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We consider the estimation of the mixing distribution of a normal distribution where both the shift and scale are unobserved random variables. We argue that in general, the model is not identifiable. We give an elegant non-constructive…
Generalized linear models are flexible tools for the analysis of diverse datasets, but the classical formulation requires that the parametric component is correctly specified and the data contain no atypical observations. To address these…
Existing two-sample testing techniques, particularly those based on choosing a kernel for the Maximum Mean Discrepancy (MMD), often assume equal sample sizes from the two distributions. Applying these methods in practice can require…
The Neyman-Pearson (NP) binary classification paradigm constrains the more severe type of error (e.g., the type I error) under a preferred level while minimizing the other (e.g., the type II error). This paradigm is suitable for…
Large language models (LLMs) have demonstrated impressive capabilities, but still suffer from inconsistency issues (e.g. LLMs can react differently to disturbances like rephrasing or inconsequential order change). In addition to these…
Optimum designs for parameter estimation in generalized regression models are standardly based on the Fisher information matrix (cf. Atkinson et al (2014) for a recent exposition). The corresponding optimality criteria are related to the…
For basic machine learning problems, expected error is used to evaluate model performance. Since the distribution of data is usually unknown, we can make simple hypothesis that the data are sampled independently and identically distributed…
A Lagrange multiplier theorem is derived for the case of an imprecise objective function and a precise constraint. The proof uses methods of analysis which deal in a direct, algebraic way with imprecisions. They include imprecise…
In real life we often deal with independent but not identically distributed observations (i.n.i.d.o), for which the most well-known statistical model is the multiple linear regression model (MLRM) without random covariates. While the…
Large language models (LLMs) are prone to hallucinations and sensitive to prompt perturbations, often resulting in inconsistent or unreliable generated text. Different methods have been proposed to mitigate such hallucinations and…
Large Language Models (LLMs) have grown increasingly powerful, yet ensuring their decisions remain transparent and trustworthy requires self-consistency -- no contradictions in their internal reasoning. Our study reveals that even on simple…
Despite the rapid expansion of Large Language Models (LLMs) in healthcare, robust and explainable evaluation of their ability to assess clinical trial reporting according to CONSORT standards remains an open challenge. In particular,…
The random variate m is, in combinatorics, a basis for comparing permutations, as well as the solution to a centuries-old riddle involving the mishandling of hats. In statistics, m is the test statistic for a disused null hypothesis…
It is important for official statistics production to apply ML with statistical rigor, as it presents both opportunities and challenges. Although machine learning has enjoyed rapid technological advances in recent years, its application…
Orthogonal group synchronization aims to recover orthogonal group elements from their noisy pairwise measurements. It has found numerous applications including computer vision, imaging science, and community detection. Due to the orthogonal…
A statistical model is said to be un-normalised when its likelihood function involves an intractable normalising constant. Two popular methods for parameter inference for these models are MC-MLE (Monte Carlo maximum likelihood estimation),…
We give a general proof of the strong consistency of the Maximum Likelihood Estimator for the case of independent non-identically distributed (i.n.i.d) data, assuming that the density functions of the random variables follow a particular…
Researchers are increasingly turning to machine learning (ML) algorithms to investigate causal heterogeneity in randomized experiments. Despite their promise, ML algorithms may fail to accurately ascertain heterogeneous treatment effects…
If the log likelihood is approximately quadratic with constant Hessian, then the maximum likelihood estimator (MLE) is approximately normally distributed. No other assumptions are required. We do not need independent and identically…
Standard maximum likelihood estimation cannot be applied to discrete energy-based models in the general case because the computation of exact model probabilities is intractable. Recent research has seen the proposal of several new…