Related papers: Minimum Relative Entropy Inference for Normal and …
Exponential models of distributions are widely used in machine learning for classiffication and modelling. It is well known that they can be interpreted as maximum entropy models under empirical expectation constraints. In this work, we…
The paper search for the minimum of the entropy of a two- dimensional distribution in the Fr\'echet class, the class of distributions with given marginals. The main result for discrete distributions is an algorithm for building the…
Minimum disparity estimation in controlled branching processes is dealt with by assuming that the offspring law belongs to a general parametric family. Under some regularity conditions it is proved that the minimum disparity estimators…
Hierarchical Bayesian inference is often conducted with estimates of the target distribution derived from Monte Carlo sums over samples from separate analyses of parts of the hierarchy or from mock observations used to estimate sensitivity…
Motivated by various computational applications, we investigate the problem of estimating nested expectations. Building upon recent work by the authors, we propose a novel Monte Carlo estimator for nested expectations, inspired by sparse…
In the idealized Morgan model of crossover, we study the probability distributions of shared DNA (identical by descent) between individuals having a wide range of relationships (not just lineal descendants), especially cases for which…
Renewal models are widely used in statistical epidemiology as semi-mechanistic models of disease transmission. While primarily used for estimating the instantaneous reproduction number, they can also be used for generating projections,…
We propose extensions and improvements of the statistical analysis of distributed multipoles (SADM) algorithm put forth by Chipot et al. in [6] for the derivation of distributed atomic multipoles from the quantum-mechanical electrostatic…
We give a categorical treatment, in the spirit of Baez and Fritz, of relative entropy for probability distributions defined on standard Borel spaces. We define a category suitable for reasoning about statistical inference on standard Borel…
This paper proposes famillies of multimatricvariate and multimatrix variate distributions based on elliptically contoured laws in the context of real normed division algebras. The work allows to answer the following inference problems about…
We propose a novel approach to perform approximate Bayesian inference in complex models such as Bayesian neural networks. The approach is more scalable to large data than Markov Chain Monte Carlo, it embraces more expressive models than…
For real symmetric matrices that are accessible only through matrix vector products, we present Monte Carlo estimators for computing the diagonal elements. Our probabilistic bounds for normwise absolute and relative errors apply to Monte…
We analyse a multilevel Monte Carlo method for the approximation of distribution functions of univariate random variables. Since, by assumption, the target distribution is not known explicitly, approximations have to be used. We provide an…
We describe an approach to improving model fitting and model generalization that considers the entropy of distributions of modelling residuals. We use simple simulations to demonstrate the observational signatures of overfitting on ordered…
In this paper we propose a family of multivariate asymmetric distributions over an arbitrary subset of set of real numbers which is defined in terms of the well-known elliptically symmetric distributions. We explore essential properties,…
It is important to estimate the errors of probabilistic inference algorithms. Existing diagnostics for Markov chain Monte Carlo methods assume inference is asymptotically exact, and are not appropriate for approximate methods like…
We construct the generalized entropy optimized by a given arbitrary statistical distribution with a finite linear expectation value of a random quantity of interest. This offers, via the maximum entropy principle, a unified basis for a…
Monte Carlo methods to evaluate and maximize the likelihood function enable the construction of confidence intervals and hypothesis tests, facilitating scientific investigation using models for which the likelihood function is intractable.…
We introduce a new approach for amortizing inference in directed graphical models by learning heuristic approximations to stochastic inverses, designed specifically for use as proposal distributions in sequential Monte Carlo methods. We…
We introduce a new class of Monte Carlo based approximations of expectations of random variables such that their laws are only available via certain discretizations. Sampling from the discretized versions of these laws can typically…