Related papers: Statistical Decisions Using Likelihood Information…

We analyze selected iterated conditionals in the framework of conditional random quantities. We point out that it is instructive to examine Lewis's triviality result, which shows the conditions a conditional must satisfy for its probability…

Prediction of future observations is a fundamental problem in statistics. Here we present a general approach based on the recently developed inferential model (IM) framework. We employ an IM-based technique to marginalize out the unknown…

The likelihood principle makes strong claims about the nature of statistical evidence but is controversial. Its claims are undermined by the existence of several examples that are assumed to show that it allows, with unity probability,…

This article presents a Bayesian inferential method where the likelihood for a model is unknown but where data can easily be simulated from the model. We discretize simulated (continuous) data to estimate the implicit likelihood in a…

Bayesian likelihood-free methods implement Bayesian inference using simulation of data from the model to substitute for intractable likelihood evaluations. Most likelihood-free inference methods replace the full data set with a summary…

Combining distributions is an important issue in decision theory and Bayesian inference. Logarithmic pooling is a popular method to aggregate expert opinions by using a set of weights that reflect the reliability of each information source.…

The standard approach to Bayesian inference is based on the assumption that the distribution of the data belongs to the chosen model class. However, even a small violation of this assumption can have a large impact on the outcome of a…

This paper tackles the challenge presented by small-data to the task of Bayesian inference. A novel methodology, based on manifold learning and manifold sampling, is proposed for solving this computational statistics problem under the…

Data-driven risk analysis involves the inference of probability distributions from measured or simulated data. In the case of a highly reliable system, such as the electricity grid, the amount of relevant data is often exceedingly limited,…

Some scientific research questions ask to guide decisions and others do not. By their nature frequentist hypothesis-tests yield a dichotomous test decision as result, rendering them rather inappropriate for latter types of research…

Models of updating a set of priors either do not allow a decision maker to make inference about her priors (full bayesian updating or FB) or require an extreme degree of selection (maximum likelihood updating or ML). I characterize a…

Empirical research in Natural Language Processing (NLP) has adopted a narrow set of principles for assessing hypotheses, relying mainly on p-value computation, which suffers from several known issues. While alternative proposals have been…

The Bayesian brain hypothesis has been a leading theory in understanding perceptual decision-making under uncertainty. While extensive psychophysical evidence supports the notion of the brain performing Bayesian computations, how…

The likelihood function plays a pivotal role in statistical inference; it is adaptable to a wide range of models and the resultant estimators are known to have good properties. However, these results hinge on correct specification of the…

We consider Bayesian model selection in generalized linear models that are high-dimensional, with the number of covariates p being large relative to the sample size n, but sparse in that the number of active covariates is small compared to…

Laplace's "add-one" rule of succession modifies the observed frequencies in a sequence of heads and tails by adding one to the observed counts. This improves prediction by avoiding zero probabilities and corresponds to a uniform Bayesian…

Nonparametric and nonlinear measures of statistical dependence between pairs of random variables are important tools in modern data analysis. In particular the emergence of large data sets can now support the relaxation of linearity…

Large-scale datasets are increasingly being used to inform decision making. While this effort aims to ground policy in real-world evidence, challenges have arisen as selection bias and other forms of distribution shifts often plague…

In the case of informative sampling the sampling scheme explicitly or implicitly depends on the response variable. As a result, the sample distribution of response variable can- not be used for making inference about the population. In this…

In Bayesian statistics, the marginal likelihood, also known as the evidence, is used to evaluate model fit as it quantifies the joint probability of the data under the prior. In contrast, non-Bayesian models are typically compared using…