Bayesian Inference Framework Research Articles

Bayesian Inference for Estimating Heat Sources Through Temperature Assimilation

Abstract This paper utilizes a Bayesian inference framework to address the two-dimensional (2D) steady-state heat conduction problem, focusing on the estimation of unknown distributed heat sources in a thermally conducting medium with uniform conductivity. The goal is to infer the locations, strength, and shape of heaters by assimilating temperature data in Euclidean space, employing a Fourier series to represent each heater's shape. The Markov Chain Monte Carlo (MCMC) method, incorporating the random-walk Metropolis–Hasting (MH) algorithm and parallel tempering, is utilized for posterior distribution exploration in both unbounded and wall-bounded domains. It is found that multiple solutions arise in cases where the number of temperature sensors is less than the number of unknown states. Moreover, smaller heaters introduce greater uncertainty in estimated strength. To address the challenge of estimating the heater's strength and shape simultaneously due to their strong correlation, our method incorporates sharp priors on one to ensure accurate and feasible solutions of the other. The diffusive nature of heat conduction smooths out any deformations in the temperature contours, especially in the presence of multiple heaters positioned near each other, impacting convergence. In wall-bounded domains with Neumann boundary conditions, the inference of heater parameters tends to be more accurate than in unbounded domains.

Fisher Meets Bayes: The Value of Randomisation for Bayesian Inference of Causal Effects

SummaryFor a Bayesian agent with beliefs about the relationship between covariates and potential outcomes, deterministically selecting an assignment that yields optimal covariate balance rationally dominates randomisation. However, randomisation—by enabling control over the probabilities of erroneous causal conclusions due to unknown covariate imbalances—offers insurance against the possibility that an agent's beliefs may be misleading. For the most part, such rational justifications for optimum assignment have presupposed the framework of Bayesian inference, while such epistemic justifications for randomisation have presupposed the framework of significance testing. In this paper, I build on a conception of balance that seems inextricable from the significance testing framework, Fisherian balance, to show that it implies an analogous epistemic justification for randomisation within the framework of Bayesian inference. Consequently, for the choice between optimum and random assignment, this paper shows that epistemic justifications need not be wedded to significance testing nor must Bayesian inference be wedded to rational justifications.

Evidence to inform spatiotemporal management of a western Pacific Ocean tuna purse seine fishery.

Fisheries can profoundly impact co-occurring species exposed to incidental capture. Spatiotemporal fisheries management holds substantial potential to balance socioeconomic benefits with ecological costs to threatened bycatch species. This study estimated the effect of the spatial and temporal distribution of effort by a western Pacific Ocean tuna purse seine fishery on catch rates of target and at-risk species by fitting spatially explicit generalized additive multilevel regression models within a Bayesian inference framework to observer data. Mean field prediction surfaces defined catch rate hotspots for tunas, silky sharks, rays, and whale sharks, informing the design of candidate area-based management strategies. Due to limited sample sizes, odontocete and marine turtle catch rate geospatial patterns were summarized using simple 2D hexagonal binning. Effort could be focused in two areas within core fishing grounds to reduce overlap with hotspots for silky sharks, rays, and whale sharks without affecting target catch. Effort could be shifted outside of core fishing areas to zones with higher target tuna catch rates to reduce overlap with hotspots for at-risk species. Sparse and small marine turtle and whale shark hotspots occurred across the fishing grounds. Results did not identify opportunities for temporally dynamic spatial management to balance target and at-risk catch rates. Research on the economic and operational viability of alternative spatial management strategies is a priority. A small subset of sets had disproportionately large odontocete captures. Real-time fleet communication, move-on rules, and avoiding sets on dolphin schools might reduce odontocete catch rates. Managing set association type and mesh size present additional opportunities to balance catch rates of at-risk and target species. Employing output controls that effectively constrain the fishery would alter the spatial management strategy to focus fishing within zones with the lowest ratio of at-risk bycatch to target tuna catch. Findings inform the design of alternative spatial management strategies to avoid catch rate hotspots of at-risk species without compromising the catch of principal market species.

Bayesian finite element model inversion of offshore wind turbine structures for joint parameter-load estimation

Operating in harsh and unsteady marine environment, offshore wind turbine (OWT) structures are exposed to unpredictable wind and wave loads. Identifying the structural loads and their effects on the OWTs allow for predicting the remaining fatigue life of these structures and improving the structural design procedure. In this paper, a finite element (FE) model inversion method is presented to estimate the unknown loads and model parameters of OWTs using sparse measurement data. A realistic FE model of an OWT structure with jacket substructure is created in the open-source simulation platform, OpenSees. A Bayesian inference framework is presented to integrate the measured data with the FE model to estimate unknown wind loads and mass of rotor-nacelle assembly. To evaluate the performance of this data assimilation framework, the effect of sensor type, number of sensors, and modeling errors on the estimation accuracy of wind loads and model parameters are investigated through different case studies where synthetic data are used as measurements. The results of this study are important to guide instrumentation of new OWT structures, and to understand the potential limitations and sources of error in the real-world application of this data assimilation framework for joint model parameter and input load estimation.

