The combination of human forecasters’ subjective probability estimates usually improves upon the estimates provided by individual forecasters. In order to combine the probability estimates in a Bayes optimal way, prior work proposed a normative Bayesian fusion model that models the estimates with a beta distribution conditioned on their truth value. However, this model assumes conditionally independent probability estimates, although estimates provided by different forecasters are usually correlated. Here, we introduce a Bayesian model for combining subjective probability estimates that explicitly considers their correlation. We assume that an estimate provided by a forecaster for a given query depends on both the forecaster’s skill and the query’s difficulty. The correlation between probability estimates provided by different forecasters is assumed to be caused by the queries that make the forecasters provide similar estimates, for example, correct and highly confident estimates for very easy queries. Our model represents the probability estimates with a beta distribution conditioned on their truth value. It explicitly models the forecasters’ skills and the queries’ difficulties with skill parameters specific for each forecaster and difficulty parameters specific for each query. In this way, it can model the correlations between probability estimates and consider it when combining the estimates. Evaluations on a data set consisting of the subjective probability estimates of 85 human forecasters for 180 queries show improved fusion performance in terms of Brier score compared to related Bayesian fusion models. In particular, it outperforms independent fusion models that suffer from overconfidence.

This article investigates phonological complexity by using artificial neural network and Bayesian structural equation models to derive representations of phonological complexity from counts of the segments associated with particular features in languages’ phonemic inventories. These latent representations can then be used alongside principal component analysis to further analyse how interactions between phonological features affect overall complexity, and what phonological complexity patterns a model can detect in a phonological feature data set. The results indicate that the per-feature segment counts investigated tend to contribute positively to a language’s complexity, and that the latent complexity variables approximate a log-normal distribution. This implies that phonological complexifications co-occur with other complexifications diachronically while tending to be more constrained at the upper and lower ends of the complexity range.

A key factor in ensuring the accuracy of computer simulations that model physical systems is the proper calibration of their parameters based on real-world observations or experimental data. Bayesian methods provide a robust framework for quantifying and propagating the uncertainties that inevitably arise. Nevertheless, they produce predictions unable to represent the observed datapoints when paired with inexact models. Additionally, the quantified uncertainties of these overconfident models cannot be propagated to other Quantities of Interest (QoIs) reliably. A promising solution involves embedding a model inadequacy term in the inference parameters, allowing the quantified model form uncertainty to influence non-observed QoIs. In this work, we revisit this embedded formulation and analyze how different likelihood constructions affect the inference of model form uncertainty, particularly under the presence of prescribed measurement noise and unavoidable model discrepancies. Two additional likelihood formulations, the global moment-matching and relative global moment-matching likelihoods, are introduced to explore alternative ways of representing the residual distribution. The behavior of these likelihoods is examined alongside existing formulations to show how different treatments of measurement noise and discrepancies shape the inferred parameter posteriors, and thereby affect the uncertainty ultimately propagated to the QoIs. Particular attention is given to how the uncertainty associated with the model inadequacy term propagates to the QoIs for the posteriors obtained from different likelihood formulations, enabling a more comprehensive statistical analysis of the prediction’s reliability. Finally, the proposed approach is applied to estimate the uncertainty in the predicted heat flux from a transient thermal simulation using temperature observations.

We explore the effects of fiscal policy shocks on aggregate output and inflation. We use the Bayesian econometric methodology of Baumeister and Hamilton applied to the fiscal structural vector autoregressive model to evaluate key elasticities and fiscal multipliers using U.S. data. In our baseline specification that ends before Covid pandemic, the government spending multiplier is equal to approximately $0.57$ and tax multiplier is approximately $-0.35$ after one year. The short-term output elasticity of government spending is statistically insignificant and the output elasticity of taxes is approximately equal to $2.26$.

This study presents a framework that combines Bayesian inference with reinforcement learning to guide drone-based sampling for methane source estimation. Synthetic gas concentration and wind observations are generated using a calibrated model derived from real-world drone measurements, providing a more representative testbed that captures atmospheric boundary layer variability. We compare three path planning strategies—preplanned, myopic (short-sighted), and non-myopic (long-term)—and find that non-myopic policies trained via deep reinforcement learning consistently yield more precise and accurate estimates of both source location and emission rate. We further investigate centralized multi-agent collaboration and observe comparable performance to independent agents in the tested single-source scenario. Our results suggest that effective source term estimation depends on correctly identifying the plume and obtaining low-noise concentration measurements within it. Precise localization further requires sampling in close proximity to the source, including slightly upwind. In more complex environments with multiple emission sources, multi-agent systems may offer advantages by enabling individual drones to specialize in tracking distinct plumes. These findings support the development of intelligent, data-driven sampling strategies for drone-based environmental monitoring, with potential applications in climate monitoring, emission inventories, and regulatory compliance.

Approaches to linguistic areas have largely focused either on purely qualitative investigation of area-formation processes, on quantitative and qualitative exploration of synchronic distributions of linguistic features without considering time, or on theoretical issues related to the definition of the notion ‘linguistic area’. What is still missing are approaches that supplement qualitative research on area-formation processes with quantitative methods. Taking a bottom-up approach, we bypass notional issues and propose to quantify area-formation processes by (i) measuring the change in linguistic similarity given a geographical space, a sociocultural setting, a time span, a language sample, and a set of linguistic data, and (ii) testing the tendency and magnitude of the process using Bayesian inference. Applying this approach to the expression of reflexivity in a dense sample of languages in northwestern Europe from the early Middle Ages to the present, we show that the method yields robust quantitative evidence for a substantial gain in linguistic similarity that sets the languages of Britain and Ireland apart from languages spoken outside of Britain and Ireland and cross-cuts lines of linguistic ancestry.

