Convergence time and phase transition in a non-monotonic family of probabilistic cellular automata

Alex Ramos - UFPE

In this talk, we will consider a one-dimensional probabilistic cellular automaton where their components assume two possible states, zero and one,and interact with their two nearest neighbors at each time step. Under the local interaction, if the component is in the same state as its two neighbors, it does not change its state. In the other cases, a component in state zero turns into a one with probability α and a component in state one turns into a zero with probability 1-β. For certain values of α and β, we show that the process will always converge weakly to δ the measure concentrated on the configuration where all the components are zeros. Moreover, the mean time of this convergence is finite, and we describe an upper bound in this case, which is a linear function of the initial distribution. We also exhibit some results obtains from mean-field approximation and Monte Carlo simulations, which show coexistence of three distinct behaviours for some values of parameters α and β. This work was developed joint with A. Leite.

Reparametrization of COM-Poisson Regression Models with Applications in the Analysis of Experimental Data

Clarice Demétrio - ESALQ/USP

In the analysis of count data often the equidispersion assumption is not suitable,hence the Poisson regression model is inappropriate. As a generalization of the Poisson distribution the COM-Poisson distribution can deal with under-, equi- and overdispersed count data. It is a member of the exponential family of distributions and has the Poisson and geometric distributions as special cases, as well as the Bernoulli distribution as a limiting case. In spite of the nice properties of the COM-Poisson distribution, its location parameter does not correspond to the expectation, which complicates the interpretation of regression models specified using this distribution. In this paper, we propose a straightforward reparametrization of the COM-Poisson distribution based on an approximation to the expectation of this distribution. The main advantage of our new parametrization is the straightforward interpretation of the regression coeficients in terms of the expectation of the count response variable, as usual in the context of generalized linear models. Furthermore, the estimation and inference for the new COM-Poisson regression model can be done based on the likelihood paradigm. We carried out simulation studies to verify the finite sample properties of the maximum likelihood estimators. The results from our simulation study show that the maximum likelihood estimators are unbiased and consistente for both regression and dispersion parameters. We observed that the empirical correlation between the regression and dispersion parameter estimators is close to zero, which suggests that these parameters are orthogonal. We illustrate the application of the proposed model through the analysis of three data sets with over-, under- and equidispersed count data. The study of distribution properties through a consideration of dispersion, zero-inflated and heavy tail indices, together with the results of data analysis show the exibility over standard approaches. Therefore, we encourage the application of the new parametrization for the analysis of count data in the context of COM-Poisson regression models. The computational routines for fitting the original and new version of the COM-Poisson regression model and the analyzed data sets are available.

Why and how to measure the reliability of scientific co-authorship networks

Juliana Cobre - ICMC/USP

In this talk, we explain the association between a research group and a network and the different points of view that we can do it, more precisely what represents the nodes and the edges in such network. We justify why is important to measure statistically the reliability of scientific co-authorship networks, i. e., why it is not deterministic. In this study, we measure the reliability of networks by taking into account unreliable researchers and perfectly reliable edges. Some different inferential procedures presented and discussed are Bayesian inference using non-informative and informative priors. This is joint work with Sandra Cristina de Oliveira (UNESP-Tupã)

Hydrodynamic limit for the Atlas model

Manuel Cabezas - Pontifícia Universidad Católica de Chile

The Atlas model is an interacting particle system where one starts with Poisson marks in [0,∞) which represent particles. As time runs, these particles perform independent Brownian motions, with the only exception being that, at any time, the leftmost particle has a drift to the right. Our main concern is to identify the possible behaviors of the leftmost particle (transience to the right, transience to the left, recurrence) as a function of the bias.