Bayesian Multilayered Mediation Analysis for Cancer Pharmacogenomics

ABSTRACTMultiomic data from multilevel biological systems are becoming common and motivate integrative modelling approaches to decipher within‐ and cross‐platform dependencies. Mediation analysis aims to identify mediating mechanisms that regulate the effect of an exposure on an outcome. In multiomic contexts, identification of genomic mediators of disease outcomes provides a deeper understanding of mechanisms of disease and corresponding therapeutic targets. While there has been significant work on joint modelling of high‐dimensional potential mediators, approaches that can identify individual mediators in presence of high‐dimensional potential mediators are lacking. We posit that the multiomic data are interrelated following multilayered Gaussian graphical models that include undirected and directed acyclic graphs as special cases. We develop a Bayesian inferential framework for multilayered mediation analysis with continuous, binary, and ordinal outcomes using probit models. As opposed to existing approaches focusing on identifying joint mediation effects, we decompose the joint effect into effects attributable to individual mediators in the framework of interventional mediation analysis. Simulations demonstrate our method outperforms other existing approaches to identify mediators that have nonzero indirect effects to the outcome. We apply our method to multiomic analysis on drug sensitivity outcomes of palbociclib and agents for endocrine therapy, standard care for breast cancer.

Seismic Discrimination Using Regional Distance Coda-Wave Ratios

Abstract This study utilizes regional seismic coda-wave amplitude ratios to distinguish earthquakes and declared nuclear explosions in the Democratic People’s Republic of Korea (DPRK). We compute the coda spectral ratios at common stations to isolate source information from propagation and site effects. The resulting frequency-dependent amplitude ratios help identify differences between source types at DPRK. We use parametric models to validate observations, linking them to seismic source parameters. Our method effectively distinguishes the spectral signatures of explosions, nearby earthquakes, and a post-explosion collapse event. The measurements show clear differences between source-type combinations and agree with estimated seismic source models. Notably, the coda spectral ratios between explosions and earthquakes indicate that explosive sources exhibit relatively lower high-frequency S-wave energy and corner frequency compared to P waves. We leverage these spectral differences to develop a Bayesian inference framework for seismic source discrimination at the DPRK test site. This study demonstrates that spectral differences between source types can be exploited in coda spectral ratios to provide critical information for seismic discrimination.

Salient object detection with bayesian inference based on radar and camera fusion used in UAV obstacle avoidance

Most existing salient object detection methods are sensitive to background noise and rely on prior information in UAV obstacle avoidance applications despite detection methods witnessing rapid progress. In this paper, we propose an efficient framework for salient object detection based on radar-camera fusion and iterative Bayesian optimization. A rough salient object (RSO) image is first built through radar and camera calibration. Next, the RSO image is used to calculate the edge response based on the receptive field mechanism of the primary visual cortex to construct the contour image. Finally, the above two images and the 2D Gaussian distribution are jointly integrated into an iterative Bayesian optimization scheme to get the final salient object image. Different from typical detection methods, this method suppresses background noise by filtering out irrelevant pixels using fusion information. The Bayesian inference framework’s detection performance is improved by precise spatial prior, consisting of optimized contour and RSO images. Experimental results indicate that the presented algorithm performs well against state-of-the-art salient object detection methods on several reference datasets in different evaluation metrics.

Bayesian self-calibration and imaging in very long baseline interferometry

Context. Self-calibration methods with the CLEAN algorithm have been widely employed in very long baseline interferometry (VLBI) data processing in order to correct antenna-based amplitude and phase corruptions present in the data. However, human interaction during the conventional CLEAN self-calibration process can impose a strong effective prior, which in turn may produce artifacts within the final image and hinder the reproducibility of final results. Aims. In this work, we aim to demonstrate a combined self-calibration and imaging method for VLBI data in a Bayesian inference framework. The method corrects for amplitude and phase gains for each antenna and polarization mode by inferring the temporal correlation of the gain solutions. Methods. We use Stokes I data of M87 taken with the Very Long Baseline Array (VLBA) at43 GHz, pre-calibrated using the rPICARD CASA-based pipeline. For antenna-based gain calibration and imaging, we use the Bayesian imaging software resolve. To estimate gain and image uncertainties, we use a variational inference method. Results. We obtain a high-resolution M87 Stokes I image at 43 GHz in conjunction with antenna-based gain solutions using our Bayesian self-calibration and imaging method. The core with counter-jet structure is better resolved, and extended jet emission is better described compared to the CLEAN reconstruction. Furthermore, uncertainty estimation of the image and antenna-based gains allows us to quantify the reliability of the result. Conclusions. Our Bayesian self-calibration and imaging method is able to reconstruct robust and reproducible Stokes I images and gain solutions with uncertainty estimation by taking into account the uncertainty information in the data.

