Sequential Quasi Monte Carlo We develop a new class of algorithms, SQMC (Sequential Quasi Monte Carlo), as a variant of SMC (Sequential Monte Carlo) based on low-discrepancy points. The complexity of SQMC is O(N log N) where N is the number of simulations at each iteration, and its error rate is smaller than the Monte…

The algebraic method in experimental designs This seminar is part of the 3rd Carlo Alberto Stochastics Workshop

Chain event graphs and the geometry of causation This seminar is part of the 3rd Carlo Alberto Stochastics Workshop

Testability and consistency Bayesian consistency theorems come in (at least) three distinct types, e.g. Doob's prior-almost-sure consistency on Polish spaces, Schwartz's Hellinger consistency with KL-priors and the `tailfree' weak consistency of Dirichlet posteriors. In this talk we ask the question how these notions of convergence are related and argue that one characterises them most conveniently…

Adaptive testing of conditional association through recursive mixture modeling In many case-control studies, a central goal is to test for association or dependence between the predictors and the response. Relevant covariates must be conditioned on to avoid false positives and loss in power. Conditioning on covariates is easy in parametric frameworks such as the logistic…

Deviance Information Criteria for the frailty model We are concerned with model selection for the frailty model by use of the deviance information criterion (DIC). The DIC is a Bayesian model selection criterion proposed by Spiegelhalter et al. (2002).  A difficulty in applying the DIC to the frailty model lies on the unspecified baseline hazard…

A Bayesian nonparametric model for undirected and multi-edges networks In this talk, I will present ongoing work on a Bayesian nonparametric specification for either undirected or multi-edge directed networks, building on the framework of completely random measures. The formulation allows for an unbounded number of nodes in the network, while encouraging a sparse set of…

Bayesian inference in two–piece and skew–symmetric distributions using Jeffreys priors We study the Jeffreys prior and the independence Jeffreys prior of general classes of univariate location–scale two–piece and skew–symmetric models. For the case of two– piece models, Jeffreys priors are shown not to allow for Bayesian inference in the wide and practically relevant class of…

Bayesian density estimation for compositional data using random Bernstein polynomials We propose a Bayesian nonparametric model for single density estimation, for data in the p-dimensional simplex space, say S_p. The proposal is based on a particular class of multivariate Bernstein polynomials on S_p and extends the Dirichlet-Bernstein prior for density estimation, for data in a closed,…

A Nonparametric Bayesian Model for Local Clustering We propose a nonparametric Bayesian local clustering (NoB-LoC) approach for heterogeneous data. Using genomics data as an example, the NoB-LoC clusters genes into gene sets and simultaneously creates multiple partitions of samples, one for each gene set. In other words, the sample partitions are nested within the gene sets. Inference is guided by…

Species Sampling Processes: predicting the unpredictable and estimating measures of diversity The sampling of species problem relates to the issue of how to infer the relative species abundances from finite data, when many species occurring in the population are not present in the sample. Although these abundances can be seen to be the ultimate measure…

Semiparametric capture-recapture with heterogeneous capture probabilities Capture-recapture experiments are commonly used to estimate the size of a closed population. Link (2003) has underlined identifiability problems when one wants to make inference with heterogeneous capture probabilities in a semiparametric framework. If subject-specific capture probabilities are random effects with no assumption on the mixing distribution, the conditional…

Bayesian inference for regression discontinuity designs with application to Italian university grants evaluations Regression discontinuity (RD) designs are usually interpreted as local randomized experiments: A RD design can be considered as though it were a randomized experiment for units with a realized value of a so-called forcing variable falling immediately around a pre-fixed threshold. Motivated…

On scaling limits of Markov branching trees Probabilists and combinatorists are interested since a long time in the asymptotic description of large random trees, as, for example, large uniform trees (chosen uniformly at random in a certain class of trees) or large conditioned Galton-Watson trees. After recalling classical results on that topic, we will develop…

Exchangeable Hoeffding decompositions: characterizations and counterexamples Since the pioneering work of Hoeffding in 1948, the so-called Hoeffding-ANOVA decompositions proved to be a very effective tool in obtaining limit theorems and have been widely used in various applications. In this talk, we present the main elements of the theory of Hoeffding decompositions for (infinitely extendible) exchangeable…

Universality and chaos I will describe some recent advances involving universality results for homogeneous sums, both in a classic and free setting. Many connection with influence functions, as well as applications to random matrices will be highlighted.

The combinatorial structure underlying the beta process is that of a continuum of Blackwell-MacQueen urn schemes We uncover a novel urn scheme underlying conditionally independent sequences of Bernoulli processes that share a common beta process hazard measure. As shown by Thibaux and Jordan (2007), in the special case when the underlying beta process has a…

Integrals and cubature sums

Computer emulation with non-stationary Gaussian processes Computer codes are used widely in modern scientific research in complex chemical, thermodynamical and astrophysical processes. These codes deterministically map vectors of high-dimensional inputs into a scalar or vector-valued output, and must be run for many different input configurations to provide an adequate knowledge of the response surface. However,…

Calibrating hybrid pseudo likelihood ratios for a parameter of interest For inference about a parameter of interest in the presence of nuisance parameters, we consider a pseudo likelihood obtained from a genuine or composite likelihood by replacing the nuisance component with an estimate based on a generic estimating equation. Suitable adjustments are developed for the…