arXiv subjects

Joseph Marsh

Publications and source records attributed to Joseph Marsh.

4 recordsLinked to original sources

arXiv2026

A Neural Estimation Framework for Aggregated Relational Data under Intractable Likelihoods

Aggregated relational data (ARD) consists of survey responses to questions of the form ``how many people do you know who~$X$?'' and is widely used in survey statistics for indirect inference about populations and social networks. The dominant ARD inference target is hidden-population size estimation via the Network Scale-Up Method (NSUM), but ARD is also used for personal-network-size estimation, mixing-pattern recovery, and inference about latent network structure. Bayesian inference for ARD almost universally assumes that, conditional on a respondent's degree, the counts reported for different subpopulations are independent. There are, however, reasons to question this assumption, as homophily, latent-space clustering, and imperfect recall may all induce cross-population dependence. We develop a simulation-based neural estimation framework for ARD which requires only a simulator, so it can be applied to generative models whose likelihood cannot be written down or efficiently evaluated. The framework trains a permutation-invariant neural Bayes estimator that returns, for each marginal parameter, a posterior median and a 95% credible interval, by minimising a multi-quantile pinball loss with a cumulative-gap construction that rules out quantile crossing by design. We demonstrate the framework on three structurally distinct intractable extensions of NSUM-style ARD inference: a stochastic block model, a latent-space model, and a recall-subset model. We apply the framework to ARD Household Survey collected in Rwanda. The framework provides inference on any new survey drawn from the training distribution, and extends the reach of ARD modelling to network-structure and cognitive-process assumptions beyond those currently accessible to likelihood-based inference.

stat.ME↗

arXiv2026

Bayesian Inference for Non-Conjugate Distance Dependent Chinese Restaurant Process Models

The distance dependent Chinese Restaurant Process (ddCRP) provides a flexible prior distribution for clustering observations, incorporating covariate information through pairwise distances and accommodating a rich variety of cluster structures. When cluster parameters are conjugate to the likelihood, Bayesian inference is straightforward. In the non-conjugate setting, however, inference becomes substantially more challenging due to the trans-dimensional parameter spaces that arise as cluster assignments change. We develop a reversible jump Markov chain Monte Carlo (RJMCMC) framework to address this challenge, targeting the dimension-changing nature of cluster parameter vectors when observation assignments are updated. We introduce and compare several proposal strategies for birth and death moves, including prior-based, independence, and data-driven moment-matching proposals that target regions of high posterior density. For fixed-dimensional moves, we propose a posterior resampling strategy that improves acceptance rates while maintaining computational efficiency. Through a simulation study and an application to Old Faithful eruption durations, we demonstrate moment-matched proposals offer a principled, data-driven alternative to prior-based proposals. The resulting methodology provides a general RJMCMC framework for ddCRP models with non-conjugate likelihoods, demonstrated here on both discrete and continuous observation models.

stat.ME↗

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

A Reduced Basis Decomposition Approach to Efficient Data Collection in Pairwise Comparison Studies

Comparative judgement studies elicit quality assessments through pairwise comparisons, typically analysed using the Bradley-Terry model. A challenge in these studies is experimental design, specifically, determining the optimal pairs to compare to maximize statistical efficiency. Constructing static experimental designs for these studies requires spectral decomposition of a covariance matrix over pairs of pairs, which becomes computationally infeasible for studies with more than approximately 150 objects. We propose a scalable method based on reduced basis decomposition that bypasses explicit construction of this matrix, achieving computational savings of two to three orders of magnitude. We establish eigenvalue bounds guaranteeing approximation quality and characterise the rank structure of the design matrix. Simulations demonstrate speedup factors exceeding 100 for studies with 64 or more objects, with negligible approximation error. We apply the method to construct designs for a 452-region spatial study in under 7 minutes and enable real-time design updates for classroom peer assessment, reducing computation time from 15 minutes to 15 seconds.

stat.ME↗