Bayesian Black Hole Photogrammetry

We propose an analytic dual-cone accretion model for horizon-scale images of the cores of low-luminosity active galactic nuclei, including those observed by the Event Horizon Telescope (EHT). Our model is of synchrotron emission from an axisymmetric, magnetized plasma, constrained to flow within two oppositely oriented cones that are aligned with the black hole’s spin axis. We show this model can accurately reproduce images of a variety of time-averaged general relativistic magnetohydrodynamic simulations and that it accurately recovers the black hole spin, orientation, emission scale height, peak emission radius, and fluid flow direction from these simulations within a Bayesian inference framework using radio interferometric data. We show that nontrivial topologies in the images of relativistic accretion flows around black holes can result in nontrivial multimodal solutions when applied to observations with a sparse array, such as the EHT 2017 observations of M87*. The presence of these degeneracies underscores the importance of employing Bayesian techniques to adequately sample the posterior space for the interpretation of EHT measurements. We fit our model to the EHT observations of M87* and find a 95% highest posterior density interval for the mass-to-distance ratio of θ g ∈ (2.84, 3.75) μas, and give an inclination of θ o ∈ (11°, 24°). These new measurements are consistent with mass measurements from the EHT and stellar dynamical estimates and with the spin axis inclination inferred from properties of the M87* jet.

Disentangling the Faraday rotation sky

Context. Magnetic fields permeate the diffuse interstellar medium (ISM) of the Milky Way, and are essential to explain the dynamical evolution and current shape of the Galaxy. Magnetic fields reveal themselves via their influence on the surrounding matter, and as such are notoriously hard to measure independently of other tracers. Aims. In this work, we attempt to disentangle an all-sky map of the line-of-sight (LoS)-parallel component of the Galactic magnetic field from the Faraday effect, utilizing several tracers of the Galactic electron density, ne. Additionally, we aim to produce a Galactic electron dispersion measure map and quantify several tracers of the structure of the ionized medium of the Milky Way. Methods. The method developed to reach these aims is based on information field theory, a Bayesian inference framework for fields, which performs well when handling noisy and incomplete data and constraining high-dimensional-parameter spaces. We rely on compiled catalogs of extragalactic Faraday rotation measures and Galactic pulsar dispersion measures, a well as data on bremsstrahlung and the hydrogen α spectral line to trace the ionized medium of the Milky Way. Results. We present the first full sky map of the LoS-averaged Galactic magnetic field. Within this map, we find LoS-parallel and LoS-averaged magnetic field strengths of up to 4 µG, with an all-sky root mean square of 1.1 µG, which is consistent with previous local measurements and global magnetic field models. Additionally, we produce a detailed electron dispersion measure map that agrees with existing parametric models at high latitudes but suffers from systematic effects in the disk. Further analysis of our results with regard to the 3D structure of ne reveals that it follows a Kolmogorov-type turbulence for most of the sky. From the reconstructed dispersion measure and emission measure maps, we construct several tracers of variability in ne along the LoS. Conclusions. This work demonstrates the power of consistent joint statistical analysis including multiple datasets and physical quantities and defines a road map toward a full three-dimensional joint reconstruction of the Galactic magnetic field and the ionized ISM.

Efficient approximate Bayesian inference for quantifying uncertainty in multiscale animal movement models

It is becoming increasingly important for wildlife managers and conservation ecologists to understand which resources are selected or avoided by an animal and how to best predict future spatial distributions of animal populations in the long term. However, inferring the patterns of space use by animals is a challenging multiscale inference problem, and formal uncertainty quantification of parameter estimates is an essential component of models that provide useful predictions across scales. In this study, we develop an approximate Bayesian inference framework for step selection models of animal movement which quantifies the uncertainty in estimates of resource selection and avoidance parameters within the Bayesian paradigm. The framework allows joint inference of movement and resource selection parameters of animals and is multiscale in that parameters inferred from fine scale movement steps scale to produce predictions of long-term patterns of space use. Our analysis focuses on simulated movement data in which we test the performance of our framework by altering movement parameters in the data-generating process. In our simulations, individuals respond to two environmental covariates and we employ all combinations of positive and negative selection coefficients corresponding to attraction to an environmental feature and avoidance of an environmental feature, respectively. In all scenarios, we recover the movement parameters used for the simulation of synthetic movement data using variational inference, an approximate Bayesian method, allowing us to formally quantify the uncertainty associated with each parameter for varying data set sizes. Our framework successfully recovered all combinations of movement parameters of the simulated data and accurately captured their posterior distributions given the available data suggesting that the framework is reliable and suitable for inferring how animals select resources and move on a landscape.Notably, our analysis shows that even for reasonably large data sets (circa 10,000 observations) there can still be considerable uncertainty associated with resource selection parameters which can in turn lead to inaccurate predictions of long term space use if not properly incorporated into the modelling approach. To further illustrate the utility of our approach, we also present a case study of its application to an example data set consisting of GPS locations of a fisher (Martes pennanti) Our approach will be of interest to ecologists looking to address conservation questions such as when and where animals are likely to spend most of their time. Furthermore, the approach could be used to predict new suitable areas for conservation based on how GPS collared animal use or avoid resources while including uncertainty around the predictions, thereby helping to make informed management decisions.

