## Ciclo de Palestras – Segundo Semestre de 2011

As palestras ocorreram no Auditório do Laboratório de Sistemas Estocásticos (LSE), sala I-044b, as 15:30 h, a menos de algumas exceções devidamente indicadas.

**Lista completa (palestras previstas para datas futuras podem sofrer alterações)**

In this talk I will talk about this class of model and discuss how fully Bayesian and semi-Bayesian approaches benefit from the exponential family representation. Finally I will talk about my recent work applying the online EM algorithm to this class of problem.

**Percolação com uma linha de defeitos**

**Sacha Friedli (UFMG)**

É bem conhecido que em sistemas subcríticos a correlação entre pontos distantes decresce exponencialmente com a distância. Nesta palestra consideraremos o processo de percolação de Bernoulli, em que elos da rede cúbica são independentemente abertos com probabilidade p, e fechados com probabilidade 1-p. Introduziremos uma linha de defeitos em que os elos são abertos com probabilidade p’ < p, e estudaremos o efeito de p’ e da dimensão sobre o decaimento exponencial da fase subcrítica. Em particular pretendemos apresentar (de maneira não-técnica) a origem da influência de p’ e a sua conexão com as propriedades de recorrência/transiência de um passeio aleatório com incrementos independentes.

**Motor cognition: neurophysiological underpinning of planning, imagining and predicting upcoming actions**

**Claudia Domingues Vargas (UFRJ)**

Motor systems are exquisitely adapted to transform an action goal into the production of a movement of greatest fit in a given context. This transformation, called motor planning, is thought to be performed through internal models of actions. These models operate by continuously monitoring the motor output and by making future predictions of changes in body states and of the immediate environment. Because of the delays inherent to sensorimotor processing, the ability to predict the future state of the motor system in a variable environment (context) is considered crucial to create efficient movements and appropriate behaviors. In this colloquium I intend to explore how the brain activity associated with motor planning changes as a function of the context in which this movement shall be performed. Furthermore, I will present results showing that lesions in specific brain regions can affect the capacity of making predictions of one’s own and/or of other’s upcoming actions.

#### 16/11

*A hierarchical approach to modeling allele-specific gene expression*

Jon Wakefield (Washington)

**Robust estimation in time series, unit root test based on ranks and counting process**

**Valderio A. Reisen (UFES)**

In this talk the following research topics will be discussed.

Robust estimation: It is well-known that the sample autocovariance is not robust to the presence of additive outliers. Hence, the definition of an autocovariance estimator which is robust to additive outlier can be very useful for time-series modeling. The robust autocovariance estimator proposed by Ma and Genton (2000) is studied and applied to time series with different correlation structures such as short and long memory. Based on the robust autocorrelation function, a robust estimator of the parameter d in ARFIMA(p, d, q) is proposed. Some simulations are used to support the use of this method when a time series has additive outliers.

DF unit root test based on ranks: In this subject, the classical Dickey-Fuller (DF) test will be studied in the context of unit root time series with outliers. Based on the ranks of the observations, a robust DF test is proposed. The test is robust against outliers observations. The asymptotic distribution of the test is obtained.

Counting process: The Integer-valued Autoregressive Moving Average (INARMA) models have suggested modeling observed count time series. This research is concerned with the problem of modeling INAR processes under seasonal, unit root and long memory properties.

**O teorema ergódico subaditivo e suas aplicações**

**Enrique D. Andjel (Provence)**

O teorema ergódico subaditivo foi inicialmente provado por Kingman. Ele dá condições suficientes para convergência quase certa de X_n/n onde {X_n} é uma sequência subaditiva de variáveis aleatórias. Veremos como uma versão um pouco mais geral deste teorema permite deduzir resultados de interesse para a percolação de primeira passagem e para alguns sistemas de partículas unidimensionais, como o processo de contato ou o processo de exclusão.

**Limiting the shrinkage for the exceptional: the Clemente problem**

**Luiz Raul Pericchi (Puerto Rico)**

Modern Statistics is made of the sensible combination of direct evidence (the data directly relevant or the “individual data”) and indirect evidence (the data and knowledge indirectly relevant or the “group data”). The admissible procedures are a combination of the two sources of information, and the advance of technology is making indirect evidence more substantial and ubiquitous. It has been pointed out however, that in “borrowing strength” a fundamental problem of Statistics is to treat in a fundamentally different way exceptional cases, cases that do not adapt to the central “aurea mediocritas”. This is what has been recently coined as “the Clemente problem”, Efron (2010). In this article we put forward that the problem is caused by the simultaneous use of square loss function and conjugate (light tailed) priors which is the usual procedure. We propose in their place to use robust penalties, in the form of losses that penalize more severely huge errors, or (equivalently) priors of heavy tails which make more probable the exceptional. Using heavy tailed prior we can reproduce in a Bayesian way, Efron and Morris’ “limited translated estimators” (with Double Exponential Priors) and “discarding priors estimators” (with Cauchy-like priors) which discard the prior in the presence of conflict. Both Empirical Bayes and Full Bayes approaches are able to alleviate the Clemente Problem and furthermore beat the James- Stein estimator in terms of smaller square errors, for sensible Robust Bayes priors. We model in parallel Empirical Bayes and Fully Bayesian hierarchical models, illustrating that the differences among sensible versions of both are minute, as compared with the effect due to the robust assumptions. We also propose a heavy tailed Beta2 distribution for variances that arises naturally as an alternative to the usual Inverted-Gamma distribution. This adds stability and robustness, and strickenly produce a marginal for the location, which is the first known “Horseshoe” (optimal) prior in closed analytical form. This has been put recently to the test Fuquene, Perez and Pericchi (2011) in a Dynamical Bayesian model for detection of structural changes and outliers.

**Nonparametric estimation of diffusions: a differential equations approach**

**Omiros Papaspiliopoulos (Pompeu Fabra)**

We consider estimation of scalar functions which determine the dynamics of diffusion processes. It has been recently shown that nonparametric maximum likelihood is ill-posed in this context. We adopt a probabilistic approach to regularize the problem by the adoption of a prior distribution for the unknown functional. A Gaussian prior measure is specified in the function space by means of its precision operator, which is defined as an appropriate differential operator. We establish that a Bayesian Gaussian conjugate analysis for the drift of one-dimensional non-linear diffusions is feasible given high-frequency data. This is achieved by expressing the log-likelihood as a quadratic function of the drift, with sufficient statistics given by the so-called local time process and the end points of the observed path. Computationally efficient posterior inference is carried out using a finite element method.

We embed this technology in partially observed situations and adopt a data augmentation approach whereby we iteratively generate missing data paths and draws from the unknown functional. Our methodology is applied to estimate the drift of models used in molecular dynamics and financial econometrics using high and low frequency observations. We discuss extensions to other partially observed schemes and connections to other types of non-parametric inference.

Joint work with Yvo Pokern (UCL), Gareth O. Roberts (Warwick) and Andrew M. Stuart (Warwick)