arXiv subjects

James T. Thorson

Publications and source records attributed to James T. Thorson.

7 recordsLinked to original sources

arXiv2026

Sequential reduction for discrete latent variables in ecological and evolutionary models using RTMB

Statistical models of ecological and evolutionary dynamics often include latent variables that are either continuous (e.g., average body size) or discrete (e.g., numerical abundance). Mixed-type hierarchical models containing both are typically fitted using Markov chain Monte Carlo (MCMC), which can be prohibitively slow for large models. Here, we introduce an alternative in the R package RTMB that automates the sequential reduction of small groups of related discrete variables, allowing them to be efficiently marginalized. Sequential reduction is combined with automatic differentiation and the Laplace approximation to estimate parameters and predict both continuous and discrete variables. We demonstrate speed and flexibility using demographic examples (occupancy, dynamic occupancy, N-mixture, and open dynamic N-mixture models), benchmarking RTMB against JAGS and unmarked. We then develop two novel applications. The first is a multi-site open N-mixture model with a spatial latent variable governing site-specific initial abundance and recruitment, which shows that continuous Gaussian Markov random fields can be estimated jointly with discrete abundance dynamics in under a minute. The second is phylogenetic trait imputation for a published data set of female Liolaemus lizards, where we jointly impute a binary trait (viviparity), estimate its state-switching rates, and estimate its effect on a continuous trait (body size) during ancestral state reconstruction. This indicates that phylogenetic comparative methods can estimate linkages among discrete and continuous traits. We envision that intuitive and efficient specification of mixed-type models will allow more expressive representation of ecological and evolutionary dynamics.

q-bio.PE↗

arXiv2026

A unifying theory for the evaluation of conditional Akaike information for mixed-effects models

We propose two methods to evaluate the conditional Akaike information (cAI) for mixed-effects models with no restriction on cluster size. Method 1 is designed for continuous data and includes formulae for the derivatives of fixed and random effects estimators with respect to observations. Method 2, compatible with any type of observation, requires modeling the marginal (or prior) distribution of random effects as a multivariate normal distribution. Simulations show that Method 1 performs well with Gaussian data but struggles with skewed continuous distributions, whereas Method 2 consistently performs well across various distributions, including normal, gamma, negative binomial, and Tweedie, with flexible link functions. A case study demonstrates the differences in model selection for real-world data between the conventional AIC and the conditional AIC. Based on our findings, we recommend Method 2 as a distributionally robust cAI criterion for model selection in mixed-effects models.

stat.ME↗

arXiv2026

Implementing neural network mixed-effects models in Template Model Builder (TMB)

Neural network mixed-effects models (NMMs) have gained traction by combining the strong representation and predictive power of artificial neural networks with the capacity of mixed-effects modeling to capture complex correlation structures. However, existing estimation approaches rely heavily on manual derivations of objective functions and gradients, which inherently forces simplifying approximations and severely constrains the complexity and accuracy of NMMs. In this work, we introduce a general framework for implementing NMMs using Template Model Builder (TMB). By leveraging automatic differentiation and Laplace approximation, TMB requires users to specify only the negative joint log-likelihood and any regularization terms. The framework automatically integrates out random effects and evaluates the marginal objective function alongside its exact gradients, eliminating the need for manual derivations or ad hoc approximations. We demonstrate the efficiency, flexibility, and statistical performance of TMB-based NMMs across two numerical examples, including an application to monotonic NMMs. Reproducible code is provided to facilitate broader adoption.

stat.ML↗

arXiv2026

Leveraging Sparsity to Improve No-U-Turn Sampling Efficiency for Hierarchical Bayesian Models

