Related papers: Enriched Pitman-Yor processes
In a given problem, the Bayesian statistical paradigm requires the specification of a prior distribution that quantifies relevant information about the unknowns of main interest external to the data. In cases where little such information…
This paper presents a novel Bayesian approach for hyperspectral image unmixing. The observed pixels are modeled by a linear combination of material signatures weighted by their corresponding abundances. A spike-and-slab abundance prior is…
We give a extensive account of a recent new way of applying the Dirichlet form theory to random Poisson measures. The main application is to obtain existence of density for thelaws of random functionals of L\'evy processes or solutions of…
Evidential Deep Learning (EDL) is a popular framework for uncertainty-aware classification that models predictive uncertainty via Dirichlet distributions parameterized by neural networks. Despite its popularity, its theoretical foundations…
Predictive recursion (PR) is a fast algorithm for nonparametric estimation of a mixing density, with connections to sequential Bayesian updating under a Dirichlet process prior and rigorous frequentist consistency guarantees. Extending PR…
The Euler-Poisson (EP) system models the dynamics of a variety of physical processes, including charge transport, collisional plasmas, and certain cosmological wave phenomena. In this work, we establish sharp critical threshold conditions…
Recent advances in Bayesian models for random partitions have led to the formulation and exploration of Exchangeable Sequences of Clusters (ESC) models. Under ESC models, it is the cluster sizes that are exchangeable, rather than the…
Some linear integro-differential operators have old and classical representations as the Dirichlet-to-Neumann operators for linear elliptic equations, such as the 1/2-Laplacian or the generator of the boundary process of a reflected…
Statistical modelling in the presence of data organized in groups is a crucial task in Bayesian statistics. The present paper conceives a mixture model based on a novel family of Bayesian priors designed for multilevel data and obtained by…
Micro and survey datasets often contain private information about individuals, like their health status, income or political preferences. Previous studies have shown that, even after data anonymization, a malicious intruder could still be…
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…
The entropic way of formulating Heisenberg's uncertainty principle not only plays a fundamental role in applications of quantum information theory but also is essential for manifesting genuine nonclassical features of quantum systems. In…
Variance parameters in additive models are typically assigned independent priors that do not account for model structure. We present a new framework for prior selection based on a hierarchical decomposition of the total variance along a…
The ongoing unprecedented exponential explosion of available computing power, has radically transformed the methods of statistical inference. What used to be a small minority of statisticians advocating for the use of priors and a strict…
This paper studies posterior concentration behavior of the base probability measure of a Dirichlet measure, given observations associated with the sampled Dirichlet processes, as the number of observations tends to infinity. The base…
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…
In the present paper new insights into the study of the Non-central Dirichlet distribution are provided. This latter is the analogue of the Dirichlet distribution obtained by replacing the Chi-Squared random variables involved in its…
We consider the problem of drawing samples from posterior distributions formed under a Dirichlet prior and a truncated multinomial likelihood, by which we mean a Multinomial likelihood function where we condition on one or more counts being…
Copula-based dependence modeling often relies on parametric formulations. This is mathematically convenient, but can be statistically inefficient when the parametric families are not suitable for the data and model in focus. A Bayesian…
Exceptional points (EPs) are complex singularities of parametric linear operators where two or more eigenvalues and eigenvectors coalesce. EPs are attracting increasing interest in mechanical metamaterials due to their strong potentials for…