Related papers: Normalized random measures driven by increasing ad…
A naive theory of additive perturbations on a continuous probability distribution is presented. We propose a new privatization mechanism based on a naive theory of a perturbation on a probability using wavelets, such as a noise perturbs the…
Self-normalized processes are basic to many probabilistic and statistical studies. They arise naturally in the the study of stochastic integrals, martingale inequalities and limit theorems, likelihood-based methods in hypothesis testing and…
Many popular Bayesian nonparametric priors can be characterized in terms of exchangeable species sampling sequences. However, in some applications, exchangeability may not be appropriate. We introduce a {novel and probabilistically coherent…
Covariate measurement error in nonparametric regression is a common problem in nutritional epidemiology and geostatistics, and other fields. Over the last two decades, this problem has received substantial attention in the frequentist…
A discrete-time stochastic process derived from a model of basketball is used to generalize any discrete distribution. The generalized distributions can have one or two more parameters than the parent distribution. Those derived from…
Dirichlet process mixtures are particularly sensitive to the value of the precision parameter controlling the behavior of the latent partition. Randomization of the precision through a prior distribution is a common solution, which leads to…
Random measures provide flexible parameters for Bayesian nonparametric models. Given two different priors for a random measure, we develop a natural framework to investigate the rate at which the corresponding posteriors merge, as the…
This article introduces a novel framework for nonparametric priors on real-valued random vectors, which can be viewed as a multivariate generalization of neutral-to-the right priors. It is based on randomizing the exponent measure of a…
This paper introduces a new approach to the study of rates of convergence for posterior distributions. It is a natural extension of a recent approach to the study of Bayesian consistency. In particular, we improve on current rates of…
In this paper, we introduce the notion of Gaussian processes indexed by probability density functions for extending the Mat\'ern family of covariance functions. We use some tools from information geometry to improve the efficiency and the…
Normalisation in probability theory turns a subdistribution into a proper distribution. It is a partial operation, since it is undefined for the zero subdistribution. This partiality makes it hard to reason equationally about normalisation.…
We present a survey of some of our recent results on Bayesian nonparametric inference for a multitude of stochastic processes. The common feature is that the prior distribution in the cases considered is on suitable sets of piecewise…
In this work, we present a method to generate probability distributions and classes of probability distributions, which broadens a process of probability distribution construction. In this method, distribution classes are built from…
Probabilistic regression models the entire predictive distribution of a response variable, offering richer insights than classical point estimates and directly allowing for uncertainty quantification. While diffusion-based generative models…
The Hierarchical Dirichlet process is a discrete random measure serving as an important prior in Bayesian non-parametrics. It is motivated with the study of groups of clustered data. Each group is modelled through a level two Dirichlet…
In this paper we show that there is a link between approximate Bayesian methods and prior robustness. We show that what is typically recognized as an approximation to the likelihood, either due to the simulated data as in the Approximate…
We study distributional similarity measures for the purpose of improving probability estimation for unseen cooccurrences. Our contributions are three-fold: an empirical comparison of a broad range of measures; a classification of similarity…
The modality is important topic for modelling. Using parametric models is an efficient way when real data set shows trimodality. In this paper we propose a new class of trimodal probability distributions, that is, probability distributions…
Modern applications routinely collect high-dimensional data, leading to statistical models having more parameters than there are samples available. A common solution is to impose sparsity in parameter estimation, often using penalized…
Bayesian models that mix multiple Dirichlet prior parameters, called Multi-Dirichlet priors (MD) in this paper, are gaining popularity. Inferring mixing weights and parameters of mixed prior distributions seems tricky, as sums over…