Related papers: On econometric inference and multiple use of the s…

Bayesian inference and uncertainty quantification in a general class of non-linear inverse regression models is considered. Analytic conditions on the regression model $\{\mathscr G(\theta): \theta \in \Theta\}$ and on Gaussian process…

Regression models are used for inference and prediction in a wide range of applications providing a powerful scientific tool for researchers and analysts from different fields. In many research fields the amount of available data as well as…

This paper studies models in which hypothesis tests have trivial power, that is, power smaller than size. This testing impossibility, or impossibility type A, arises when any alternative is not distinguishable from the null. We also study…

We consider the standard non-parametric regression model with Gaussian errors but where the data consist of different samples. The question to be answered is whether the samples can be adequately represented by the same regression function.…

A substantial school in the philosophy of science identifies Bayesian inference with inductive inference and even rationality as such, and seems to be strengthened by the rise and practical success of Bayesian statistics. We argue that the…

Pre-analysis plans (PAPs) have become standard in experimental economics research, but it is nevertheless common to see researchers deviating from their PAPs to supplement preregistered estimates with non-prespecified findings. While such…

In statistical inference, uncertainty is unknown and all models are wrong. That is to say, a person who makes a statistical model and a prior distribution is simultaneously aware that both are fictional candidates. To study such cases,…

Cognitive diagnosis models have been popularly used in fields such as education, psychology, and social sciences. While parametric likelihood estimation is a prevailing method for fitting cognitive diagnosis models, nonparametric…

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,…

Most existing binary classification methods target on the optimization of the overall classification risk and may fail to serve some real-world applications such as cancer diagnosis, where users are more concerned with the risk of…

Between the two dominant schools of thought in statistics, namely, Bayesian and classical/frequentist, a main difference is that the former is grounded in the mathematically rigorous theory of probability while the latter is not. In this…

We point out that the Neyman-Pearson lemma applies to Bayes factors if we consider expected type-1 and type-2 error rates. That is, the Bayes factor is the test statistic that maximises the expected power for a fixed expected type-1 error…

Exponential random graph models (ERGMs) are a widely used framework for network data, enabling hypothesis testing on the structural mechanisms underlying observed networks. Bayesian ERGMs provide principled uncertainty quantification and…

A great deal of effort has been devoted to reducing the risk of spurious scientific discoveries, from the use of sophisticated validation techniques, to deep statistical methods for controlling the false discovery rate in multiple…

We propose a unified framework for establishing existence of nonparametric M-estimators, computing the corresponding estimates, and proving their strong consistency when the class of functions is exceptionally rich. In particular, the…

In this paper we consider the problem of inference on a class of sets describing a collection of admissible models as solutions to a single smooth inequality. Classical and recent examples include, among others, the Hansen-Jagannathan (HJ)…

For nearly any challenging scientific problem evaluation of the likelihood is problematic if not impossible. Approximate Bayesian computation (ABC) allows us to employ the whole Bayesian formalism to problems where we can use simulations…

In this paper we consider the issue of paradigm evaluation by applying Bayes' theorem along the following nested hierarchy of progressively more complex structures: i) parameter estimation (within a model), ii) model selection and…

Ideally, a meta-analysis will summarize data from several unbiased studies. Here we consider the less than ideal situation in which contributing studies may be compromised by measurement error. Measurement error affects every study design,…

Bayesian inference is often utilized for uncertainty quantification tasks. A recent analysis by Xu and Raginsky 2022 rigorously decomposed the predictive uncertainty in Bayesian inference into two uncertainties, called aleatoric and…