arXiv subjects

Cole C. Monnahan

Publications and source records attributed to Cole C. Monnahan.

3 recordsLinked to original sources

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↗

arXiv2024

Why not a thin plate spline for spatial models? A comparative study using Bayesian inference

Spatial modelling often uses Gaussian random fields to capture the stochastic nature of studied phenomena. However, this approach incurs significant computational burdens (O(n3)), primarily due to covariance matrix computations. In this study, we propose to use a low-rank approximation of a thin plate spline as a spatial random effect in Bayesian spatial models. We compare its statistical performance and computational efficiency with the approximated Gaussian random field (by the SPDE method). In this case, the dense matrix of the thin plate spline is approximated using a truncated spectral decomposition, resulting in computational complexity of O(kn2) operations, where k is the number of knots. Bayesian inference is conducted via the Hamiltonian Monte Carlo algorithm of the probabilistic software Stan, which allows us to evaluate performance and diagnostics for the proposed models. A simulation study reveals that both models accurately recover the parameters used to simulate data. However, models using a thin plate spline demonstrate superior execution time to achieve the convergence of chains compared to the models utilizing an approximated Gaussian random field. Furthermore, thin plate spline models exhibited better computational efficiency for simulated data coming from different spatial locations. In a real application, models using a thin plate spline as spatial random effect produced similar results in estimating a relative index of abundance for a benthic marine species when compared to models incorporating an approximated Gaussian random field. Although they were not the more computational efficient models, their simplicity in parametrization, execution time and predictive performance make them a valid alternative for spatial modelling under Bayesian inference.

stat.ME↗

arXiv2014

ss3sim: An R package for fisheries stock assessment simulation with Stock Synthesis

Simulation testing is an important approach to evaluating fishery stock assessment methods. In the last decade, the fisheries stock assessment modeling framework Stock Synthesis (SS3) has become widely used around the world. However, there lacks a generalized and scriptable framework for SS3 simulation testing. Here, we introduce ss3sim, an R package that facilitates reproducible, flexible, and rapid end-to-end simulation testing with SS3. ss3sim requires an existing SS3 model configuration along with plain-text control files describing alternative population dynamics, fishery properties, sampling scenarios, and assessment approaches. ss3sim then generates an underlying 'truth' from a specified operating model, samples from that truth, modifies and runs an estimation model, and synthesizes the results. The simulations can be run in parallel, reducing runtime, and the source code is free to be modified under an open-source MIT license. ss3sim is designed to explore structural differences between the underlying truth and assumptions of an estimation model, or between multiple estimation model configurations. For example, ss3sim can be used to answer questions about model misspecification, retrospective patterns, and the relative importance of different types of fisheries data. We demonstrate the software with an example, discuss how ss3sim complements other simulation software, and outline specific research questions that ss3sim could address.

q-bio.QM↗