Related papers: Bayesian Nonparametric Analysis of Multivariate Ti…
We propose a Bayesian nonparametric model for mixed-type bounded data, where some variables are compositional and others are interval-bounded. Compositional variables are non-negative and sum to a given constant, such as the proportion of…
We investigate Bayesian non-parametric inference of the $\Lambda$-measure of $\Lambda$-coalescent processes with recurrent mutation, parametrised by probability measures on the unit interval. We give verifiable criteria on the prior for…
The remarkable generalization performance of large-scale models has been challenging the conventional wisdom of the statistical learning theory. Although recent theoretical studies have shed light on this behavior in linear models and…
In this publication, we combine two Bayesian non-parametric models: the Gaussian Process (GP) and the Dirichlet Process (DP). Our innovation in the GP model is to introduce a variation on the GP prior which enables us to model structured…
We investigate an empirical Bayesian nonparametric approach to a family of linear inverse problems with Gaussian prior and Gaussian noise. We consider a class of Gaussian prior probability measures with covariance operator indexed by a…
This work studies nonparametric Bayesian estimation of the intensity function of an inhomogeneous Poisson point process in the important case where the intensity depends on covariates, based on the observation of a single realisation of the…
The spectral densities of ensembles of non-Hermitian sparse random matrices are analysed using the cavity method. We present a set of equations from which the spectral density of a given ensemble can be efficiently and exactly calculated.…
We propose a general nonparametric Bayesian framework for binary regression, which is built from modeling for the joint response-covariate distribution. The observed binary responses are assumed to arise from underlying continuous random…
Spectral density matrix estimation of multivariate time series is a classical problem in time series and signal processing. In modern neuroscience, spectral density based metrics are commonly used for analyzing functional connectivity among…
We develop nonparametric Bayesian modelling approaches for Poisson processes, using weighted combinations of structured beta densities to represent the point process intensity function. For a regular spatial domain, such as the unit square,…
For a Bayesian, real-time forecasting with the posterior predictive distribution can be challenging for a variety of time series models. First, estimating the parameters of a time series model can be difficult with sample-based approaches…
Missing values are ubiquitous in (data) science, with potential detrimental consequences for any statistical analysis. As a consequence, a wealth of methods and theoretical results have been developed in recent years. Still, many questions…
When we use simulation to assess the performance of stochastic systems, the input models used to drive simulation experiments are often estimated from finite real-world data. There exist both input model and simulation estimation…
Bayesian nonparametric mixture models are common for modeling complex data. While these models are well-suited for density estimation, recent results proved posterior inconsistency of the number of clusters when the true number of…
We consider the asymptotic behavior of posterior distributions and Bayes estimators based on observations which are required to be neither independent nor identically distributed. We give general results on the rate of convergence of the…
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…
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…
We propose a new framework for imposing monotonicity constraints in a Bayesian nonparametric setting based on numerical solutions of stochastic differential equations. We derive a nonparametric model of monotonic functions that allows for…
Ensemble learning is a mainstay in modern data science practice. Conventional ensemble algorithms assign to base models a set of deterministic, constant model weights that (1) do not fully account for individual models' varying accuracy…
In this paper the Bayesian analysis is applied to assign a probability density to the value of a quantity having a definite sign. This analysis is logically consistent with the results, positive or negative, of repeated measurements.…