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In the usual Bayesian setting, a full probabilistic model is required to link the data and parameters, and the form of this model and the inference and prediction mechanisms are specified via de Finetti's representation. In general, such a…
Recent developments in big data and analytics research have produced an abundance of large data sets that are too big to be analyzed in their entirety, due to limits on computer memory or storage capacity. To address these issues,…
We investigate statistical inference across time scales. We take as toy model the estimation of the intensity of a discretely observed compound Poisson process with symmetric Bernoulli jumps. We have data at different time scales:…
This paper presents a novel approach to stochastic mortality modelling by using the Conway--Maxwell--Poisson (CMP) distribution to model death counts. Unlike standard Poisson or negative binomial distributions, the CMP is a more adaptable…
Estimating the entropy rate of discrete time series is a challenging problem with important applications in numerous areas including neuroscience, genomics, image processing and natural language processing. A number of approaches have been…
An unbinned statistical test on cluster-like deviations from Poisson processes for point process data is introduced, presented in the context of time variability analysis of astrophysical sources in count rate experiments. The measure of…
The predictive Bayesian view involves eliciting a sequence of one-step-ahead predictive distributions in lieu of specifying a likelihood function and prior distribution. Recent methods have leveraged predictive distributions which are…
This work is motivated by the analysis of ecological interaction networks. Poisson stochastic blockmodels are widely used in this field to decipher the structure that underlies a weighted network, while accounting for covariate effects.…
We present a rigorous description of the general problem of aperture photometry in high energy astrophysics photon-count images, in which the statistical noise model is Poisson, not Gaussian. We compute the full posterior probability…
It has historically been a challenge to perform Bayesian inference in a design-based survey context. The present paper develops a Bayesian model for sampling inference in the presence of inverse-probability weights. We use a hierarchical…
Markov jump processes (or continuous-time Markov chains) are a simple and important class of continuous-time dynamical systems. In this paper, we tackle the problem of simulating from the posterior distribution over paths in these models,…
The distribution $\mu_{cl}$ of a Poisson cluster process in $X=\mathbb{R}^{d}$ (with i.i.d. clusters) is studied via an auxiliary Poisson measure on the space of configurations in $\mathfrak{X}=\sqcup_{n} X^n$, with intensity measure…
A validated simulation model primarily requires performing an appropriate input analysis mainly by determining the behavior of real-world processes using probability distributions. In many practical cases, probability distributions of the…
We consider non-parametric Bayesian estimation of the drift coefficient of a one-dimensional stochastic differential equation from discrete-time observations on the solution of this equation. Under suitable regularity conditions that are…
We describe a measurement device principle based on discrete iterations of Bayesian updating of system state probability distributions. Although purely classical by nature, these measurements are accompanied with a progressive collapse of…
The Pitman-Yor process is a random probability distribution, that can be used as a prior distribution in a nonparametric Bayesian analysis. The process is of species sampling type and generates discrete distributions, which yield of the…
An informative sampling design leads to the selection of units whose inclusion probabilities are correlated with the response variable of interest. Model inference performed on the resulting observed sample will be biased for the population…
In this paper we consider parameter estimation for discretely observed diffusion processes. In particular, we focus on data that are observed at low frequency and methodology that can estimate parameters with uncertainty quantification.…
Increasingly complex datasets pose a number of challenges for Bayesian inference. Conventional posterior sampling based on Markov chain Monte Carlo can be too computationally intensive, is serial in nature and mixes poorly between posterior…
Frequentist-style large-sample properties of Bayesian posterior distributions, such as consistency and convergence rates, are important considerations in nonparametric problems. In this paper we give an analysis of Bayesian asymptotics…