Related papers: Quantile pyramids for Bayesian nonparametrics
Indirect inference (II) is a methodology for estimating the parameters of an intractable (generative) model on the basis of an alternative parametric (auxiliary) model that is both analytically and computationally easier to deal with. Such…
This paper presents a simple model that mimics quantum mechanics (QM) results in terms of probability fields of free particles subject to self-interference, without using Schr\"{o}dinger equation or wavefunctions. Unlike the standard QM…
It is notorious that quantum mechanics cannot predict well-defined values for all physical quantities. Less well-known, however, is the fact that quantum mechanics is unable to furnish -- without additional assumptions -- probabilistic…
Non-negative Matrix Factorization (NMF) is a popular tool for data exploration. Bayesian NMF promises to also characterize uncertainty in the factorization. Unfortunately, current inference approaches such as MCMC mix slowly and tend to get…
We propose quantum devices that can realize probabilistically different projective measurements on a qubit. The desired measurement basis is selected by the quantum state of a program register. First we analyze the phase-covariant…
In this paper, we employ variational arguments to establish a connection between ensemble methods for Neural Networks and Bayesian inference. We consider an ensemble-based scheme where each model/particle corresponds to a perturbation of…
One of the main concepts in quantum physics is a density matrix, which is a symmetric positive definite matrix of trace one. Finite probability distributions can be seen as a special case when the density matrix is restricted to be…
One of the key elements of probabilistic seismic risk assessment studies is the fragility curve, which represents the conditional probability of failure of a mechanical structure for a given scalar measure derived from seismic ground…
We propose a posterior for Bayesian Likelihood-Free Inference (LFI) based on generalized Bayesian inference. To define the posterior, we use Scoring Rules (SRs), which evaluate probabilistic models given an observation. In LFI, we can…
After experimenting with a number of non-probabilistic methods for dealing with uncertainty many researchers reaffirm a preference for probability methods [1] [2], although this remains controversial. The importance of being able to form…
Predicting the winner of an election is of importance to multiple stakeholders. To formulate the problem, we consider an independent sequence of categorical data with a finite number of possible outcomes in each. The data is assumed to be…
Simulation models often lack tractable likelihood functions, making likelihood-free inference methods indispensable. Approximate Bayesian computation generates likelihood-free posterior samples by comparing simulated and observed data…
Recursive Bayesian inference, in which posterior beliefs are updated in light of accumulating data, is a tool for implementing Bayesian models in applications with streaming and/or very large data sets. As the posterior of one iteration…
Bayesian approach, as a useful tool for quantifying uncertainties, has been widely used for solving inverse problems of partial differential equations (PDEs). One of the key difficulties for employing Bayesian approach for the issue is how…
Bayesian models provide recursive inference naturally because they can formally reconcile new data and existing scientific information. However, popular use of Bayesian methods often avoids priors that are based on exact posterior…
Given discrete time observations over a growing time interval, we consider a nonparametric Bayesian approach to estimation of the L\'evy density of a L\'evy process belonging to a flexible class of infinite activity subordinators. Posterior…
Copulas are a powerful tool for modeling multivariate distributions as they allow to separately estimate the univariate marginal distributions and the joint dependency structure. However, known parametric copulas offer limited flexibility…
Accurate and precise covariance matrices will be important in enabling planned cosmological surveys to detect new physics. Standard methods imply either the need for many N-body simulations in order to obtain an accurate estimate, or a…
A critical literature review and comprehensive simulation study is used to show that (a) non-parametric bootstrap is a viable alternative to commonly taught and used methods in basic estimation tasks (mean, variance, quartiles, correlation)…
A collection of quantile curves provides a complete picture of conditional distributions. Properly centered and scaled versions of estimated curves at various quantile levels give rise to the so-called quantile regression process (QRP). In…