Bayesian Inference Research Articles

Five new species of endophytic Penicillium from rubber trees in the Brazilian Amazon.

The Amazon rainforest is the world's most diverse ecosystem, full of fauna and flora. Among the trees that make up the forest are the rubber trees of the genus Hevea (H. brasiliensis and H. guianensis), which stand out for the industrial use of latex. It was previously shown that endophytic fungi colonize the leaves, stems, and roots of Hevea spp. In this study, 47 Penicillium spp. and three Talaromyces spp. isolates were analyzed using specific DNA barcodes: internal transcribed spacers region (ITS), β-tubulin (BenA), calmodulin (CaM), and the DNA-dependent RNA polymerase II second largest subunit (RPB2) genes and additionally, for species delimitation, the genealogical concordance phylogenetic species recognition (GCPSR) criteria were applied. The phylogenetic analyses placed the Penicillium isolates into four sections Lanata-Divaricata, Sclerotiora, Citrina, and Fasciculata. The morphological and molecular characteristics resulted in the discovery of five new species (P. heveae sp. nov., P. acrean sp. nov., P. aquiri sp. nov., P. amazonense sp. nov., and P. pseudomellis sp. nov.). The five new species were also compared to closely related species, with observations on morphologically distinguishing features and colony appearances. Bayesian inference and maximum likelihood analysis have supported the placement of P. heveae sp. nov. as a sister group to P. globosum; P. acrean sp. nov. and P. aquiri sp. nov. as sister groups to P. sumatrense; P. amazonense sp. nov. closely related to isolates of P. rolfsii, and P. pseudomellis sp. nov. closely related to P. mellis. The study of endophytic Penicillium species of rubber trees and the description of five new taxa of Penicillium sect. Citrina, Lanata-Divaricata, and Sclerotiora as endophytes add to the fungal biodiversity knowledge in native rubber trees. Reports of fungi in native tropical plants may reveal taxonomic novelties, potential pathogen control agents, and producers of molecular bioactive compounds of medical and agronomic interest.

Bayesian inference of frequency-specific functional connectivity in MEG imaging using a spectral graph model

Abstract Understanding the relationship between structural connectivity (SC) and functional connectivity (FC) of the human brain is an important goal of neuroscience. Highly detailed mathematical models of neural masses exist that can simulate the interactions between functional activity and structural wiring. These models are often complex and require intensive computation. Most importantly, they do not provide a direct or intuitive interpretation of this structure–function relationship. In this study, we employ the emerging concepts of spectral graph theory to obtain this mapping in terms of graph harmonics, which are eigenvectors of the structural graph’s Laplacian matrix. In order to imbue these harmonics with biophysical underpinnings, we leverage recent advances in parsimonious spectral graph modeling (SGM) of brain activity. Here, we show that such a model can indeed be cast in terms of graph harmonics, and can provide a closed-form prediction of FC in an arbitrary frequency band. The model requires only three global, spatially invariant parameters, yet is capable of generating rich FC patterns in different frequency bands. Only a few harmonics are sufficient to reproduce realistic FC patterns. We applied the method to predict FC obtained from pairwise magnitude coherence of source-reconstructed resting-state magnetoencephalography (MEG) recordings of 36 healthy subjects. To enable efficient model inference, we adopted a deep neural network-based Bayesian procedure called simulation-based inference. Using this tool, we were able to speedily infer not only the single most likely model parameters, but also their full posterior distributions. We also implemented several other benchmark methods relating SC to FC, including graph diffusion and coupled neural mass models. The present method was shown to give the best performance overall. Notably, we discovered that a single biophysical parameterization is capable of fitting FCs from all relevant frequency bands simultaneously, an aspect that did not receive adequate attention in prior computational studies.

