Related papers: Likelihood, Replicability and Robbins' Confidence …
The low replication rate of published studies has long concerned the social science community, making understanding the replicability a critical problem. Several studies have shown that relevant research communities can make predictions…
Empirical likelihood serves as a powerful tool for constructing confidence intervals in nonparametric regression and regression discontinuity designs (RDD). The original empirical likelihood framework can be naturally extended to these…
Approximate confidence distribution computing (ACDC) offers a new take on the rapidly developing field of likelihood-free inference from within a frequentist framework. The appeal of this computational method for statistical inference…
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…
We investigate the relation between frequentist and Bayesian approaches. Namely, we find the "frequentist" Bayes prior \pi_{f}(\lambda,x_{obs}) = -\frac{\int_{-\infty}^{x_{obs}}\frac{\partial f(x,\lambda)}{\partial…
Linear models are foundational tools in statistics and ubiquitous across the applied sciences. However, conventional statistical inference -- such as $t$-tests and $F$-tests -- are only valid at fixed sample sizes, making them unsuitable…
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…
Attempts to replicate probabilistic reasoning in expert systems have typically overlooked a critical ingredient of that process. Probabilistic analysis typically requires extensive judgments regarding interdependencies among hypotheses and…
This chapter provides a overview of Bayesian inference, mostly emphasising that it is a universal method for summarising uncertainty and making estimates and predictions using probability statements conditional on observed data and an…
Causal inference with observational data can be performed under an assumption of no unobserved confounders (unconfoundedness assumption). There is, however, seldom clear subject-matter or empirical evidence for such an assumption. We…
Little effort has been devoted to studying generalised notions or models of (un)predictability, yet is an important concept throughout physics and plays a central role in quantum information theory, where key results rely on the supposed…
If the prior probability distributions of all possible hypothetical true means and all possible observed means of a continuous variable are conditional on the universal set of all numbers (i.e., before the nature of a study is known and a…
A new method is proposed for the correction of confidence intervals when the original interval does not have the correct nominal coverage probabilities in the frequentist sense. The proposed method is general and does not require any…
Generalised Bayesian inference updates prior beliefs using a loss function, rather than a likelihood, and can therefore be used to confer robustness against possible mis-specification of the likelihood. Here we consider generalised Bayesian…
The original frequentist approach for computing confidence intervals involves the construction of the confidence belt which provides a mapping of the observation in data into a subset of values for the parameter. There are different…
Probability-like parameters appearing in some statistical models, and their prior distributions, are reinterpreted through the notion of `circumstance', a term which stands for any piece of knowledge that is useful in assigning a…
Rapid advancements in data science require us to have fundamentally new frameworks to tackle prevalent but highly non-trivial "irregular" inference problems, to which the large sample central limit theorem does not apply. Typical examples…
In clinical trials, inferences on clinical outcomes are often made conditional on specific selective processes. For instance, only when a treatment demonstrates a significant effect on the primary outcome, further analysis is conducted to…
With the advent of high-performance computing, Bayesian methods are increasingly popular tools for the quantification of uncertainty throughout science and industry. Since these methods impact the making of sometimes critical decisions in…
We provide a general solution to a fundamental open problem in Bayesian inference, namely poor uncertainty quantification, from a frequency standpoint, of Bayesian methods in misspecified models. While existing solutions are based on…