Related papers: Bayesian Inference for Multivariate Monotone Densi…

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 consider a non-parametric Bayesian model for conditional densities. The model is a finite mixture of normal distributions with covariate dependent multinomial logit mixing probabilities. A prior for the number of mixture components is…

We consider a Bayesian method for simultaneous quantile regression on a real variable. By monotone transformation, we can make both the response variable and the predictor variable take values in the unit interval. A representation of…

Uncovering genuine relationships between a response variable of interest and a large collection of covariates is a fundamental and practically important problem. In the context of Gaussian linear models, both the Bayesian and non-Bayesian…

We explain how effective automatic probability density function estimates can be constructed using contemporary Bayesian inference engines such as those based on no-U-turn sampling and expectation propagation. Extensive simulation studies…

In statistical modeling of computer experiments sometimes prior information is available about the underlying function. For example, the physical system simulated by the computer code may be known to be monotone with respect to some or all…

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…

In this paper we propose methods for inference of the geometric features of a multivariate density. Our approach uses multiscale tests for the monotonicity of the density at arbitrary points in arbitrary directions. In particular, a…

We propose the density ratio permutation test, a hypothesis test that assesses whether the ratio between two densities is proportional to a known function based on independent samples from each distribution. The test uses an efficient…

Many statistical models can be simulated forwards but have intractable likelihoods. Approximate Bayesian Computation (ABC) methods are used to infer properties of these models from data. Traditionally these methods approximate the posterior…

In this paper we provide new methodology for inference of the geometric features of a multivariate density in deconvolution. Our approach is based on multiscale tests to detect significant directional derivatives of the unknown density at…

Given i.i.d. data from an unknown distribution, we consider the problem of predicting future items. An adaptive way to estimate the probability density is to recursively subdivide the domain to an appropriate data-dependent granularity. A…

Bayesian density deconvolution using nonparametric prior distributions is a useful alternative to the frequentist kernel based deconvolution estimators due to its potentially wide range of applicability, straightforward uncertainty…

Suppose that a compound Poisson process is observed discretely in time and assume that its jump distribution is supported on the set of natural numbers. In this paper we propose a non-parametric Bayesian approach to estimate the intensity…

The need to estimate smooth probability distributions (a.k.a. probability densities) from finite sampled data is ubiquitous in science. Many approaches to this problem have been described, but none is yet regarded as providing a definitive…

We introduce a multiscale test statistic based on local order statistics and spacings that provides simultaneous confidence statements for the existence and location of local increases and decreases of a density or a failure rate. The…

Outer measures can be used for statistical inference in place of probability measures to bring flexibility in terms of model specification. The corresponding statistical procedures such as Bayesian inference, estimators or hypothesis…

In this paper, we study a class of non-parametric density estimators under Bayesian settings. The estimators are piecewise constant functions on binary partitions. We analyze the concentration rate of the posterior distribution under a…

When we use the normal mixture model, the optimal number of the components describing the data should be determined. Testing homogeneity is good for this purpose; however, to construct its theory is challenging, since the test statistic…

A random set is a generalisation of a random variable, i.e. a set-valued random variable. The random set theory allows a unification of other uncertainty descriptions such as interval variable, mass belief function in Dempster-Shafer theory…