Data assimilation is a core component of numerical weather prediction systems. The large quantity of data processed during assimilation requires the computation to be distributed across increasingly many compute nodes; yet, existing approaches suffer from synchronization overhead in this setting. In this article, we exploit the formulation of data assimilation as a Bayesian inference problem and apply a message-passing algorithm to solve the spatial inference problem. Since message passing is inherently based on local computations, this approach lends itself to parallel and distributed computation. In combination with a GPU-accelerated implementation, we can scale the algorithm to very large grid sizes while retaining good accuracy and compute and memory requirements.

We present an hierarchical Bayes approach to modeling parameter heterogeneity in generalized linear models. The model assumes that there are relevant subpopulations and that within each subpopulation the individual-level regression coefficients have a multivariate normal distribution. However, class membership is not known a priori, so the heterogeneity in the regression coefficients becomes a finite mixture of normal distributions. This approach combines the flexibility of semiparametric, latent class models that assume common parameters for each sub-population and the parsimony of random effects models that assume normal distributions for the regression parameters. The number of subpopulations is selected to maximize the posterior probability of the model being true. Simulations are presented which document the performance of the methodology for synthetic data with known heterogeneity and number of sub-populations. An application is presented concerning preferences for various aspects of personal computers.

This paper proposes a novel collapsed Gibbs sampling algorithm that marginalizes model parameters and directly samples latent attribute mastery patterns in diagnostic classification models. This estimation method makes it possible to avoid boundary problems in the estimation of model item parameters by eliminating the need to estimate such parameters. A simulation study showed the collapsed Gibbs sampling algorithm can accurately recover the true attribute mastery status in various conditions. A second simulation showed the collapsed Gibbs sampling algorithm was computationally more efficient than another MCMC sampling algorithm, implemented by JAGS. In an analysis of real data, the collapsed Gibbs sampling algorithm indicated good classification agreement with results from a previous study.

Cognitive diagnostic models (CDMs) are discrete latent variable models popular in educational and psychological measurement. In this work, motivated by the advantages of deep generative modeling and by identifiability considerations, we propose a new family of DeepCDMs, to hunt for deep discrete diagnostic information. The new class of models enjoys nice properties of identifiability, parsimony, and interpretability. Mathematically, DeepCDMs are entirely identifiable, including even fully exploratory settings and allowing to uniquely identify the parameters and discrete loading structures (the “$\mathbf{Q}$\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\textbf{Q}$$\end{document}-matrices”) at all different depths in the generative model. Statistically, DeepCDMs are parsimonious, because they can use a relatively small number of parameters to expressively model data thanks to the depth. Practically, DeepCDMs are interpretable, because the shrinking-ladder-shaped deep architecture can capture cognitive concepts and provide multi-granularity skill diagnoses from coarse to fine grained and from high level to detailed. For identifiability, we establish transparent identifiability conditions for various DeepCDMs. Our conditions impose intuitive constraints on the structures of the multiple $\mathbf{Q}$\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\textbf{Q}$$\end{document}-matrices and inspire a generative graph with increasingly smaller latent layers when going deeper. For estimation and computation, we focus on the confirmatory setting with known $\mathbf{Q}$\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\textbf{Q}$$\end{document}-matrices and develop Bayesian formulations and efficient Gibbs sampling algorithms. Simulation studies and an application to the TIMSS 2019 math assessment data demonstrate the usefulness of the proposed methodology.

Traditional mediation analysis assumes that a study population is homogeneous and the mediation effect is constant over time, which may not hold in some applications. Motivated by smoking cessation data, we propose a latent class dynamic mediation model that explicitly accounts for the fact that the study population may consist of different subgroups and the mediation effect may vary over time. We use a proportional odds model to accommodate the subject heterogeneities and identify latent subgroups. Conditional on the subgroups, we employ a Bayesian hierarchical nonparametric time-varying coefficient model to capture the time-varying mediation process, while allowing each subgroup to have its individual dynamic mediation process. A simulation study shows that the proposed method has good performance in estimating the mediation effect. We illustrate the proposed methodology by applying it to analyze smoking cessation data.