Influence of Sires on Population Substructure in Dülmen Wild Horses

The objectives of the present study were to analyze the influence of the stallions employed in the Dülmen wild horses on the genetic diversity and population substructure using Bayesian cluster analysis. The Dülmen wild horse is maintained as a unique horse population exposed to the natural conditions all year round in the Merfelder Bruch near Dülmen in Westphalia, Germany. Stallions selected for breeding have to prove their abilities to survive under this harsh environment. We used multilocus genotypic information from a set of 29 autosomal microsatellites to determine the paternity of 185 male foals sired by nine stallions. As females could not be sampled, we could not make inferences on all yearlings and test whether there are differences in the genetic population parameters between both sexes. The mean number of progeny was 19.92 with a range of 2–32, caused by the length of the service period per stallion. The average observed and unbiased expected heterozygosity was 0.688 and 0.631, the mean number of alleles was 4.448, and Wright’s FIS was −0.173. Pairwise genetic distances (FST and Nei’s unbiased genetic distances) were significant and varied between 0.038 to 0.091 and 0.085 to 0.290, respectively. Neighbor-joining dendrogram plots clustered a large proportion of the paternal progeny groups in different branches. Posterior Bayesian analyses using seven paternal half-sib groups with 10–74 members supported a maximum of six clusters, with two paternal progeny groups not differing, and a median of five clusters, with two groups of two sires each falling into the same clusters. When sires were employed in non-consecutive years, progeny from these different years of the same sires were grouped in the same cluster, whereas the progeny of one sire from two consecutive years were in different clusters. We were able to distinguish male progeny from Dülmen wild horse stallions and to show the effects of stallion use on the genetic substructure in the Dülmen wild horse herd. In conclusion, the analyses showed the genetic potential of the Dülmen wild horse stallions to maintain a high genetic diversity and also the effects in which breeding seasons and for how long stallions are used to sire foals. The selection of stallions may be sensitive for the further development of genetic diversity and preserve this closed population as a valuable resource for further studies on the evolution of the horse.

Genetic characterisation of Annona crassiflora as basis for conservation and breeding

Abstract Annona crassiflora is a fruit-bearing tree species native to the Cerrado that has ecological and economic potential, mainly due to the production of attractive and useful fruits for a number of species, including humans. To provide a basis for its conservation and breeding, the objective was to assess the diversity and genetic structure of natural populations of the species using inter-simple sequence repeat (ISSR) molecular markers. Eight populations were analysed in the state of Minas Gerais, Brazil, with 24 individuals randomly sampled in each population, reaching a total of 192 trees. Ten ISSR primers were used, resulting in high genetic diversity for the combined data (H* = 0.35 and I* = 0.52). However, a wide range of representative values was observed in the individual assessment of populations, with JAN, GM and MC standing out for their low genetic diversity, resulting in H* of 0.19, 0.23 and 0.24 and I* of 0.28, 0.34 and 0.35, respectively. An analysis of molecular variance showed greater variation within populations, indicating gene flow (Nm), but genetic differentiation between populations was moderate. Bayesian analysis, although resulting in four genetic groups, revealed the presence of a majority group for the GM and JAN populations. We propose measures to maintain these populations, such as raising awareness of local extractivism and planting genetically divergent seedlings. Furthermore, we recommend including of all populations in conservation and breeding programmes, aiming to cover the maximum genetic variation for the species.

Overcoming bias in estimating epidemiological parameters with realistic history-dependent disease spread dynamics

Epidemiological parameters such as the reproduction number, latent period, and infectious period provide crucial information about the spread of infectious diseases and directly inform intervention strategies. These parameters have generally been estimated by mathematical models that involve an unrealistic assumption of history-independent dynamics for simplicity. This assumes that the chance of becoming infectious during the latent period or recovering during the infectious period remains constant, whereas in reality, these chances vary over time. Here, we find that conventional approaches with this assumption cause serious bias in epidemiological parameter estimation. To address this bias, we developed a Bayesian inference method by adopting more realistic history-dependent disease dynamics. Our method more accurately and precisely estimates the reproduction number than the conventional approaches solely from confirmed cases data, which are easy to obtain through testing. It also revealed how the infectious period distribution changed throughout the COVID-19 pandemic during 2020 in South Korea. We also provide a user-friendly package, IONISE, that automates this method.