Analysts routinely use Bayesian hierarchical models to understand natural processes. The no-U-turn sampler (NUTS) is the most widely used algorithm to sample high-dimensional, continuously differentiable models. But NUTS is slowed by high correlations, especially in high dimensions, limiting the complexity of applied analyses. Here we introduce Sparse NUTS (SNUTS), which preconditions (decorrelates and descales) posteriors using a sparse precision matrix ($Q$). We use Template Model Builder (TMB) to efficiently compute $Q$ from the mode of the Laplace approximation to the marginal posterior, then pass the preconditioned posterior to NUTS through the Bayesian software Stan for sampling. We apply SNUTS to seventeen diverse case studies to demonstrate that preconditioning with $Q$ converges one to two orders of magnitude faster than Stan's industry standard diagonal or dense preconditioners. SNUTS also outperforms preconditioning with the inverse of the covariance estimated with Pathfinder variational inference. SNUTS does not improve sampling efficiency for models with the highly varying curvature found in funnels, wide tails, or multiple modes. SNUTS is most advantageous, and can be scaled beyond $10^4$ parameters, in the presence of high dimensionality, sparseness, and high correlations, all of which are widespread in applied statistics. An open-source implementation of SNUTS is provided in the R package SparseNUTS.

stat.CO↗

arXiv2025

Analyzing the topological structure of composite dynamical systems

This chapter explores dynamical structural equation models (DSEMs) and their nonlinear generalizations into sheaves of dynamical systems. It demonstrates these two disciplines on part of the food web in the Bering Sea. The translation from DSEMs to sheaves passes through a formal construction borrowed from electronics called a netlist that specifies how data route through a system. A sheaf can be considered a formal hypothesis about how variables interact, that then specifies how observations can be tested for consistency, how missing data can be inferred, and how uncertainty about the observations can be quantified. Sheaf modeling provides a coherent mathematical framework for studying the interaction of various dynamical subsystems that together determine a larger system.

math.AT↗

arXiv2025

Introducing the generalized gamma distribution: a flexible distribution for index standardization

Fisheries scientists use regression models to estimate population quantities, such as biomass or abundance, for use in climate, habitat, stock, and ecosystem assessments. However, these models are sensitive to the chosen probability distribution used to characterize observation error. Here, we introduce the generalized gamma distribution (GGD), which has not been widely used in fisheries science. The GGD has useful properties: (1) it reduces to the lognormal distribution when the shape parameter approaches zero; (2) it reduces to the gamma distribution when the shape and scale parameters are equal; and (3) the coefficient of variation is independent of the mean. We assess the relative performance and robustness of the GGD to estimate biomass density across different observation error types in a simulation experiment. When fit to data generated from the GGD, lognormal, gamma, and Tweedie families, the GGD had low bias and high predictive accuracy. Finally, we fit spatiotemporal index standardization models using the R package sdmTMB to 15 species from three trawl surveys from the Gulf of Alaska and coast of British Columbia, Canada. When the Akaike information criterion (AIC) weight was compared among fits using the lognormal, gamma, and Tweedie families the GGD was the most commonly selected model.

stat.ME↗

arXiv2024

tinyVAST: R package with an expressive interface to specify lagged and simultaneous effects in multivariate spatio-temporal models

Multivariate spatio-temporal models are widely applicable, but specifying their structure is complicated and may inhibit wider use. We introduce the R package tinyVAST from two viewpoints: the software user and the statistician. From the user viewpoint, tinyVAST adapts a widely used formula interface to specify generalized additive models, and combines this with arguments to specify spatial and spatio-temporal interactions among variables. These interactions are specified using arrow notation (from structural equation models), or an extended arrow-and-lag notation that allows simultaneous, lagged, and recursive dependencies among variables over time. The user also specifies a spatial domain for areal (gridded), continuous (point-count), or stream-network data. From the statistician viewpoint, tinyVAST constructs sparse precision matrices representing multivariate spatio-temporal variation, and parameters are estimated by specifying a generalized linear mixed model (GLMM). This expressive interface encompasses vector autoregressive, empirical orthogonal functions, spatial factor analysis, and ARIMA models. To demonstrate, we fit to data from two survey platforms sampling corals, sponges, rockfishes, and flatfishes in the Gulf of Alaska and Aleutian Islands. We then compare eight alternative model structures using different assumptions about habitat drivers and survey detectability. Model selection suggests that towed-camera and bottom trawl gears have spatial variation in detectability but sample the same underlying density of flatfishes and rockfishes, and that rockfishes are positively associated with sponges while flatfishes are negatively associated with corals. We conclude that tinyVAST can be used to test complicated dependencies representing alternative structural assumptions for research and real-world policy evaluation.

stat.ME↗