Related papers: Fiducial Inference and Decision Theory
Reliable inference requires that artificial intelligence (AI) models provide trustworthy uncertainty estimates, not merely accurate predictions. Recent advances in Bayesian learning have made significant progress toward this goal, and…
Confidence estimates are often "detection-like" - driven by positive evidence in favour of a decision. This empirical observation has been interpreted as showing that human metacognition is limited by biases or heuristics. Here, we show…
This article extends the hypotheses assessment method to the case with two competing simple hypotheses. In doing so we further clarify the benefits that hypotheses assessments can bring to classical statistical analyses. Given that…
The notion of confidence distributions is applied to inference about the parameter in a simple autoregressive model, allowing the parameter to take the value one. This makes it possible to compare to asymptotic approximations in both the…
A fundamental question in causal inference is whether it is possible to reliably infer manipulation effects from observational data. There are a variety of senses of asymptotic reliability in the statistical literature, among which the most…
A fundamental class of inferential problems are those characterised by there having been a substantial degree of pre-data (or prior) belief that the value of a model parameter $\theta_j$ was equal or lay close to a specified value…
Between Bayesian and frequentist inference, it's commonly believed that the former is for cases where one has a prior and the latter is for cases where one has no prior. But the prior/no-prior classification isn't exhaustive, and most…
Bayesian inference requires specification of a single, precise prior distribution, whereas frequentist inference only accommodates a vacuous prior. Since virtually every real-world application falls somewhere in between these two extremes,…
This paper develops a category-theoretic approach to uncertainty, informativeness and decision-making problems. It is based on appropriate first order fuzzy logic in which not only logical connectives but also quantifiers have fuzzy…
It is recognised that the Bayesian approach to inference can not adequately cope with all the types of pre-data beliefs about population quantities of interest that are commonly held in practice. In particular, it generally encounters…
A central challenge in statistical inference is the presence of confounding variables that may distort observed associations between treatment and outcome. Conventional "causal" methods, grounded in assumptions such as ignorability, exclude…
In the canonical examples underlying Shafer-Dempster theory, beliefs over the hypotheses of interest are derived from a probability model for a set of auxiliary hypotheses. Beliefs are derived via a compatibility relation connecting the…
Bayesian inference gets its name from *Bayes's theorem*, expressing posterior probabilities for hypotheses about a data generating process as the (normalized) product of prior probabilities and a likelihood function. But Bayesian inference…
Statistical science (as opposed to mathematical statistics) involves far more than probability theory, for it requires realistic causal models of data generators - even for purely descriptive goals. Statistical decision theory requires more…
The relationship between belief networks and relational databases is examined. Based on this analysis, a method to construct belief networks automatically from statistical relational data is proposed. A comparison between our method and…
Belief function theory provides a flexible way to combine information provided by different sources. This combination is usually followed by a decision making which can be handled by a range of decision rules. Some rules help to choose the…
We marshall the arguments for preferring Bayesian hypothesis testing and confidence sets to frequentist ones. We define admissible solutions to inference problems, noting that Bayesian solutions are admissible. We give seven weaker…
(l) I have enough evidence to render the sentence S probable. (la) So, relative to what I know, it is rational of me to believe S. (2) Now that I have more evidence, S may no longer be probable. (2a) So now, relative to what I know, it is…
Bayesian inference is an important technique throughout statistics. The essence of Beyesian inference is to derive the posterior belief updated from prior belief by the learned information, which is a set of differentially private answers…
Posterior probabilistic statistical inference without priors is an important but so far elusive goal. Fisher's fiducial inference, Dempster-Shafer theory of belief functions, and Bayesian inference with default priors are attempts to…