Related papers: Things Bayes can't do

Identifying small subsets of features that are relevant for prediction and/or classification tasks is a central problem in machine learning and statistics. The feature selection task is especially important, and computationally difficult,…

Consider a multinomial regression model where the response, which indicates a unit's membership in one of several possible unordered classes, is associated with a set of predictor variables. Such models typically involve a matrix of…

Bayesian hypothesis testing is re-examined from the perspective of an a priori assessment of the test statistic distribution under the alternative. By assessing the distribution of an observable test statistic, rather than prior parameter…

Bayesian networks provide an elegant formalism for representing and reasoning about uncertainty using probability theory. Theyare a probabilistic extension of propositional logic and, hence, inherit some of the limitations of propositional…

As artificial agents become increasingly capable, what internal structure is *necessary* for an agent to act competently under uncertainty? Classical results show that optimal control can be *implemented* using belief states or world…

Invariant prediction [Peters et al., 2016] analyzes feature/outcome data from multiple environments to identify invariant features - those with a stable predictive relationship to the outcome. Such features support generalization to new…

Principal component regression uses principal components as regressors. It is particularly useful in prediction settings with high-dimensional covariates. The existing literature treating of Bayesian approaches is relatively sparse. We…

Recently, optional stopping has been a subject of debate in the Bayesian psychology community. Rouder (2014) argues that optional stopping is no problem for Bayesians, and even recommends the use of optional stopping in practice, as do…

Maximum a posteriori and Bayes estimators are two common methods of point estimation in Bayesian Statistics. It is commonly accepted that maximum a posteriori estimators are a limiting case of Bayes estimators with 0-1 loss. In this paper,…

This paper studies the multiplicity-correction effect of standard Bayesian variable-selection priors in linear regression. Our first goal is to clarify when, and how, multiplicity correction happens automatically in Bayesian analysis, and…

Formulating a statistical inverse problem as one of inference in a Bayesian model has great appeal, notably for what this brings in terms of coherence, the interpretability of regularisation penalties, the integration of all uncertainties,…

Causal asymmetry is one of the great surprises in predictive modelling: the memory required to predict the future differs from the memory required to retrodict the past. There is a privileged temporal direction for modelling a stochastic…

The formulation of Bayesian inverse problems involves choosing prior distributions; choices that seem equally reasonable may lead to significantly different conclusions. We develop a computational approach to better understand the impact of…

Bayesian inference paradigms are regarded as powerful tools for solution of inverse problems. However, when applied to inverse problems in physical sciences, Bayesian formulations suffer from a number of inconsistencies that are often…

Prediction becomes more challenging with missing covariates. What method is chosen to handle missingness can greatly affect how models perform. In many real-world problems, the best prediction performance is achieved by models that can…

Bayesian optimisation has gained great popularity as a tool for optimising the parameters of machine learning algorithms and models. Somewhat ironically, setting up the hyper-parameters of Bayesian optimisation methods is notoriously hard.…

Construction methods for prior densities are investigated from a predictive viewpoint. Predictive densities for future observables are constructed by using observed data. The simultaneous distribution of future observables and observed data…

An agent observes a clue, and an analyst observes an inference: a ranking of events on the basis of how corroborated they are by the clue. We prove that if the inference satisfies the axioms of Villegas (1964) except for the classic…

An agent is a misspecified Bayesian if she updates her belief using Bayes' rule given a subjective, possibly misspecified model of her signals. This paper shows that a belief sequence is consistent with misspecified Bayesian updating if and…

The proposed approach extends the confidence posterior distribution to the semi-parametric empirical Bayes setting. Whereas the Bayesian posterior is defined in terms of a prior distribution conditional on the observed data, the confidence…