arXiv subjects

Nathan A. Judd

Publications and source records attributed to Nathan A. Judd.

3 recordsLinked to original sources

arXiv2026

Subordinated Wright-Fisher Priors

A new class of time-dependent Dirichlet priors is introduced as a generalisation of the Wright-Fisher diffusion, allowing discontinuities in the trajectories, as well as non-Markovian memory. This class is obtained as a simple stochastic time-change (subordination), interpreted as a hyper-prior assigned to the operational time-clock of a Wright-Fisher diffusion. Explicit representations and exact sampling algorithms are obtained for prior and posterior distributions of the process and of its clock, given partially exchangeable data sampled at discrete time-points. Computability and conjugacy rely on a novel class of discrete dual processes, generalising existing results on duality and computable filters.

math.ST↗

arXiv2026

Neural Methods for Multiple Systems Estimation Models

Estimating the size of hidden populations using Multiple Systems Estimation (MSE) is a critical task in quantitative sociology; however, practical application is often hindered by imperfect administrative data and computational constraints. Real-world datasets frequently suffer from censoring and missingness due to privacy concerns, while standard inference methods, such as Maximum Likelihood Estimation (MLE) and Markov chain Monte Carlo (MCMC), can become computationally intractable or fail to converge when data are sparse. To address these limitations, we propose a novel simulation-based Bayesian inference framework utilizing Neural Bayes Estimators (NBE) and Neural Posterior Estimators (NPE). These neural methods are amortized: once trained, they provide instantaneous, computationally efficient posterior estimates, making them ideal for use in secure research environments where computational resources are limited. Through extensive simulation studies, we demonstrate that neural estimators achieve accuracy comparable to MCMC while being orders of magnitude faster and robust to the convergence failures that plague traditional samplers in sparse settings. We demonstrate our method on two real-world cases estimating the prevalence of modern slavery in the UK and female drug use in North East England.

stat.AP↗

arXiv2025

Statistical Crime Linkage: Evaluating approaches within the Covenant for Using AI in Policing

Linking crimes by modus operandi has long been employed as an effective tool for crime investigation. The standard statistical method that underpins statistical crime linkage has been logistic regression. The simplicity and interpretability of this approach has been seen as an advantage for law enforcement agencies using statistical crime linkage. In 2023, the National Police Chiefs' Council published the Covenant for Using Artificial Intelligence in Policing designed to guide the development of novel methods for use within policing. In this article, we investigate more statistical and machine learning methods that could underpin crime linkage models. We investigate a range of methods including regression-, sampling-, and machine learning-based techniques and evaluate them against the principles of Explainability and Transparency from the Covenant. We investigate our methods on a new data set on romance fraud in the UK, where 361 victims of fraud reported the behaviours and characteristics of the suspects involved in their case. We propose a sensitive, Explainable, and Transparent machine learning model for crime linkage and demonstrate how this method could support crime linkage efforts by law enforcement agencies using a dataset of romance fraud with unknown linkage status.

stat.AP↗