Related papers: Extended probabilities and their application to st…
A novel approach to improve prediction and inference in M-estimation by integrating external information from heterogeneous populations is proposed. Our method leverages joint asymptotics to combine estimates from external and internal…
This article explains, and discusses the merits of, three approaches for analyzing the certainty with which statistical results can be extrapolated beyond the data gathered. Sometimes it may be possible to use more than one of these…
The statistical inverse problem of estimating the probability distribution of an infinite-dimensional unknown given its noisy indirect observation is studied in the Bayesian framework. In practice, one often considers only…
Mathematical psychology has a long tradition of modeling probabilistic choice via distribution-free random utility models and associated random preference models. For such models, the predicted choice probabilities often form a bounded and…
We present two methods for bounding the probabilities of benefit and harm under unmeasured confounding. The first method computes the (upper or lower) bound of either probability as a function of the observed data distribution and two…
Random-effects models are frequently used to synthesise information from different studies in meta-analysis. While likelihood-based inference is attractive both in terms of limiting properties and of implementation, its application in…
The recurrence times between extreme events have been the central point of statistical analyses in many different areas of science. Simultaneously, the Poincar\'e recurrence time has been extensively used to characterize nonlinear dynamical…
Bayesian inference systems should be able to explain their reasoning to users, translating from numerical to natural language. Previous empirical work has investigated the correspondence between absolute probabilities and linguistic…
Classical probability theory supports probability measures, assigning a fixed positive real value to each event, these measures are far from satisfactory in formulating real-life occurrences. The main innovation of this paper is the…
Although the specification of bivariate probability models using a collection of assumed conditional distributions is not a novel concept, it has received considerable attention in the last decade. In this study, a bivariate…
Counterfactual explanations utilize feature perturbations to analyze the outcome of an original decision and recommend an actionable recourse. We argue that it is beneficial to provide several alternative explanations rather than a single…
We examine a new approach to modeling uncertainty based on plausibility measures, where a plausibility measure just associates with an event its plausibility, an element is some partially ordered set. This approach is easily seen to…
Inferring models, predicting the future, and estimating the entropy rate of discrete-time, discrete-event processes is well-worn ground. However, a much broader class of discrete-event processes operates in continuous-time. Here, we provide…
The definition of probabilities in eternally inflating universes requires a measure to regulate the infinite spacetime volume, and much of the current literature uses a global time cutoff for this purpose. Such measures have been found to…
Bayes' theorem incorporates distinct types of information through the likelihood and prior. Direct observations of state variables enter the likelihood and modify posterior probabilities through consistent updating. Information in terms of…
Applying a machine learning model for decision-making in the real world requires to distinguish what the model knows from what it does not. A critical factor in assessing the knowledge of a model is to quantify its predictive uncertainty.…
We give a finite-sample analysis of predictive inference procedures after model selection in regression with random design. The analysis is focused on a statistically challenging scenario where the number of potentially important…
A spectral approach to Bayesian inference is presented. It pursues the emulation of the posterior probability density. The starting point is a series expansion of the likelihood function in terms of orthogonal polynomials. From this…
In causal inference, and specifically in the \textit{Causes of Effects} problem, one is interested in how to use statistical evidence to understand causation in an individual case, and so how to assess the so-called {\em probability of…
Let $\alpha_n(\cdot)=P\bigl(X_{n+1}\in\cdot\mid X_1,\ldots,X_n\bigr)$ be the predictive distributions of a sequence $(X_1,X_2,\ldots)$ of $p$-dimensional random vectors. Suppose $$\alpha_n= \mathcal{N} _p (M_n,Q_n)$$ where…