Related papers: Beta processes, stick-breaking, and power laws
Without imposing prior distributional knowledge underlying multivariate time series of interest, we propose a nonparametric change-point detection approach to estimate the number of change points and their locations along the temporal axis.…
In bayesian wavelet shrinkage, the already proposed priors to wavelet coefficients are assumed to be symmetric around zero. Although this assumption is reasonable in many applications, it is not general. The present paper proposes the use…
The computation and inversion of the binomial and negative binomial cumulative distribution functions play a key role in many applications. In this paper, we explain how methods used for the central beta distribution function (described in…
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…
We analytically derive the bit-string probability distributions of subsystems of random pure states and depolarized random states using the Dirichlet distribution. We identify the exact Beta distribution as the universal statistical law of…
Gaussian processes retain the linear model either as a special case, or in the limit. We show how this relationship can be exploited when the data are at least partially linear. However from the perspective of the Bayesian posterior, the…
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…
Many scientific and industrial processes produce data that is best analysed as vectors of relative values, often called compositions or proportions. The Dirichlet distribution is a natural distribution to use for composition or proportion…
Statistical inference can be seen as information processing involving input information and output information that updates belief about some unknown parameters. We consider the Bayesian framework for making inferences about dynamical…
The advent of Generative Artificial Intelligence (GAI) has heralded an inflection point that changed how society thinks about knowledge acquisition. While GAI cannot be fully trusted for decision-making, it may still provide valuable…
We introduce the beta generalized exponential distribution that includes the beta exponential and generalized exponential distributions as special cases. We provide a comprehensive mathematical treatment of this distribution. We derive the…
Posterior tempering reduces the influence of the likelihood in the calculation of the posterior by raising the likelihood to a fractional power $\alpha$. The resulting power posterior - also known as an $\alpha$-posterior or fractional…
This study developed a new statistical model and method for analyzing the precision of binary measurement methods from collaborative studies. The model is based on beta-binomial distributions. In other words, it assumes that the sensitivity…
Simplex-valued data appear throughout statistics and machine learning, for example in the context of transfer learning and compression of deep networks. Existing models for this class of data rely on the Dirichlet distribution or other…
Aleatoric uncertainty captures the inherent randomness of the data, such as measurement noise. In Bayesian regression, we often use a Gaussian observation model, where we control the level of aleatoric uncertainty with a noise variance…
We study full Bayesian procedures for high-dimensional linear regression. We adopt data-dependent empirical priors introduced in [1]. In their paper, these priors have nice posterior contraction properties and are easy to compute. Our paper…
Bayesian Additive Regression Trees (BART) is a fully Bayesian approach to modeling with ensembles of trees. BART can uncover complex regression functions with high dimensional regressors in a fairly automatic way and provide Bayesian…
In wavelet shrinkage and thresholding, most of the standard techniques do not consider information that wavelet coefficients might be bounded, although information about bounded energy in signals can be readily available. To address this,…
We present a positive solution to the so-called Bernoulli Conjecture concerning the characterization of sample boundedness of Bernoulli processes. We also discuss some applications and related open problems.
This paper explores large sample properties of the two-parameter $(\alpha,\theta)$ Poisson--Dirichlet Process in two contexts. In a Bayesian context of estimating an unknown probability measure, viewing this process as a natural extension…