Branching Brownian motion with absorption What does the genealogy of a population under selection look like? This question is crucial for ecology and evolutionary biology and yet it is not fully understood. Recently, Brunet and Derrida have conjectured that for a whole class of models of such populations, we can expect the genealogy to be…

High dimensional jump processes with stochastic volatility We deal with the problem of identifying jumps in multiple financial time series using the stochastic volatility model combined with a jump process. We develop efficient MCMC algorithms to perform Bayesian inference for the parameters and the latent states of the proposed models. In the univariate case we…

Functions, Manifolds and Statistical Linguistics Functional Data Analysis concerns the statistical study of curves and surfaces. An extension, Functional Object Data Analysis, looks at the statistical analysis of curves and surfaces which live in restricted spaces, such as on manifolds. One particular example of these are the covariance functions associated with the underlying curves. These…

Dependent Generalised Dirichlet Process Priors We propose a novel Bayesian nonparametric process prior for modelling a collections of random discrete distributions. This process is defined by combining a Generalised Dirichlet Process with a suitable Beta regression framework that introduces dependence among the discrete random distributions. This strategy allows for covariate dependent clustering of the observations.…

Concentration inequalities in the infinite urn scheme for occupancy counts and the missing mass, with applications to Good-Turing estimators and adaptive statistical text compression An infinite urn scheme is defined by a probability mass function over positive integers. A random allocation consists of a sample of N independent drawings according to this probability distribution where…

Path and parameter inference for Markov jump processes A variety of phenomena are best described using dynamical models which operate on a discrete state-space and in continuous time. The most common example is the Markov jump processes whose applications range from systems biology, genetics, computing networks and human-computer interactions. Posterior computations typically involve approximations like…

Fast Quantification of Uncertainty and Robustness with Variational Bayes In Bayesian analysis, the posterior follows from the data and a choice of a prior and a likelihood. These choices may be somewhat subjective and reasonably vary over some range. Thus, we wish to measure the sensitivity of posterior estimates to variation in these choices. While…

Bayesian nonparametric approaches for the analysis of compositional data based on Bernstein polynomials We will discuss Bayesian nonparametric procedures for density estimation and fully nonparametric regression for compositional data, that is, data supported in a multidimensional simplex. The procedures are based on modified classes of Bernstein polynomials. We show that the modified classes retain the…

Bayesian modelling of networks in business intelligence problems Complex network data problems are increasingly common in many fields of application. Our motivation is drawn from strategic marketing studies monitoring customer choices of specific products, along with co-subscription networks encoding multiple purchasing behavior. Data are available for several agencies within the same insurance company, and our…

A Bayesian Nonparametric model for microbiome data analysis We develop a statistical model to analyse microbiome profiling data based on sequencing of genetic fingerprints in 16S ribosomal RNA. The analysis allows us to quantify the uncertainty in  ecological ordination and clustering methods commonly applied in microbiome research. In addition, it can be extended into a…

Predicting the Present with Bayesian Structural Time Series This article describes a system for short term forecasting based on an ensemble prediction that averages over different combinations of predictors. The system combines a structural time series model for the target series with regression component capturing the contributions of contemporaneous search query data. A spike-and-slab prior…

Bayesian Factor Models in High Dimensions Sparse Bayesian factor models are routinely implemented for parsimonious dependence modeling and dimensionality reduction in high-dimensional applications. We provide theoretical understanding of such Bayesian procedures in terms of posterior convergence rates in inferring high-dimensional covariance matrices where the dimension can be larger than the sample size. We will also…

Nonparametric Bayesian inference for discretely sampled diffusions We consider the nonlinear statistical inverse problem ofmaking inference on the unknown parameters of a diffusion processdescribing the solution of a stochastic differential equation. Theobservation regime is such that the process is sampled at discretetime points that are a fixed distance apart, and we investigate theasymptotic regime when…

Robust Approximate Bayesian Inference The likelihood function is the basis of both frequentist and Bayesian methods. However, the stability of likelihood-based procedures requires strict adherence to the model assumptions: mild deviations from the model can lead to misleading inferential results. A possible Bayesian solution to robustness is to use a of robust pseudo likelihood, such…

The information complexity of sequential resource allocation I will talk about sequential resource allocation, under the so-called stochastic multi-armed bandit model. In this model, an agent interacts with a set of (unknown) probability distributions, called 'arms' (in reference to 'one-armed bandits', another name for slot machines in a casino). When the agent draws an arm,…

An inferential theory of clustering for functional data Recently, it has been shown that Morse theory can be exploited to de- velop a sound inferential background for clustering: one can rigorously define both population and empirical clusters by means of the gradient flows asso- ciated to the population density p and the estimated density pˆ.…

Bayesian inference for intra-tumor heterogeneity in mutations and copy number variation Tissue samples from the same tumor are heterogeneous. They consist of different subclones that can be characterized by differences in DNA nucleotide sequences and copy numbers on multiple loci. Inference on tumor heterogeneity thus involves the identification of the subclonal copy number and single…

Relative exchangeability Symmetry arguments lie at the heart of classical considerations in inductive inference and statistics.  In statistics, de Finetti's notion of exchangeability is the most prominent symmetry assumption, laying the foundation for Bayesian inference.  In practice, many statistical and scientific problems exhibit only partial symmetry determined by some underlying structure in a population.  As…

Exact simulation of the Wright-Fisher diffusion The Wright-Fisher family of diffusion processes is a class of evolutionary models widely used in population genetics, with applications also in finance and Bayesian statistics. Simulation and inference from these diffusions is therefore of widespread interest. However, simulating a Wright-Fisher diffusion is difficult because there is no known closed-form…