Role of interleukin-18 in mediating the impacts of celiac disease on osteoporosis: a Mendelian randomization study

BackgroundExtensive observational data suggest a link between celiac disease (CeD) and osteoporosis, but the causality and mediating mechanism remain undetermined. Herein, we performed a Mendelian randomization (MR) study to address these concerns.MethodsWe obtained the summary-level statistics for CeD from a large genome-wide association study (GWAS) comprising 4,533 cases and 10,750 controls of European ancestry. The GWAS data for osteoporosis-related traits and inflammatory cytokines were derived from the UK Biobank, FinnGen, IEU OpenGWAS database, or GWAS catalog. Two-sample MR with the inverse variance-weighted methods were employed to evaluate the genetic association between CeD and osteoporosis-related traits. The potential inflammatory mediators from CeD to osteoporosis were explored using two-step mediation analyses.ResultsThe primary MR analyses demonstrated causal associations between genetically predicted CeD and osteoporosis (odds ratio [OR]: 1.110, 95% confidence interval [CI]: 1.043–1.182, p=0.001), total body bone mineral density (β: -0.025, p=0.039), and osteoporotic fracture (OR: 1.124, 95% CI: 1.009–1.253, p=0.034). Extensive sensitivity analyses consolidated these findings. Among the candidate inflammatory cytokines, only interleukin-18 was observed to mediate the effects of CeD on osteoporosis, with an indirect OR of 1.020 (95% CI: 1.000–1.040, p=0.048) and a mediation proportion of 18.9%. The mediation effects of interleukin-18 could be validated in other datasets (OR: 1.015, 95% CI: 1.001–1.029, p=0.041). Bayesian colocalization analysis supported the role of interleukin-18 in osteoporosis.ConclusionThe present MR study reveals that CeD is associated with an increased risk of developing osteoporosis, which may be partly mediated by upregulation of interleukin-18.

Morphological and phylogenetic analyses reveal eight novel species of Pestalotiopsis (Sporocadaceae, Amphisphaeriales) from southern China

Plants play an important role in maintaining the ecological balance of the biosphere, but often suffer from pathogenic fungi during growth. During our continuing mycological surveys of plant pathogens from terrestrial plants in Jiangxi and Yunnan provinces, China, 24 strains of Pestalotiopsis isolated from diseased and healthy tissues of plant leaves represented eight new species, viz. P. alpinicola, P. camelliicola, P. cyclosora, P. eriobotryae, P. gardeniae, P. hederae, P. machiliana and P. mangifericola. Multi-locus (ITS, tef1-α and tub2) phylogenetic analyses were performed using maximum-likelihood and Bayesian inference to reveal their taxonomic placement within Pestalotiopsis. Both molecular phylogenetic analyses and morphological comparisons supported them as eight independent taxa within Pestalotiopsis. Illustrations and descriptions of these eight taxa were provided, in conjunction with comparisons with closely related taxa in the genus. This work highlights the large potential for new fungal species associated with diseased plant leaves.

Infection and infestation-related adverse events of biologics in psoriasis: insights from the Food and Drug Administration Adverse Event Reporting System (FAERS)

ABSTRACT Objective The study aims to thoroughly assess the adverse events related to infections and infestations associated with biological agents used for psoriasis using the U.S. Food and Drug Administration’s Adverse Event Reporting System (FAERS) database. Methods We analyzed FAERS data from the first quarter of 2004 to the fourth quarter of 2023. The study included TNF-α inhibitors (etanercept, infliximab, adalimumab), IL-12/23 inhibitors (ustekinumab), IL-23p19 inhibitors (guselkumab), and IL-17 inhibitors (secukinumab, ixekizumab). We used disproportionality analysis and Bayesian methods to quantify the related adverse event (AE) signals. Results Most AEs related to infections and infestations are already listed on the drug packaging labels. Notably, TNF-α inhibitors are associated with a significantly higher incidence of tuberculosis-related diseases compared to other biological agents. In contrast, IL-17 inhibitors show a greater variety and number of fungal infection-related AEs than their counterparts. Furthermore, our study has identified new potential AEs that require the attention of clinicians. Conclusion In clinical practice, it is advisable to monitor the risks of infections and infestations in patients receiving biological agents for psoriasis to enable early detection and intervention. Our findings highlight the need for further epidemiological investigations to establish causality and guide clinical practice in managing these risks effectively.

Two replications of Wiechert et al.'s (2023) online Think/No-Think study in undergraduate students.