Brain activation and connectivity analyses in task-based functional magnetic resonance imaging (fMRI) experiments with multiple subjects are currently at the forefront of data-driven neuroscience. In such experiments, interest often lies in understanding activation of brain voxels due to external stimuli and strong association or connectivity between the measurements on a set of pre-specified groups of brain voxels, also known as regions of interest (ROI). This article proposes a joint Bayesian additive mixed modeling framework that simultaneously assesses brain activation and connectivity patterns from multiple subjects. In particular, fMRI measurements from each individual obtained in the form of a multi-dimensional array/tensor at each time are regressed on functions of the stimuli. We impose a low-rank parallel factorization decomposition on the tensor regression coefficients corresponding to the stimuli to achieve parsimony. Multiway stick-breaking shrinkage priors are employed to infer activation patterns and associated uncertainties in each voxel. Further, the model introduces region-specific random effects which are jointly modeled with a Bayesian Gaussian graphical prior to account for the connectivity among pairs of ROIs. Empirical investigations under various simulation studies demonstrate the effectiveness of the method as a tool to simultaneously assess brain activation and connectivity. The method is then applied to a multi-subject fMRI dataset from a balloon-analog risk-taking experiment, showing the effectiveness of the model in providing interpretable joint inference on voxel-level activations and inter-regional connectivity associated with how the brain processes risk. The proposed method is also validated through simulation studies and comparisons to other methods used within the neuroscience community.

The Gibbs sampler can be used to obtain samples of arbitrary size from the posterior distribution over the parameters of a structural equation model (SEM) given covariance data and a prior distribution over the parameters. Point estimates, standard deviations and interval estimates for the parameters can be computed from these samples. If the prior distribution over the parameters is uninformative, the posterior is proportional to the likelihood, and asymptotically the inferences based on the Gibbs sample are the same as those based on the maximum likelihood solution, for example, output from LISREL or EQS. In small samples, however, the likelihood surface is not Gaussian and in some cases contains local maxima. Nevertheless, the Gibbs sample comes from the correct posterior distribution over the parameters regardless of the sample size and the shape of the likelihood surface. With an informative prior distribution over the parameters, the posterior can be used to make inferences about the parameters underidentified models, as we illustrate on a simple errors-in-variables model.

Two marginal one-parameter item response theory models are introduced, by integrating out the latent variable or random item parameter. It is shown that both marginal response models are multivariate (probit) models with a compound symmetry covariance structure. Several common hypotheses concerning the underlying covariance structure are evaluated using (fractional) Bayes factor tests. The support for a unidimensional factor (i.e., assumption of local independence) and differential item functioning are evaluated by testing the covariance components. The posterior distribution of common covariance components is obtained in closed form by transforming latent responses with an orthogonal (Helmert) matrix. This posterior distribution is defined as a shifted-inverse-gamma, thereby introducing a default prior and a balanced prior distribution. Based on that, an MCMC algorithm is described to estimate all model parameters and to compute (fractional) Bayes factor tests. Simulation studies are used to show that the (fractional) Bayes factor tests have good properties for testing the underlying covariance structure of binary response data. The method is illustrated with two real data studies.

This paper presents a hierarchical Bayes circumplex model for ordinal ratings data. The circumplex model was proposed to represent the circular ordering of items in psychological testing by imposing inequalities on the correlations of the items. We provide a specification of the circumplex, propose identifying constraints and conjugate priors for the angular parameters, and accommodate theory-driven constraints in the form of inequalities. We investigate the performance of the proposed MCMC algorithm and apply the model to the analysis of value priorities data obtained from a representative sample of Dutch citizens.

A two-step Bayesian propensity score approach is introduced that incorporates prior information in the propensity score equation and outcome equation without the problems associated with simultaneous Bayesian propensity score approaches. The corresponding variance estimators are also provided. The two-step Bayesian propensity score is provided for three methods of implementation: propensity score stratification, weighting, and optimal full matching. Three simulation studies and one case study are presented to elaborate the proposed two-step Bayesian propensity score approach. Results of the simulation studies reveal that greater precision in the propensity score equation yields better recovery of the frequentist-based treatment effect. A slight advantage is shown for the Bayesian approach in small samples. Results also reveal that greater precision around the wrong treatment effect can lead to seriously distorted results. However, greater precision around the correct treatment effect parameter yields quite good results, with slight improvement seen with greater precision in the propensity score equation. A comparison of coverage rates for the conventional frequentist approach and proposed Bayesian approach is also provided. The case study reveals that credible intervals are wider than frequentist confidence intervals when priors are non-informative.

