Related papers: Density Estimation via Bayesian Inference Engines

Although discrete mixture modeling has formed the backbone of the literature on Bayesian density estimation, there are some well known disadvantages. We propose an alternative class of priors based on random nonlinear functions of a uniform…

Histograms are convenient non-parametric density estimators, which continue to be used ubiquitously. Summary quantities estimated from histogram-based probability density models depend on the choice of the number of bins. We introduce a…

This article revisits the problem of Bayesian shape-restricted inference in the light of a recently developed approximate Gaussian process that admits an equivalent formulation of the shape constraints in terms of the basis coefficients. We…

It has historically been a challenge to perform Bayesian inference in a design-based survey context. The present paper develops a Bayesian model for sampling inference in the presence of inverse-probability weights. We use a hierarchical…

In order to develop reliable services using machine learning, it is important to understand the uncertainty of the model outputs. Often the probability distribution that the prediction target follows has a complex shape, and a mixture…

It is well known that the output of a Neural Network trained to disentangle between two classes has a probabilistic interpretation in terms of the a-posteriori Bayesian probability, provided that a unary representation is taken for the…

We consider the problem of Bayesian density estimation on the positive semiline for possibly unbounded densities. We propose a hierarchical Bayesian estimator based on the gamma mixture prior which can be viewed as a location mixture. We…

Neural network-based methods for (un)conditional density estimation have recently gained substantial attention, as various neural density estimators have outperformed classical approaches in real-data experiments. Despite these empirical…

Bayesian inference is an effective approach for solving statistical learning problems especially with uncertainty and incompleteness. However, inference efficiencies are physically limited by the bottlenecks of conventional computing…

We consider estimating the parameters of a Gaussian mixture density with a given number of components best representing a given set of weighted samples. We adopt a density interpretation of the samples by viewing them as a discrete Dirac…

Approximate Bayesian Computation is a family of likelihood-free inference techniques that are well-suited to models defined in terms of a stochastic generating mechanism. In a nutshell, Approximate Bayesian Computation proceeds by computing…

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…

This paper describes how to specify probability models for data analysis via a backward induction procedure. The new approach yields coherent, prior-free uncertainty assessment. After presenting some intuition-building examples, the new…

Recent advances in computing power and the potential to make more realistic assumptions due to increased flexibility have led to the increased prevalence of simulation models in economics. While models of this class, and particularly…

State-space models (SSMs) provide a flexible framework for modelling time-series data. Consequently, SSMs are ubiquitously applied in areas such as engineering, econometrics and epidemiology. In this paper we provide a fast approach for…

We describe a method to computationally estimate the probability density function of a univariate random variable by applying the maximum entropy principle with some local conditions given by Gaussian functions. The estimation errors and…

The number of modes in a probability density function is representative of the complexity of a model and can also be viewed as the number of subpopulations. Despite its relevance, there has been limited research in this area. A novel…

The Design of Experiments (DOEs) is a fundamental scientific methodology that provides researchers with systematic principles and techniques to enhance the validity, reliability, and efficiency of experimental outcomes. In this study, we…

Kernel density estimation is a popular method for estimating unseen probability distributions. However, the convergence of these classical estimators to the true density slows down in high dimensions. Moreover, they do not define meaningful…

Expectation propagation is a general prescription for approximation of integrals in statistical inference problems. Its literature is mainly concerned with Bayesian inference scenarios. However, expectation propagation can also be used to…