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…

The generalised autocovariance function The generalised autocovariance  function is defined for a stationary stochastic process as the inverse Fourier transform of the power transformation of the spectral density function. Depending on the value of the transformation parameter, this function nests the inverse  and the traditional autocovariance functions. A frequency domain non-parametric estimator based on the…

Applications of Bayesian Networks to Operational Risks, Healthcare, Biotechnology and Customer Surveys Modelling cause and effect relationships has been a major challenge for statisticians in a wide range of application areas. Bayesian Networks combine graphical analysis with Bayesian analysis to represent descriptive causality maps linking measured and target variables. Such maps can be used for…

On frequentist coverage of Bayesian credible sets Adaptive techniques for nonparametric estimation have been widely stud- ied in the literature and many rate-adaptive results have been provided for a variety of statistical problems. However an adaptive estimator without any knowledge of its uncertainty is rather uninformative, since one knows that the estimator is optimally close…

Collaboration in social networks The very notion of social network implies that linked individuals interact repeatedly with each other. This notion allows them not only to learn successful strategies and adapt to them, but also to condition their own behavior on the behavior of others, in a strategic forward looking manner. Game theory of repeated…

Using secondary outcomes and covariates to sharpen inference in randomized experiments with noncompliance Restrictions implied by the randomization of treatment assignment on the joint distribution of a primary outcome and an auxiliary variable are used to tighten nonparametric bounds for intention-to-treat effects on the primary outcome for some latent subpopulations, without requiring the exclusion restriction…

The Bernstein - von Mises theorem: relaxing its assumptions and extending it to nonregular models The Bernstein - von Mises theorem is an important result in Bayesian asymptotics, giving conditions under which the posterior distribution of a finite-dimensional parameter can be approximated by the Gaussian distribution. On one hand, this result quantifies consistency and efficiency…

Design of experiments: from physical to simulated Since Fisher’s times, the principles for planning scientific experiments correctly have been at the heart of the statistical debate. This is particularly important in a clinical context, for ethical as well as inferential reasons. After a brief excursus through the history of experimental design, this presentation will deal…

Diffusion trees as priors The Dirichlet diffusion tree has attractive theoretical properties and empirical performance on various tasks. We present an extension which removes the restriction to binary trees allowing arbitrary branching structure, the Pitman Yor diffusion tree. We show this process is exchangeable and projective. Both the DDT and PYDT can be constructed as…

Ancestral lineages under local regulation The spatial embeddings of genealogies in models with fluctuating population sizes and local regulation are relatively complicated random walks in a space-time dependent random environment. They seem presently not well understood. We use the supercritical discrete-time contact process on Z^d as the simplest non-trivial example of a locally regulated population…

"Optimal Hiring and Retention Policies for Heterogeneous Workers who Learn"

Efficient MCMC for Continuous Time Discrete State Systems A variety of phenomena are best described using dynamical models whichoperate on a discrete state space and in continuous time. Examplesinclude Markov jump processes, continuous time Bayesian networks,renewal processes and other point processes, with applications rangingfrom systems biology, neuroscience, genetics, computing networks andhuman-computer interactions. Posterior computations typically…

Towards Uncertainty Quantification and Inference in the stochastic SIR Epidemic Model We introduce a novel method to conduct inference with models defined through a continuous-time Markov process, and we apply these results to a classical stochastic SIR model as a case study. We obtain approximations for first and second moments for the state variables. These…

Symmetries of probability distributions, their geometric meaning and financial applications The talk starts with the known put-call symmetry property and its application to semi-static hedging of barrier options. Then it is explained how to interpret this property geometrically and extend it in various ways, most importantly for the multivariate (multiasset) case that would correspond to…

A Bayesian analysis of reversible time series with an uncertain length of memory We propose a Bayesian analysis of reversible time series using a Probabilistic Suffix Automaton (PSA) model. We show that PSAs have a representation as higher-order Markov chains, and that the class of reversible PSAs generalize reversible variable-order Markov chains. The analysis uses…

"Impossibility Results for Nondifferentiable Functionals"

"Finitely additive probabilities in statistics"

"Subjective probability as a normative theory of rational belief"

"Extensions of Mallows' distribution on permutations and the q-exchangeability"