This study develops Markov Chain Monte Carlo (MCMC) estimation theory for the General Condorcet Model (GCM), an item response model for dichotomous response data which does not presume the analyst knows the correct answers to the test a priori (answer key). In addition to the answer key, respondent ability, guessing bias, and difficulty parameters are estimated. With respect to data-fit, the study compares between the possible GCM formulations, using MCMC-based methods for model assessment and model selection. Real data applications and a simulation study show that the GCM can accurately reconstruct the answer key from a small number of respondents.

An observer is to make inference statements about a quantity p, called a propensity and bounded between 0 and 1, based on the observation that p does or does not exceed a constant c. The propensity p may have an interpretation as a proportion, as a long-run relative frequency, or as a personal probability held by some subject. Applications in medicine, engineering, political science, and, most especially, human decision making are indicated. Bayes solutions for the observer are obtained based on prior distributions in the mixture of beta distribution family; these are then specialized to power-function prior distributions. Inference about log p and log odds is considered. Multiple-action problems are considered in which the focus of inference shifts to the process generating the propensities p, both in the case of a process parameter π known to the subject and unknown. Empirical Bayes techniques are developed for observer inference about c when π is known to the subject. A Bayes rule, a minimax rule and a beta-minimax rule are constructed for the subject when he is uncertain about π.

Estimating dependence relationships between variables is a crucial issue in many applied domains and in particular psychology. When several variables are entertained, these can be organized into a network which encodes their set of conditional dependence relations. Typically however, the underlying network structure is completely unknown or can be partially drawn only; accordingly it should be learned from the available data, a process known as structure learning. In addition, data arising from social and psychological studies are often of different types, as they can include categorical, discrete and continuous measurements. In this paper, we develop a novel Bayesian methodology for structure learning of directed networks which applies to mixed data, i.e., possibly containing continuous, discrete, ordinal and binary variables simultaneously. Whenever available, our method can easily incorporate known dependence structures among variables represented by paths or edge directions that can be postulated in advance based on the specific problem under consideration. We evaluate the proposed method through extensive simulation studies, with appreciable performances in comparison with current state-of-the-art alternative methods. Finally, we apply our methodology to well-being data from a social survey promoted by the United Nations, and mental health data collected from a cohort of medical students. R code implementing the proposed methodology is available athttps://github.com/FedeCastelletti/bayes_networks_mixed_data.

Many physical systems exhibit limit-cycle oscillations that can typically be modeled as stochastically driven self-oscillators. In this work, we focus on a self-oscillator model where the nonlinearity is on the damping term. In various applications, it is crucial to determine the nonlinear damping term and the noise intensity of the driving force. This article presents a novel approach that employs a deep operator network (DeepONet) for parameter identification of self-oscillators. We build our work upon a system identification methodology based on the adjoint Fokker–Planck formulation, which is robust to the finite sampling interval effects. We employ DeepONet as a surrogate model for the operator that maps the first Kramers–Moyal (KM) coefficient to the first and second finite-time KM coefficients. The proposed approach can directly predict the finite-time KM coefficients, eliminating the intermediate computation of the solution field of the adjoint Fokker–Planck equation. Additionally, the differentiability of the neural network readily facilitates the use of gradient-based optimizers, further accelerating the identification process. The numerical experiments demonstrate that the proposed methodology can recover desired parameters with a significant reduction in time while maintaining an accuracy comparable to that of the classical finite-difference approach. The low computational time of the forward path enables Bayesian inference of the parameters. Metropolis-adjusted Langevin algorithm is employed to obtain the posterior distribution of the parameters. The proposed method is validated against numerical simulations and experimental data obtained from a linearly unstable turbulent combustor.

