相关论文: How to Use Experimental Data to Compute the Probab…

This guide offers suggestions/insights on uncertainty quantification of nuclear structure models. We discuss a simple approach to statistical error estimates, strategies to assess systematic errors, and show how to uncover…

Test log-likelihood is commonly used to compare different models of the same data or different approximate inference algorithms for fitting the same probabilistic model. We present simple examples demonstrating how comparisons based on test…

Bayesian hypothesis testing via Bayes factors offers a principled alternative to classical p-value methods in meta-analysis, particularly suited to its cumulative and sequential nature. Unlike commonly reported p-values for standard null…

Observational astrophysics consists of making inferences about the Universe by comparing data and models. The credible intervals placed on model parameters are often as important as the maximum a posteriori probability values, as the…

In this paper, we consider one aspect of the problem of applying decision theory to the design of agents that learn how to make decisions under uncertainty. This aspect concerns how an agent can estimate probabilities for the possible…

In order to improve forecasts, a decisionmaker often combines probabilities given by various sources, such as human experts and machine learning classifiers. When few training data are available, aggregation can be improved by incorporating…

In this paper, we propose an explicit closed-form Bayes factor for the problem of two-sample hypothesis testing. The proposed approach can be regarded as a Bayesian version of the pooled-variance t-statistic and has various appealing…

Statistical pragmatism embraces all efficient methods in statistical inference. Augmentation of the collected data is used herein to obtain representative population information from a large class of non-representative population's units.…

Empirical analysis serves as an important complement to theoretical analysis for studying practical Bayesian optimization. Often empirical insights expose strengths and weaknesses inaccessible to theoretical analysis. We define two metrics…

This chapter provides a tutorial overview of first principles methods to describe the properties of matter at the ground state or equilibrium. It begins with a brief introduction to quantum and statistical mechanics for predicting the…

Identifying the Hamiltonian of a quantum system from experimental data is considered. General limits on the identifiability of model parameters with limited experimental resources are investigated, and a specific Bayesian estimation…

A Bayesian approach is developed to determine quantum mechanical potentials from empirical data. Bayesian methods, combining empirical measurements and "a priori" information, provide flexible tools for such empirical learning problems. The…

The article is devoted to new mathematical methods for psychophysical filtering of experimental data and their processing.

Due to increased awareness of data protection and corresponding laws many data, especially involving sensitive personal information, are not publicly accessible. Accordingly, many data collecting agencies only release aggregated data, e.g.…

Hypothesis testing and model choice are quintessential questions for statistical inference and while the Bayesian paradigm seems ideally suited for answering these questions, it faces difficulties of its own ranging from prior modelling to…

Constraints on cosmological parameters are often distilled from sky surveys by fitting templates to summary statistics of the data that are motivated by a fiducial cosmological model. However, recent work has shown how to estimate the…

In contrast to its common definition and calculation, interpretation of p-values diverges among statisticians. Since p-value is the basis of various methodologies, this divergence has led to a variety of test methodologies and evaluations…

Current analysis of astronomical data are confronted with the daunting task of modeling the awkward features of astronomical data, among which heteroscedastic (point-dependent) errors, intrinsic scatter, non-ignorable data collection…

Bayesian inference provides a flexible way of combining data with prior information. However, quantile regression is not equipped with a parametric likelihood, and therefore, Bayesian inference for quantile regression demands careful…

Probability Theory and Statistics are two of the most useful mathematical fields, and also two of the most difficult to learn. In other science fields, as Physics, experimentation is an useful tool to develop students intuition, but the…