The Think/No-Think (TNT) task examines the effects of attempts at suppressing particular stimuli. First, participants learn cue-target word pairs. Subsequently, they either recall (Think trials) or avoid thinking about targets whatsoever (No-Think trials) in response to cues. The critical finding is that No-Think targets are recalled less well than Baseline items (i.e., Suppression-Induced Forgetting; SIF). Wiechert et al.'s [(2023). Suppression-induced forgetting: A pre-registered replication of the think/no-think paradigm. Memory (Hove, England), 31(7), 989-1002] null-findings in Prolific workers using online video calls casted doubts on the robustness of the effect. We adapted their procedure in two replication studies testing undergraduate psychology students. The first study (N = 54) adapted Wiechert's procedure to an in-person laboratory setting using Same Probe (SP) recall and found evidence for SIF. Hypothesizing that an online test should yield SIF in undergraduates as well, study 2 replicated both the in-person laboratory (n = 54) and online (n = 54) procedures. The results suggested evidence for SIF in the in-lab setting, yet no evidence was observed in the online setting. As exploratory Bayesian analyses showed conclusive evidence for a null effect, this pattern of results does not imply that the in-lab and online settings actually differed. Yet, overall, the results cast doubts on the generalisability of the SIF-effect.

Genetic diversity and evolution of porcine hemagglutinating encephalomyelitis virus in Guangxi province of China during 2021–2024

Porcine hemagglutinating encephalomyelitis virus (PHEV) is the only known porcine neurotropic coronavirus, which is prevalent worldwide at present. It is of great significance to understand the genetic and evolutionary characteristics of PHEV in order to perform effective measures for prevention and control of this disease. In this study, a total of 6,986 tissue samples and nasopharyngeal swabs were collected from different regions of Guangxi province in southern China during 2021-2024, and were tested for PHEV using a quadruplex RT-qPCR. The positivity rate of PHEV was 2.81% (196/6,986), of which tissue samples and nasopharyngeal swabs had 2.05% (87/4,246) and 3.98% (109/2,740) positivity rates, respectively. Fifty PHEV positive samples were selected for PCR amplification and gene sequencing. Sequence analysis revealed that the nucleotide homology and amino acid similarities of S, M, and N genes were 94.3%-99.3% and 92.3%-99.2%, 95.0%-99.7% and 94.7%-100.0%, 94.0%-99.5% and 93.5%-99.3%, respectively, indicating M and N genes were more conservative than S gene. Phylogenetic trees based on these three genes revealed that PHEV strains from different countries could be divided into two groups G1 and G2, and the PHEV strains from Guangxi province obtained in this study distributed in subgroups G1c and G2b. Bayesian analysis revealed that the population size of PHEV has been in a relatively stable state since its discovery until it expanded sharply around 2015, and still on the slow rise thereafter. S gene sequences analysis indicated that PHEV strains existed variation of mutation, and recombination. The results indicated that the prevalent PHEV strains in Guangxi province had complex evolutionary trajectories and high genetic diversity. To the best of our knowledge, this is the first report on the genetic and evolutionary characteristics of PHEV in southern China.

Efficient, multimodal, and derivative-free Bayesian inference with Fisher-Rao gradient flows

Abstract In this paper, we study efficient approximate sampling for probability distributions known up to normalization constants. We specifically focus on a problem class arising in Bayesian inference for large-scale inverse problems in science and engineering applications. The computational challenges we address with the proposed methodology are: (i) the need for repeated evaluations of expensive forward models; (ii) the potential existence of multiple modes; and (iii) the fact that gradient of, or adjoint solver for, the forward model might not be feasible.

While existing Bayesian inference methods meet some of these challenges individually, we propose a framework that tackles all three systematically. Our approach builds upon the Fisher-Rao gradient flow in probability space, yielding a dynamical system for probability densities that converges towards the target distribution at a uniform exponential rate. This rapid convergence is advantageous for the computational burden outlined in (i). We apply Gaussian mixture approximations with operator splitting techniques to simulate the flow numerically; the resulting approximation can capture multiple modes thus addressing (ii). Furthermore, we employ the Kalman methodology to facilitate a derivative-free update of these Gaussian components and their respective weights, addressing the issue in (iii).

The proposed methodology results in an efficient derivative-free posterior approximation method, flexible enough to handle multi-modal distributions: Gaussian Mixture Kalman Inversion (GMKI). The effectiveness of GMKI is demonstrated both theoretically and numerically in several experiments with multimodal target distributions, including proof-of-concept and two-dimensional examples, as well as a large-scale application: recovering the Navier-Stokes initial condition from solution data at positive times.



