Related papers: Nested sampling with any prior you like
In this article, we study the binary classification problem with supervised data, in the case where the covariate-to-probability-of-success map is possibly spatially inhomogeneous. We devise nonparametric Bayesian procedures with…
A common problem in Bayesian inference is the sampling of target probability distributions at sufficient resolution and accuracy to estimate the probability density, and to compute credible regions. Often by construction, many target…
High throughput technologies have become the practice of choice for comparative studies in biomedical applications. Limited number of sample points due to sequencing cost or access to organisms of interest necessitates the development of…
In high-dimensional problems, choosing a prior distribution such that the corresponding posterior has desirable practical and theoretical properties can be challenging. This begs the question: can the data be used to help choose a good…
Exoplanet observations are currently analysed with Bayesian retrieval techniques. Due to the computational load of the models used, a compromise is needed between model complexity and computing time. Analysis of data from future facilities,…
This paper describes a Bayesian method for learning causal networks using samples that were selected in a non-random manner from a population of interest. Examples of data obtained by non-random sampling include convenience samples and…
Bayesian hierarchical models have been demonstrated to provide efficient algorithms for finding sparse solutions to ill-posed inverse problems. The models comprise typically a conditionally Gaussian prior model for the unknown, augmented by…
Bayesian deep learning counts on the quality of posterior distribution estimation. However, the posterior of deep neural networks is highly multi-modal in nature, with local modes exhibiting varying generalization performance. Given a…
The goal of this thesis is twofold; introduce the fundamentals of Bayesian inference and computation focusing on astronomical and cosmological applications, and present recent advances in probabilistic computational methods developed by the…
Divide-and-conquer based methods for Bayesian inference provide a general approach for tractable posterior inference when the sample size is large. These methods divide the data into smaller subsets, sample from the posterior distribution…
As an alternative to variable selection or shrinkage in high dimensional regression, we propose to randomly compress the predictors prior to analysis. This dramatically reduces storage and computational bottlenecks, performing well when the…
Approximate Bayesian computation (ABC) methods are standard tools for inferring parameters of complex models when the likelihood function is analytically intractable. A popular approach to improving the poor acceptance rate of the basic…
Consistent sampling is a technique for specifying, in small space, a subset $S$ of a potentially large universe $U$ such that the elements in $S$ satisfy a suitably chosen sampling condition. Given a subset $\mathcal{I}\subseteq U$ it…
Data sets for statistical analysis become extremely large even with some difficulty of being stored on one single machine. Even when the data can be stored in one machine, the computational cost would still be intimidating. We propose a…
We introduce non-stationary Mat\'ern field priors with stochastic partial differential equations, and construct correlation length-scaling with hyperpriors. We model both the hyperprior and the Mat\'ern prior as continuous-parameter random…
Standard deep neural networks (DNNs) are commonly trained in an end-to-end fashion for specific tasks such as object recognition, face identification, or character recognition, among many examples. This specificity often leads to…
Estimation of the population size $n$ from $k$ i.i.d.\ binomial observations with unknown success probability $p$ is relevant to a multitude of applications and has a long history. Without additional prior information this is a notoriously…
Sum-product networks (SPNs) are probabilistic models characterized by exact and fast evaluation of fundamental probabilistic operations. Its superior computational tractability has led to applications in many fields, such as machine…
The recently introduced nested sampling algorithm allows the direct and efficient calculation of the partition function of atomistic systems. We demonstrate its applicability to condensed phase systems with periodic boundary conditions by…
This paper considers properties of an optimization based sampler for targeting the posterior distribution when the likelihood is intractable and auxiliary statistics are used to summarize information in the data. Our reverse sampler…