arXiv subjects

Neil A. Spencer

Publications and source records attributed to Neil A. Spencer.

8 recordsLinked to original sources

arXiv2026

Robust Bayesian Predictive Model Selection using Bregman Divergence

Predictive Bayesian model comparison often relies on leave-one-out (LOO) cross-validation criteria such as the expected log predictive density (ELPD). However, model rankings can be overly sensitive to outliers and tail mismatch because ELPD is based on the log score. We propose a score-matched generalized ELPD framework that replaces the log score by a Bregman scoring rule to update model parameters through a generalized posterior and to evaluate LOO predictive utility. Candidate posterior predictive distributions are ranked by out-of-sample utility under the chosen scoring rule, yielding a direct proper-score generalization of standard ELPD. We focus especially on the $β$-divergence family, where $β$ controls the sensitivity of predictive comparison to low-density observations. Under model misspecification, the procedure asymptotically selects the model whose predictive distribution is closest to the data-generating process under the chosen Bregman divergence. A simulation study and applications to microbial and forensic data show that the generalized ELPD can change the selected model through reduced sensitivity to low-density observations.

stat.ME↗

arXiv2026

Robust model selection using likelihood as data

Model selection is a central task in statistics, but standard methods are not robust in misspecified settings where the true data-generating process (DGP) is not in the set of candidate models. The key limitation is that existing methods -- including information criteria and Bayesian posteriors -- do not quantify uncertainty about how well each candidate model approximates the true DGP. In this paper, we introduce a novel approach to model selection based on modeling the likelihood values themselves. Specifically, given $K$ candidate models and $n$ observations, we view the $n\times K$ matrix of negative log-likelihood values as a random data matrix and observe that the expectation of each row is equal to the vector of Kullback--Leibler divergences between the $K$ models and the true DGP, up to an additive constant. We use a multivariate normal model to estimate and quantify uncertainty in this expectation, providing calibrated inferences for robust model selection under misspecification. The procedure is easy to compute, interpretable, and comes with theoretical guarantees, including consistency.

stat.ME↗

arXiv2023

Strong uniform laws of large numbers for bootstrap means and other randomly weighted sums

This article establishes novel strong uniform laws of large numbers for randomly weighted sums such as bootstrap means. By leveraging recent advances, these results extend previous work in their general applicability to a wide range of weighting procedures and in their flexibility with respect to the effective bootstrap sample size. In addition to the standard multinomial bootstrap and the m-out-of-n bootstrap, our results apply to a large class of randomly weighted sums involving negatively orthant dependent (NOD) weights, including the Bayesian bootstrap, jackknife, resampling without replacement, simple random sampling with over-replacement, independent weights, and multivariate Gaussian weighting schemes. Weights are permitted to be non-identically distributed and possibly even negative. Our proof technique is based on extending a proof of the i.i.d. strong uniform law of large numbers to employ strong laws for randomly weighted sums; in particular, we exploit a recent Marcinkiewicz--Zygmund strong law for NOD weighted sums.

math.PR↗

arXiv2023

Projective, Sparse, and Learnable Latent Position Network Models

When modeling network data using a latent position model, it is typical to assume that the nodes' positions are independently and identically distributed. However, this assumption implies the average node degree grows linearly with the number of nodes, which is inappropriate when the graph is thought to be sparse. We propose an alternative assumption -- that the latent positions are generated according to a Poisson point process -- and show that it is compatible with various levels of sparsity. Unlike other notions of sparse latent position models in the literature, our framework also defines a projective sequence of probability models, thus ensuring consistency of statistical inference across networks of different sizes. We establish conditions for consistent estimation of the latent positions, and compare our results to existing frameworks for modeling sparse networks.

math.ST↗

arXiv2021

Faster MCMC for Gaussian Latent Position Network Models

Latent position network models are a versatile tool in network science; applications include clustering entities, controlling for causal confounders, and defining priors over unobserved graphs. Estimating each node's latent position is typically framed as a Bayesian inference problem, with Metropolis within Gibbs being the most popular tool for approximating the posterior distribution. However, it is well-known that Metropolis within Gibbs is inefficient for large networks; the acceptance ratios are expensive to compute, and the resultant posterior draws are highly correlated. In this article, we propose an alternative Markov chain Monte Carlo strategy -- defined using a combination of split Hamiltonian Monte Carlo and Firefly Monte Carlo -- that leverages the posterior distribution's functional form for more efficient posterior computation. We demonstrate that these strategies outperform Metropolis within Gibbs and other algorithms on synthetic networks, as well as on real information-sharing networks of teachers and staff in a school district.

stat.CO↗

arXiv2020

IsoCheck: An R Package to check Isomorphism for Two-level Factorial Designs with Randomization Restrictions

Factorial designs are often used in various industrial and sociological experiments to identify significant factors and factor combinations that may affect the process response. In the statistics literature, several studies have investigated the analysis, construction, and isomorphism of factorial and fractional factorial designs. When there are multiple choices for a design, it is helpful to have an easy-to-use tool for identifying which are distinct, and which of those can be efficiently analyzed/has good theoretical properties. For this task, we present an R library called IsoCheck that checks the isomorphism of multi-stage 2^n factorial experiments with randomization restrictions. Through representing the factors and their combinations as a finite projective geometry, IsoCheck recasts the problem of searching over all possible relabelings as a search over collineations, then exploits projective geometric properties of the space to make the search much more efficient. Furthermore, a bitstring representation of the factorial effects is used to characterize all possible rearrangements of designs, thus facilitating quick comparisons after relabeling. We present several examples with R code to illustrate the usage of the main functions in IsoCheck. Besides checking equivalence and isomorphism of 2^n multi-stage factorial designs, we demonstrate how the functions of the package can be used to create a catalog of all non-isomorphic designs, and subsequently rank these designs based on a suitably defined ranking criterion. IsoCheck is free software and distributed under the General Public License and available from the Comprehensive R Archive Network.

stat.ME↗

arXiv2020

A Bayesian Hierarchical Model for Evaluating Forensic Footwear Evidence

When a latent shoeprint is discovered at a crime scene, forensic analysts inspect it for distinctive patterns of wear such as scratches and holes (known as accidentals) on the source shoe's sole. If its accidentals correspond to those of a suspect's shoe, the print can be used as forensic evidence to place the suspect at the crime scene. The strength of this evidence depends on the random match probability---the chance that a shoe chosen at random would match the crime scene print's accidentals. Evaluating random match probabilities requires an accurate model for the spatial distribution of accidentals on shoe soles. A recent report by the President's Council of Advisors in Science and Technology criticized existing models in the literature, calling for new empirically validated techniques. We respond to this request with a new spatial point process model for accidental locations, developed within a hierarchical Bayesian framework. We treat the tread pattern of each shoe as a covariate, allowing us to pool information across large heterogeneous databases of shoes. Existing models ignore this information; our results show that including it leads to significantly better model fit. We demonstrate this by fitting our model to one such database.

stat.AP↗

arXiv2019

Isomorphism Check for $2^n$ Factorial Designs with Randomization Restrictions

Factorial designs with randomization restrictions are often used in industrial experiments when a complete randomization of trials is impractical. In the statistics literature, the analysis, construction and isomorphism of factorial designs has been extensively investigated. Much of the work has been on a case-by-case basis -- addressing completely randomized designs, randomized block designs, split-plot designs, etc. separately. In this paper we take a more unified approach, developing theoretical results and an efficient relabeling strategy to both construct and check the isomorphism of multi-stage factorial designs with randomization restrictions. The examples presented in this paper particularly focus on split-lot designs.

stat.ME↗