Accurate assessment of adverse event (AE) incidence is critical in clinical research for drug safety. While meta-analysis serves as an essential tool to comprehensively synthesize the evidence across multiple studies, incomplete AE reporting in clinical trials remains a persistent challenge. In particular, AEs occurring below study-specific reporting thresholds are often omitted from publications, leading to left-censored data. Failure to account for these censored AE counts can result in biased AE incidence estimates. We present an R Shiny application that implements a Bayesian meta-analysis model specifically designed to incorporate censored AE data into the estimation process. This interactive tool provides a user-friendly interface for researchers to conduct AE meta-analyses and estimate the AE incidence probability using an unbiased approach. It also enables direct comparisons between models that either incorporate or ignore censoring, highlighting the biases introduced by conventional approaches. This tutorial demonstrates the Shiny application’s functionality through an illustrative example on meta-analysis of PD-1/PD-L1 inhibitor safety and highlights the importance of this tool in improving AE risk assessment. Ultimately, the new Shiny app facilitates more accurate and transparent drug safety evaluations. The Shiny-MAGEC app is available at: https://zihanzhou98.shinyapps.io/Shiny-MAGEC/.

Recent experiments aiming to measure phenomena predicted by strong-field quantum electrodynamics (SFQED) have done so by colliding relativistic electron beams and high-power lasers. In such experiments, measurements of collision parameters are not always feasible. However, precise knowledge of these parameters is required to accurately test SFQED.

Here, we present a novel Bayesian inference procedure that infers collision parameters that could not be measured on-shot. This procedure is applicable to all-optical non-linear Compton scattering experiments investigating radiation reaction. The framework allows multiple diagnostics to be combined self-consistently and facilitates the inclusion of known information pertaining to the collision parameters. Using this Bayesian analysis, the relative validity of the classical, quantum-continuous and quantum-stochastic models of radiation reaction was compared for several test cases, which demonstrates the accuracy and model selection capability of the framework and highlight its robustness if the experimental values of fixed parameters differ from their values in the models.

This paper introduces a method for pricing insurance policies using market data. The approach is designed for scenarios in which the insurance company seeks to enter a new market, in our case: pet insurance, lacking historical data. The methodology involves an iterative two-step process. First, a suitable parameter is proposed to characterize the underlying risk. Second, the resulting pure premium is linked to the observed commercial premium using an isotonic regression model. To validate the method, comprehensive testing is conducted on synthetic data, followed by its application to a dataset of actual pet insurance rates. To facilitate practical implementation, we have developed an R package called IsoPriceR. By addressing the challenge of pricing insurance policies in the absence of historical data, this method helps enhance pricing strategies in emerging markets.

This paper demonstrates how Bayesian reasoning can be used for an analog of replication analysis with qualitative research that conducts inference to best explanation. We overview the basic mechanics of Bayesian reasoning with qualitative evidence and apply our approach to recent research on climate change politics, a matter of major importance that is beginning to attract greater interest in the discipline. Our re-analysis of illustrative evidence from a prominent article on global collective-action versus distributive politics theories of climate policy largely accords with the authors’ conclusions, while illuminating the value added of Bayesian analysis. In contrast, our in-depth examination of scholarship on oil majors’ support for carbon pricing yields a Bayesian inference that diverges from the authors’ conclusions. These examples highlight the potential for Bayesian reasoning not only to improve inferences when working with qualitative evidence but also to enhance analytical transparency, facilitate communication of findings, and promote knowledge accumulation.

The ice shelves buttressing the Antarctic ice sheet determine the rate of ice-discharge into the surrounding oceans. Their geometry and buttressing strength are influenced by the local surface accumulation and basal melt rates, governed by atmospheric and oceanic conditions. Contemporary methods quantify one of these rates, but typically not both. Moreover, information about these rates is only available for recent time periods, reaching at most a few decades back since measurements are available. We present a new method to simultaneously infer the surface accumulation and basal melt rates averaged over decadal and centennial timescales. We infer the spatial dependence of these rates along flow line transects using internal stratigraphy observed by radars, using a kinematic forward model of internal stratigraphy. We solve the inverse problem using simulation-based inference (SBI). SBI performs Bayesian inference by training neural networks on simulations of the forward model to approximate the posterior distribution, therefore also quantifying uncertainties over the inferred parameters. We validate our method on a synthetic example, and apply it to Ekström Ice Shelf, Antarctica, for which independent validation data are available. We obtain posterior distributions of surface accumulation and basal melt averaging over up to 200 years before 2022.

Dynamic latent variable models generally link units’ positions on a latent dimension over time via random walks. Theoretically, these trajectories are often expected to resemble a mixture of periods of stability interrupted by moments of change. In these cases, a prior distribution such as the regularized horseshoe—that allows for both stasis and change—can prove a better theoretical and empirical fit for the underlying construct than other priors. Replicating Reuning, Kenwick, and Fariss (2019), we find that the regularized horseshoe performs better than the standard normal and the Student’s t-distribution when modeling dynamic latent variable models. Overall, the use of the regularized horseshoe results in more accurate and precise estimates. More broadly, the regularized horseshoe is a promising prior for many similar applications.

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.