Spatiotemporal Bayesian Machine Learning for Estimation of an Empirical Lower Bound for Probability of Detection with Applications to Stationary Wildlife Photography

An important parameter in the monitoring and surveillance systems is the probability of detection. Advanced wildlife monitoring systems rely on camera traps for stationary wildlife photography and have been broadly used for estimation of population size and density. Camera encounters are collected for estimation and management of a growing population size using spatial capture models. The accuracy of the estimated population size relies on the detection probability of the individual animals, and in turn depends on observed frequency of the animal encounters with the camera traps. Therefore, optimal coverage by the camera grid is essential for reliable estimation of the population size and density. The goal of this research is implementing a spatiotemporal Bayesian machine learning model to estimate a lower bound for probability of detection of a monitoring system. To obtain an accurate estimate of population size in this study, an empirical lower bound for probability of detection is realized considering the sensitivity of the model to the augmented sample size. The monitoring system must attain a probability of detection greater than the established empirical lower bound to achieve a pertinent estimation accuracy. It was found that for stationary wildlife photography, a camera grid with a detection probability of at least 0.3 is required for accurate estimation of the population size. A notable outcome is that a moderate probability of detection or better is required to obtain a reliable estimate of the population size using spatiotemporal machine learning. As a result, the required probability of detection is recommended when designing an automated monitoring system. The number and location of cameras in the camera grid will determine the camera coverage. Consequently, camera coverage and the individual home-range verify the probability of detection.

Uncertainty quantification on small angle x-ray scattering measurement using Bayesian deep learning

Small angle x-ray scattering (SAXS) is a widely recognized solution for measuring complex nanostructures. With the increasing demand for accurately assessing structural characteristics and optimizing manufacturing processes, uncertainty quantification in SAXS inverse problems has become a critical issue. However, traditional methods face challenges such as slow computation speed and inaccurate estimation of multidimensional parameters. To overcome these issues, we propose an uncertainty quantification approach suitable for SAXS measurement that approximates the posterior using Bayesian deep learning. The effectiveness and reliability of our method are illustrated by assessing structural parameters of synthetic 2D Si grating samples. The uncertainty quantification takes only about 2.3 s, thousands of times faster than the conventional Markov Chain Monte Carlo (MCMC) methods. Also, our method has superior repeatability for parameter measurement compared to the MCMC approaches. It provides the potential of efficient and reliable SAXS measurement in increasingly intricate semiconductor manufacturing.

A Bayesian learning and pricing model with multiple unknown demand parameters

A Bayesian learning and pricing model with multiple unknown demand parameters

Revisiting the effect of lens mass models in cosmological applications of strong gravitational lensing

Abstract Strong gravitational lens system catalogues are typically used to constrain a combination of cosmological and empirical power-law lens mass model parameters, often introducing additional empirical parameters and constraints from high resolution imagery. We investigate these lens models using Bayesian methods through a novel alternative that treats spatial curvature via the non-FLRW timescape cosmology. We apply Markov Chain Monte Carlo methods using the catalogue of 161 lens systems of Chen et al. (2019) in order to constrain both lens and cosmological parameters for: (i) the standard ΛCDM model with zero spatial curvature; and (ii) the timescape model. We then generate large mock data sets to further investigate the choice of cosmology on fitting simple power-law lens models. In agreement with previous results, we find that in combination with single isothermal sphere parameters, models with zero FLRW spatial curvature fit better as the free parameter approaches an unphysical empty universe, ΩM0 → 0. By contrast, the timescape cosmology is found to prefer parameter values in which its cosmological parameter, the present void fraction, is driven to fv0 → 0.73 and closely matches values that best fit independent cosmological data sets: supernovae Ia distances and the cosmic microwave background. This conclusion holds for a large range of seed values fv0 ∈ {0.1, 0.9}, and for timescape fits to both timescape and FLRW mocks. Regardless of cosmology, unphysical estimates of the distance ratios given from power-law lens models result in poor goodness of fit. With larger datasets soon available, separation of cosmology and lens models must be addressed.

A review of current practice in the design and analysis of extremely small stepped-wedge cluster randomized trials.