Big data: potencial, paradoxos e a importância renovada do pensamento estatístico

Pedro Luis do Nascimento Silva - IBGE

Vivemos numa era em que a disponibilidade e acessibilidade a dados não tem precedentes. "Big data" é uma das tendencias deste início do Milênio a confrontar o pensamento estatístico. Por um lado, há imenso potencial para aproveitar as novas fontes de informação que se tem tornado disponíveis, acessíveis e de baixo custo. Por outro lado, lacunas substanciais persistem e há imensos riscos de utilização inadequada dessas fontes pelos que desprezam as lições traduzidas nos principais fundamentos do pensamento e da metodologia estatística. Uma das falácias principais é a de que, com as imensas bases de dados disponíveis, não será mais preciso avaliar incerteza de estimativas, pois será possível "conhecer" as quantidades de interesse a partir dos "big data". Apresenta-se o conceito de "índice de defeito dos dados" proposto por Meng (2018), e usa-se este conceito para mostrar que a qualidade de estimativas baseadas em pequenas amostras bem planejadas e executadas pode superar a de estimativas baseadas em conjuntos muito maiores provenientes de fontes orgânicas sujeitas a vieses de seleção. Penso que a metodologia estatística fornece a orientação essencial necessária para obter respostas atuais, relevantes, precisas e custo-efetivas às perguntas de interesse, mesmo na era do "big data". Apresentarei alguns exemplos ara motivar a discussão dessas ideias.

Bayesian Feature Allocation Models for Tumor Heterogeneity

Peter Mueller - University of Texas

We characterize tumor variability by hypothetical latent cell types that are defined by the presence of some subset of recorded SNV's. (single nucleotide variants, that is, point mutations). Assuming that each sample is composed of some sample-specific proportions of these cell types we can then fit the observed proportions of SNV's for each sample. In other words, by fitting the observed proportions of SNV's in each sample we impute latent underlying cell types, essentially by a deconvolution of the observed proportions as a weighted average of binary indicators that define cell types by the presence or absence of different SNV's. In the first approach we use the generic feature allocation model of the Indian buffet process (IBP) as a prior for the latent cell subpopulations. In a second version of the proposed approach we make use of pairs of SNV's that are jointly recorded on the same reads, thereby contributing valuable haplotype information. Inference now requires feature allocation models beyond the binary IBP. We introduce a categorical extension of the IBP. Finally, in a third approach we replace the IBP by a prior based on a stylized model of a phylogenetic tree of cell subpopulations.

ABC-CDE: Towards Approximate Bayesian Computation with Complex High-Dimensional Data and Limited Simulations

Rafael Izbicki - UFSCar

Approximate Bayesian Computation (ABC) is typically used when the likelihood is either unavailable or intractable but where data can be simulated under different parameter settings using a forward model. Despite the recent interest in ABC, high-dimensional data and costly simulations still remain a bottleneck. There is also no consensus as to how to best assess the performance of such methods. Here we show how a nonparametric conditional density estimation (CDE) framework can help address three key challenges in ABC, namely: (i) how to efficiently estimate the posterior distribution with limited simulations and different types of data, (ii) how to tune and compare the performance of ABC and related methods with CDE as a goal without knowing the true posterior, and (iii) how to efficiently choose among a very large set of summary statistics based on a CDE loss. We provide both theoretical and empirical evidence to justify the use of such procedures and describe settings where standard ABC may fail.

In this paper we investigate the merits of replication, and provide methods that search for optimal designs (including replicates), in the context of noisy computer simulation experiments. We first show that replication offers the potential to be beneficial from both design and computational perspectives, in the context of Gaussian process surrogate modeling. We then develop a lookahead based sequential design scheme that can determine if a new run should be at an existing input location (i.e., replicate) or at a new one (explore). When paired with a newly developed heteroskedastic Gaussian process model, our dynamic design scheme facilitates learning of signal and noise relationships which can vary throughout the input space. We show that it does so efficiently, on both computational and statistical grounds. In addition to illustrative synthetic examples, we demonstrate performance on two challenging real-data simulation experiments, from inventory management and epidemiology.