Related papers: Hierarchical Species Sampling Models
Normalised generalised gamma processes are random probability measures that induce nonparametric prior distributions widely used in Bayesian statistics, particularly for mixture modelling. We construct a class of dependent normalised…
We introduce a novel statistical significance-based approach for clustering hierarchical data using semi-parametric linear mixed-effects models designed for responses with laws in the exponential family (e.g., Poisson and Bernoulli). Within…
Discrete Bayesian nonparametric models whose expectation is a convex linear combination of a point mass at some point of the support and a diffuse probability distribution allow to incorporate strong prior information, while still being…
A Bayesian approach to the classification problem is proposed in which random partitions play a central role. It is argued that the partitioning approach has the capacity to take advantage of a variety of large-scale spatial structures, if…
The Pitman-Yor process is a random discrete probability distribution of which the atoms can be used to model the relative abundance of species. The process is indexed by a type parameter $\sigma$, which controls the number of different…
Motivated by the fundamental problem of measuring species diversity, this paper introduces the concept of a cluster structure to define an exchangeable cluster probability function that governs the joint distribution of a random count and…
This paper considers the topic of finding prior distributions when a major component of the statistical model depends on a nonlinear function. Using results on how to construct uniform distributions in general metric spaces, we propose a…
Generalized linear models and the quasi-likelihood method extend the ordinary regression models to accommodate more general conditional distributions of the response. Nonparametric methods need no explicit parametric specification, and the…
In Bayesian nonparametrics there exists a rich variety of discrete priors, including the Dirichlet process and its generalizations, which are nowadays well-established tools. Despite the remarkable advances, few proposals are tailored for…
Prior specification for nonparametric Bayesian inference involves the difficult task of quantifying prior knowledge about a parameter of high, often infinite, dimension. Realistically, a statistician is unlikely to have informed opinions…
Variable selection techniques have become increasingly popular amongst statisticians due to an increased number of regression and classification applications involving high-dimensional data where we expect some predictors to be unimportant.…
Gibbs type priors have been shown to be natural generalizations of Dirichlet process (DP) priors used for intricate applications of Bayesian nonparametric methods. This includes applications to mixture models and to species sampling models…
The Hierarchical Mixture of Experts (HME) is a well-known tree-based model for regression and classification, based on soft probabilistic splits. In its original formulation it was trained by maximum likelihood, and is therefore prone to…
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…
We study nonparametric Bayesian binary classification, in the case where the unknown probability response function is possibly spatially inhomogeneous, for example, being generally flat across the domain but presenting localized sharp…
Combining distributions is an important issue in decision theory and Bayesian inference. Logarithmic pooling is a popular method to aggregate expert opinions by using a set of weights that reflect the reliability of each information source.…
We introduce a novel Bayesian estimator for the class proportion in an unlabeled dataset, based on the targeted learning framework. Our procedure requires the specification of a prior (and outputs a posterior) only for the target of…
Posterior computation in hierarchical Dirichlet process (HDP) mixture models is an active area of research in nonparametric Bayes inference of grouped data. Existing literature almost exclusively focuses on the Chinese restaurant franchise…
We derive the class of normalized generalized Gamma processes from Poisson-Kingman models (Pitman, 2003) with tempered alfa-stable mixing distribution. Relying on this construction it can be shown that in Bayesian nonparametrics, results on…
Label bias occurs when the outcome of interest is not directly observable and instead, modeling is performed with proxy labels. When the difference between the true outcome and the proxy label is correlated with predictors, this can yield…