Stepped-wedge cluster randomized trials tend to require fewer clusters than standard parallel-arm designs due to the switches between control and intervention conditions, but there are no recommendations for the minimum number of clusters. Trials randomizing an extremely small number of clusters are not uncommon, but the justification for small numbers of clusters is often unclear and appropriate analysis is often lacking. In addition, stepped-wedge cluster randomized trials are methodologically more complex due to their longitudinal correlation structure, and ignoring the distinct within- and between-period intracluster correlations can underestimate the sample size in small stepped-wedge cluster randomized trials. We conducted a review of published small stepped-wedge cluster randomized trials to understand how and why they are used, and to characterize approaches used in their design and analysis. Electronic searches were used to identify primary reports of full-scale stepped-wedge cluster randomized trials published during the period 2016-2022; the subset that randomized two to six clusters was identified. Two reviewers independently extracted information from each report and any available protocol. Disagreements were resolved through discussion. We identified 61 stepped-wedge cluster randomized trials that randomized two to six clusters: median sample size (Q1-Q3) 1426 (420-7553) participants. Twelve (19.7%) gave some indication that the evaluation was considered a "preliminary" evaluation and 16 (26.2%) recognized the small number of clusters as a limitation. Sixteen (26.2%) provided an explanation for the limited number of clusters: the need to minimize contamination (e.g. by merging adjacent units), limited availability of clusters, and logistical considerations were common explanations. Majority (51, 83.6%) presented sample size or power calculations, but only one assumed distinct within- and between-period intracluster correlations. Few (10, 16.4%) utilized restricted randomization methods; more than half (34, 55.7%) identified baseline imbalances. The most common statistical method for analysis was the generalized linear mixed model (44, 72.1%). Only four trials (6.6%) reported statistical analyses considering small numbers of clusters: one used generalized estimating equations with small-sample correction, two used generalized linear mixed model with small-sample correction, and one used Bayesian analysis. Another eight (13.1%) used fixed-effects regression, the performance of which requires further evaluation under stepped-wedge cluster randomized trials with small numbers of clusters. None used permutation tests or cluster-period level analysis. Methods appropriate for the design and analysis of small stepped-wedge cluster randomized trials have not been widely adopted in practice. Greater awareness is required that the use of standard sample size calculation methods can provide spuriously low numbers of required clusters. Methods such as generalized estimating equations or generalized linear mixed models with small-sample corrections, Bayesian approaches, and permutation tests may be more appropriate for the analysis of small stepped-wedge cluster randomized trials. Future research is needed to establish best practices for stepped-wedge cluster randomized trials with a small number of clusters.

Cloud detection for HY-1C/COCTS over the ocean based on spectral-and-textural-information-guided deep neural network

AbstractGiven that clouds can absorb and scatter radiation signals in the visible and infrared bands, cloud detection is a key preprocessing step for ocean color and sea surface temperature retrievals. In this research, a Spectral-and-Textural-Information-Guided deep neural Network (STIGNet) is designed for cloud detection in global ocean data from the Haiyang-1C (HY-1C)/Chinese Ocean Color and Temperature Scanner (COCTS). Considering the spectral and textural properties of clouds, the model incorporates HY-1C/COCTS spectral data, differences in brightness temperature (BT), local statistical characteristics of BT, and geographical location information–all of which are closely related to cloud features. Notably, an edge learning module is implemented to emphasize edge features during the training process. We construct a HY-1C/COCTS cloud detection dataset to train and test the cloud detection model. In the dataset, labels are generated by combining the Bayesian cloud detection method with a manual mask. Analysis of the resulting cloud detection images indicates that STIGNet exhibits accurate performance across various types of clouds while showing minimal overestimated errors in areas such as ocean fronts or sun glints, where they tend to occur frequently. The ablation experiments performed on physical-based input features and edge learning modules show enhancements in cloud detection accuracy. Evaluation results demonstrate an overall accuracy of 96.64%, with a cloud overestimated error of 1.61% and a cloud missed error of 1.76%. These findings highlight the effectiveness of STIGNet in generating precise cloud masks for HY-1C/COCTS data.

How distributed subcortical integration of reward and threat may inform subsequent approach-avoidance decisions.

