Related papers: Bayesian Entropy Estimation for Countable Discrete…
Dirichlet process mixture model (DPMM) is a popular Bayesian nonparametric model. In this paper, we apply this model to weighted data and then estimate the un-weighted distribution from the corresponding weighted distribution using the…
This article provides a completion to theories of information based on entropy, resolving a longstanding question in its axiomatization as proposed by Shannon and pursued by Jaynes. We show that Shannon's entropy function has a…
We present a Bayesian model for estimating the joint distribution of multivariate categorical data when units are nested within groups. Such data arise frequently in social science settings, for example, people living in households. The…
This paper introduces a general class of hierarchical nonparametric prior distributions. The random probability measures are constructed by a hierarchy of generalized species sampling processes with possibly non-diffuse base measures. The…
We consider nonparametric Bayesian estimation of a probability density $p$ based on a random sample of size $n$ from this density using a hierarchical prior. The prior consists, for instance, of prior weights on the regularity of the…
Many modern experiments, such as microarray gene expression and genome-wide association studies, present the problem of estimating a large number of parallel effects. Bayesian inference is a popular approach for analyzing such data by…
The family of log-concave density functions contains various kinds of common probability distributions. Due to the shape restriction, it is possible to find the nonparametric estimate of the density, for example, the nonparametric maximum…
This paper develops nonparametric estimation for discrete choice models based on the mixed multinomial logit (MMNL) model. It has been shown that MMNL models encompass all discrete choice models derived under the assumption of random…
This paper reconsiders the problem of calculating the expected set of probabilities <p_i>, given the observed set of items {m_i}, that are distributed among n bins with an (unknown) set of probabilities {p_i} for being placed in the ith…
A Dirichlet polynomial $d$ in one variable ${\mathcal{y}}$ is a function of the form $d({\mathcal{y}})=a_n n^{\mathcal{y}}+\cdots+a_22^{\mathcal{y}}+a_11^{\mathcal{y}}+a_00^{\mathcal{y}}$ for some $n,a_0,\ldots,a_n\in\mathbb{N}$. We will…
A compound Poisson process whose parameters are all unknown is observed at finitely many equispaced times. Nonparametric estimators of the jump and L\'evy distributions are proposed and functional central limit theorems using the uniform…
The hierarchical Dirichlet process (HDP) has become an important Bayesian nonparametric model for grouped data, such as document collections. The HDP is used to construct a flexible mixed-membership model where the number of components is…
The fidelity-based smooth min-relative entropy is a distinguishability measure that has appeared in a variety of contexts in prior work on quantum information, including resource theories like thermodynamics and coherence. Here we provide a…
The paper develops new methods of non-parametric estimation a compound Poisson distribution. Such a problem arise, in particular, in the inference of a Levy process recorded at equidistant time intervals. Our key estimator is based on…
We introduce a Bayesian approach to predictive density calibration and combination that accounts for parameter uncertainty and model set incompleteness through the use of random calibration functionals and random combination weights.…
Directional data require specialized probability models because of the non-Euclidean and periodic nature of their domain. When a directional variable is observed jointly with linear variables, modeling their dependence adds an additional…
The entropy rates of the Wright-Fisher process, the Moran process, and generalizations are computed and used to compare these processes and their dependence on standard evolutionary parameters. Entropy rates are measures of the variation…
Mixture models are commonly used in applications with heterogeneity and overdispersion in the population, as they allow the identification of subpopulations. In the Bayesian framework, this entails the specification of suitable prior…
The estimation of entropy rates for stationary discrete-valued stochastic processes is a well studied problem in information theory. However, estimating the entropy rate for stationary continuous-valued stochastic processes has not received…
In probabilistic (Bayesian) inferences, we typically want to compute properties of the posterior distribution, describing knowledge of unknown quantities in the context of a particular dataset and the assumed prior information. The marginal…