The age at first calving (AFC) is an important trait to be considered in breeding programmes of dairy buffaloes, where new approaches and technologies, such as genomic selection, are constantly applied. Thus, the objective of this study was to compare the predictive ability of different genomic single-step methods using AFC information from Murrah buffaloes. From a pedigree file containing 3320 buffaloes, 2247 cows had AFC records and 553 animals were genotyped. The following models were performed: pedigree-based BLUP (PBLUP), single-step GBLUP (ssGBLUP), weighted single-step GBLUP (WssGBLUP), and single-step Bayesian regression methods (ssBR-BayesA, BayesBπ, BayesCπ, Bayes-Lasso, and BayesRR). To compare the methodologies, the accuracy and dispersion of (G)EBVs were assessed using the LR method. Accuracy estimates for the genotyped animals ranged from 0.30 (PBLUP) to 0.39 (WssGBLUP). Predictions with the traditional model (PBLUP) were very dispersed from what was expected, while BayesCπ (0.99) and WssGBLUP (1.00) obtained the lowest dispersion. The results indicate that the use of genomic information can improve the genetic gain for AFC by increasing the accuracy and reducing inflation/deflation of predictions compared to the traditional pedigree-based model. In addition, among all genomic single-step models studied, WssGBLUP and single-step BayesA were the most advantageous methods to be used in the genomic evaluation of AFC of buffaloes from this population.

This article introduces a comprehensive framework that effectively combines experience rating and exposure rating approaches in reinsurance for both short-tail and long-tail businesses. The generic framework applies to all nonlife lines of business and products emphasizing nonproportional treaty business. The approach is based on three pillars that enable a coherent usage of all available information. The first pillar comprises an exposure-based generative model that emulates the generative process leading to the observed claims experience. The second pillar encompasses a standardized reduction procedure that maps each high-dimensional claim object to a few weakly coupled reduced random variables. The third pillar comprises calibrating the generative model with retrospective Bayesian inference. The derived calibration parameters are fed back into the generative model, and the reinsurance contracts covering future cover periods are rated by projecting the calibrated generative model to the cover period and applying the future contract terms.

When researchers design an experiment, they usually hold potentially relevant features of the experiment constant. We call these details the “topic” of the experiment. For example, researchers studying the impact of party cues on attitudes must inform respondents of the parties’ positions on a particular policy. In doing so, researchers implement just one of many possible designs . Clifford, Leeper, and Rainey (2023. “Generalizing Survey Experiments Using Topic Sampling: An Application to Party Cues.” Forthcoming in Political Behavior. https://doi.org/10.1007/s11109-023-09870-1) argue that researchers should implement many of the possible designs in parallel—what they call “topic sampling”—to generalize to a larger population of topics. We describe two estimators for topic-sampling designs: First, we describe a nonparametric estimator of the typical effect that is unbiased under the assumptions of the design; and second, we describe a hierarchical model that researchers can use to describe the heterogeneity. We suggest describing the heterogeneity across topics in three ways: (1) the standard deviation in treatment effects across topics, (2) the treatment effects for particular topics, and (3) how the treatment effects for particular topics vary with topic-level predictors. We evaluate the performance of the hierarchical model using the Strengthening Democracy Challenge megastudy and show that the hierarchical model works well.

There has been substantial interest in developing Markov chain Monte Carlo algorithms based on piecewise deterministic Markov processes. However, existing algorithms can only be used if the target distribution of interest is differentiable everywhere. The key to adapting these algorithms so that they can sample from densities with discontinuities is to define appropriate dynamics for the process when it hits a discontinuity. We present a simple condition for the transition of the process at a discontinuity which can be used to extend any existing sampler for smooth densities, and give specific choices for this transition which work with popular algorithms such as the bouncy particle sampler, the coordinate sampler, and the zigzag process. Our theoretical results extend and make rigorous arguments that have been presented previously, for instance constructing samplers for continuous densities restricted to a bounded domain, and we present a version of the zigzag process that can work in such a scenario. Our novel approach to deriving the invariant distribution of a piecewise deterministic Markov process with boundaries may be of independent interest.