相关论文: Isoperimetry between exponential and Gaussian

We compute approximate solutions to inverse problems for determining parameters in differential equation models with stochastic data on output quantities. The formulation of the problem and modeling framework define a solution as a…

In this paper we consider Bayesian estimation for the parameters of inverse Gaussian distribution. Our emphasis is on Markov Chain Monte Carlo methods. We provide complete implementation of the Gibbs sampler algorithm. Assuming an…

Tempered stable distributions are frequently used in financial applications (e.g., for option pricing) in which the tails of stable distributions would be too heavy. Given the non-explicit form of the probability density function,…

Models with intractable likelihood functions arise in areas including network analysis and spatial statistics, especially those involving Gibbs random fields. Posterior parameter es timation in these settings is termed a doubly-intractable…

We introduce the key concepts of duality mappings and metric extensor. The fundamental identities involving the duality mappings are presented, and we disclose the logical equivalence between the so-called metric tensor and the metric…

For a dynamical system satisfying the approximate product property and asymptotically entropy expansiveness, we characterize a delicate structrue of the space of invariant measures: The ergodic measures of intermediate entropies and…

In this article we compare solutions to elliptic problems having rapidly oscillated conductivity (permeability, etc) coefficient with solutions to corresponding homogenized problems obtained from two-scale extensions of the initial…

Bayesian probabilistic numerical methods are a set of tools providing posterior distributions on the output of numerical methods. The use of these methods is usually motivated by the fact that they can represent our uncertainty due to…

Inverse Probability Weighting (IPW) is widely used in empirical work in economics and other disciplines. As Gaussian approximations perform poorly in the presence of "small denominators," trimming is routinely employed as a regularization…

It is well-known that a quantum measurement can enhance the transition probability between two quantum states. Such a measurement operates after preparation of the initial state and before postselecting for the final state. Here we analyze…

Gaussian process regression is a popular Bayesian framework for surrogate modeling of expensive data sources. As part of a broader effort in scientific machine learning, many recent works have incorporated physical constraints or other a…

We study the weak convergence (in the high-frequency limit) of the parameter estimators of power spectrum coefficients associated with Gaussian, spherical and isotropic random fields. In particular, we introduce a Whittle-type approximate…

Given any two probability measures on a Euclidean space with mean 0 and finite variance, we demonstrate that the two probability measures are orthogonal in the sense of Wasserstein geometry if and only if the two spaces by spanned by the…

There is a wide range of applications where the local extrema of a function are the key quantity of interest. However, there is surprisingly little work on methods to infer local extrema with uncertainty quantification in the presence of…

We study Bayesian inference methods for solving linear inverse problems, focusing on hierarchical formulations where the prior or the likelihood function depend on unspecified hyperparameters. In practice, these hyperparameters are often…

Applications in data science, shape analysis and object classification frequently require comparison of probability distributions defined on different ambient spaces. To accomplish this, one requires a notion of distance on a given class of…

We study analogies between the rational integers on the real line and the Gaussian integers on other lines in the complex plane. This includes a Gaussian analog of Bertrands Postulate, the Chinese Remainder Theorem, and the periodicity of…

We discuss the correspondence between Gaussian process regression and Geometric Harmonics, two similar kernel-based methods that are typically used in different contexts. Research communities surrounding the two concepts often pursue…

We consider nonparametric testing in a non-asymptotic framework. Our statistical guarantees are exact in the sense that Type I and II errors are controlled for any finite sample size. Meanwhile, one proposed test is shown to achieve minimax…

By considering probability distributions over the set of assignments the expected truth values assignment to propositional variables are extended through linear operators, and the expected truth values of the clauses at any given…