Healthy and successful living involves carefully navigating rewarding and threatening situations by balancing approach and avoidance behaviours. Excessive avoidance to evade potential threats often leads to forfeiting potential rewards. However, little is known about how reward and threat information is integrated neurally to inform approach or avoidance decisions. In this preregistered study, participants (Nbehaviour=31, 17F; NMRI=28, 15F) made approach-avoidance decisions under varying reward (monetary gains) and threat (electrical stimulations) prospects during functional MRI scanning. In contrast to theorized parallel subcortical processing of reward and threat information before cortical integration, Bayesian Multivariate Multilevel analyses revealed subcortical reward and threat integration prior to indicating approach-avoidance decisions. This integration occurred in the ventral striatum, thalamus, and bed nucleus of the stria terminalis (BNST). When reward was low, risk-diminishing avoidance decisions dominated, which was linked to more positive tracking of threat magnitude prior to indicating avoidance than approach decisions across these regions. In contrast, the amygdala exhibited dual sensitivity to reward and threat. While anticipating outcomes of risky approach decisions, we observed positive tracking of threat magnitude within the salience network (dorsal anterior cingulate cortex, thalamus, periaqueductal gray, BNST). Conversely, after risk-diminishing avoidance, characterized by reduced reward prospects, we observed more negative tracking of reward magnitude in the ventromedial prefrontal cortex and ventral striatum. These findings shed light on the temporal dynamics of approach-avoidance decision-making. Importantly, they demonstrate the role of subcortical integration of reward and threat information in balancing approach and avoidance, challenging theories positing predominantly separate subcortical processing prior to cortical integration.Significance statement When deciding whether to approach or avoid situations, our decision-making involves balancing potential rewards and threats. Widespread theories of decision-making in humans propose parallel processing of reward and threat information in subcortical regions, followed by cortical integration. Challenging these notions, we found evidence for dual and integrated processing of reward and threat in subcortical regions during decision-making. In contrast, after decision-making, we observed the expected parallel processing while anticipating decision outcomes. These findings advance our understanding of approach-avoidance decision-making processes, opposing traditional views that segregate brain regions as predominantly reward-sensitive or threat-sensitive, thereby paving the way for a more nuanced perspective that takes into account the stage of decision-making.

Efficient Bayesian inference and model selection for continuous gravitational waves in pulsar timing array data

Abstract Finding and characterizing gravitational waves from individual supermassive black hole binaries is a central goal of pulsar timing array experiments, which will require analysis methods that can be efficient on our rapidly growing datasets. Here we present a novel approach built on three key elements: i) precalculating and interpolating expensive matrix operations; ii) semi-analytically marginalizing over the gravitational-wave phase at the pulsars; iii) numerically marginalizing over the pulsar distance uncertainties. With these improvements the recent NANOGrav 15yr dataset can be analyzed in minutes after an O(1 hour) setup phase, instead of an analysis taking days-weeks with previous methods. The same setup can be used to efficiently analyze the dataset under any sinusoidal deterministic model. In particular, this will aid testing the binary hypothesis by allowing for efficient analysis of competing models (e.g. incoherent, monopolar, or dipolar sine wave model) and scrambled datasets for false alarm studies. The same setup can be updated in minutes for new realizations of the data, which enables large simulation studies.

Programmable MCMC with Soundly Composed Guide Programs

Probabilistic programming languages (PPLs) provide language support for expressing flexible probabilistic models and solving Bayesian inference problems. PPLs with programmable inference make it possible for users to obtain improved results by customizing inference engines using guide programs that are tailored to a corresponding model program. However, errors in guide programs can compromise the statistical soundness of the inference. This article introduces a novel coroutine-based framework for verifying the correctness of user-written guide programs for a broad class of Markov chain Monte Carlo (MCMC) inference algorithms. Our approach rests on a novel type system for describing communication protocols between a model program and a sequence of guides that each update only a subset of random variables. We prove that, by translating guide types to context-free processes with finite norms, it is possible to check structural type equality between models and guides in polynomial time. This connection gives rise to an efficient type-inference algorithm for probabilistic programs with flexible constructs such as general recursion and branching. We also contribute a coverage-checking algorithm that verifies the support of sequentially composed guide programs agrees with that of the model program, which is a key soundness condition for MCMC inference with multiple guides. Evaluations on diverse benchmarks show that our type-inference and coverage-checking algorithms efficiently infer types and detect sound and unsound guides for programs that existing static analyses cannot handle.