposta de distribuições unimodais pode ser naturalmente estendida para dimensões maiores, usando a cópula Gaussiana multivariada. Sob os contextos univariado e multivariado, propomos algoritmos de MCMC para fazer inferência sobre os parãmetros do modelo e densidade preditiva. A metodologia é ilustrada com exemplos univariados e multivariados, e com variáveis obtidas de um conjuto de dados reais sobre moradias em Boston, E.U.A.

Gabriel Fonseca Sarmanho.
Título: Inferência Bayesiana em Modelos Multivariados de Efeitos Aleatórios para Comparações Interlaboratoriais

Jesus Eduardo Gamboa Unsihuay.
Título: Modelos Dinâmicos Gaussianos para dados heteroscedásticos

Iago Carvalho Cunha.
Título: Particle Filters and Adaptive Metropolis-Hastings Sampling Applied to Bayesian Estimation.

Neste trabalho é desenvolvida uma análise de regressão linear considerando que a variável dependente é censurada e também que algumas das variáveis explicativas são medidas com erros aditivos. Esse modelo de regressão censurado com erros de medidas é especificado assumindo distribuições com cauda pesada para o processo probabilístico. Especificamente, assume-se uma distribuição t-Student multivariada para modelar o comportamento conjunto dos erros e das verdadeiras covariáveis não observadas. Nesse sentido, o modelo será robusto o suficiente para proteger as inferências de observações atípicas e influentes. Para a estimação do modelo considera-se a metodologia de máxima verossimilhança, em que inclui-se a estimação da variância assintótica dos estimadores de máxima verossimilhança e também desenvolve-se um algoritmo do tipo EM para obter as estimativas, e também o paradigma bayesiano, onde considera-se o procedimento de aumento de dados e desenvolve-se um algoritmo MCMC para amostrar das distribuições a posteriori. A metodologia proposta é flexível o bastante para ser adaptada para distribuições com caudas pesadas vindas da classe de misturas de escala da distribuição normal. A performance da nova metodologia desenvolvida é avaliada através de um estudo Monte Carlo e também de uma análise de um estudo de caso com dados de gastos ambulatoriais.

Statistical shape analysis relates to the study of random objects, where the concept of shape corresponds to the geometrical information that is invariant under translation, rotation and scale effects (Dryden and Mardia, 1998). This talk deals with the statistical analysis of a temporal sequence of landmark data and discusses the use of the offset-normal distribution for the description of time-varying shapes. For two time points, Mardia and Walder (1994) have shown that the density function of the offset-normal distribution has a rather complicated form and discuss the difficulty of extending their results to t > 2. We show that their work can be extended to a general number of time points and that the model parameters of the offset-normal shape distribution can be estimated through the Expectation Maximization (EM) algorithm. There are, however, several issues to consider here and there are also computational difficulties to overcome. As it will be shown, these are mainly related to the computation of the expectation of a product of quadratic forms. This is a joint work with Lara Fontanella, Department of Economics, University G. d’Annunzio (Italy) and Alfred Kume, Institute of Mathematics, Statistics and Actuarial Science, University of Kent (UK).

References:
Dryden, I.L., Mardia, K.V. (1998): Statistical shape analysis. Wiley,
Chichester.
Mardia, K. V. and Walder, A. N. (1994), Shape analysis of paired landmark
data. Biometrika,
81, 185-196.

Multivariate geostatistics is based on modelling all covariances between all possible combinations of two or more variables and their locations in a continuously indexed domain. Multivariate spatial covariance models need to be built with care, since any covariance matrix that is derived from such a model has to be [UTF-8?]nonnegative-definite. In this talk, a conditional approach for multivariate spatial-statistical model construction is given. Starting with bivariate spatial models, its connection to multivariate models [UTF-8?]defined by spatial networks is given. A bivariate model is fitted to a minimum-maximum temperature dataset in the state of Colorado, USA. This is joint research with Andrew Zammit Mangion, NIASRA, University of Wollongong.

Particle Filtering has captured the attention of many researchers in various communities including those of signal processing, statistics, and econometrics, and this interest stems from its potential for coping with inference problems in state-space models. Based on the concept of sequential importance sampling and the use of Bayesian theory, particle filtering is particularly useful in dealing with nonlinear and non-Gaussian problems. The underlying principle of the methodology is the approximation of relevant distributions with random measures composed of particles (samples from the space of the unknowns) and their associated weights. While many works have been devoted to develop new and sophisticate particle filters, the problem of how selecting the number of particles still remain open. In this work we propose a method for assessing in real time the convergence of the filter, allowing the filter to automatically increase or decrease the number of particles according to specific performance requirements.

The conditional mean residual life (MRL) function is the expected remaining lifetime of a system given survival past a particular time point and the values of a set of predictor variables. This function is a valuable tool in reliability and actuarial studies when the right tail of the distribution is of interest, and can be more informative than the survivor function. In this paper, we identify theoretical limitations of some semi-parametric conditional MRL models, and propose two nonparametric methods of estimating the conditional MRL function. Asymptotic properties such as consistency and normality of our proposed estimators are established. We investigate via simulation study the empirical properties of the proposed estimators, including bootstrap pointwise confidence intervals. Using Monte Carlo simulations we compare the proposed nonparametric estimators to two popular semi-parametric methods of analysis, for varying types of data. The proposed estimators are demonstrated on the Veteran’s Administration lung cancer trial.