Inferring Binary Properties from Gravitational-Wave Signals

This review provides a conceptual and technical survey of methods for parameter estimation of gravitational-wave signals in ground-based interferometers such as Laser Interferometer Gravitational-Wave Observatory (LIGO) and Virgo. We introduce the framework of Bayesian inference and provide an overview of models for the generation and detection of gravitational waves from compact binary mergers, focusing on the essential features that are observable in the signals. Within the traditional likelihood-based paradigm, we describe various approaches for enhancing the efficiency and robustness of parameter inference. This includes techniques for accelerating likelihood evaluations, such as heterodyne/relative binning, reduced-order quadrature, multibanding, and interpolation. We also cover methods to simplify the analysis to improve convergence, via reparameterization, importance sampling, and marginalization. We end with a discussion of recent developments in the application of likelihood-free (simulation-based) inference methods to gravitational-wave data analysis.

Spike Count Analysis for MultiPlexing Inference (SCAMPI).

Understanding how neurons encode multiple simultaneous stimuli is a fundamental question in neuroscience. We have previously introduced a novel theory of stochastic encoding patterns wherein a neuron's spiking activity dynamically switches among its constituent single-stimulus activity patterns when presented with multiple stimuli (Groh et al., 2024). Here, we present an enhanced, comprehensive statistical testing framework for such " multiplexing " or " code juggling ". Our new approach evaluates whether dual-stimulus responses can be accounted for as mixtures of Poissons either anchored to or bounded by single-stimulus benchmarks. Our enhanced framework improves upon previous methods in two key ways. First, it introduces a stronger set of foils for multiplexing, including an "overreaching" category that captures overdispersed activity patterns unrelated to the single-stimulus benchmarks, reducing false detection of multiplexing/code-juggling. Second, it detects faster fluctuations - i.e. at sub-trial timescales - that would have been overlooked before. We utilize a Bayesian inference framework, considering the hypothesis with the highest posterior probability as the winner, and employ predictive recursion marginal likelihood method for the involving nonparametric density estimation. Reanalysis of previous findings confirms the general observation of "code juggling" and indicates that such juggling may well occur on faster timescales than previously suggested. We further confirm that juggling is more prevalent in (a) the inferotemporal face patch system for combinations of face stimuli than for faces and non-face objects; and (b) the primary visual cortex for distinct vs fused objects.

Bayesian Inference and Condition Assessment Based on the Deflection of Aging Reinforced Concrete Hollow Slab Bridges

This paper presents a Bayesian inference framework for updating the structural rigidity ratio of aging hollow slab RC bridges using deflection measurements. The framework models the structural rigidity ratio as a stochastic field along the hollow RC slabs, using the Karhunen–Loeve (KL) transform to capture spatial correlation and variation. Bayesian inference is then applied using deflection data from static loading tests, supported by a finite element model (FEM) and a Kriging surrogate model to enhance computational efficiency. The posterior distribution of the structural rigidity ratio is derived using a Markov chain Monte Carlo (MCMC) sampler. The proposed method was tested on an RC bridge with hollow slabs, using deflection measurements taken before and after reinforcement. The Bayesian updates indicated increased structural rigidity ratios after reinforcement, validating the effectiveness of the reinforcement. The deflection predictions from the updated models closely matched the measurements, with the 95% confidence bounds encompassing most of the data. This demonstrates the method’s validity and robustness in capturing the structural improvements post-reinforcement.

Informatics-enhanced prediction of failure strength in skeletal muscle tissue

Skeletal muscles are susceptible to injury during daily activities and competitive sports. Reliable prediction of tissue failure strength is a major challenge due to the large uncertainty in the mechanical behavior of skeletal muscle tissue. The present study reveals a strong correlation between histological characteristics and skeletal muscle failure strength by means of mechanical and histological experiments. We propose a data-driven hybrid modeling approach that enables an effective integration of data science and informatics tools to capture tissue failure strength. Uncertainty in the tissue failure strength is propagated into the posterior information of reduced model parameters via the Bayesian inference framework and parameter space compression. A histological enhancement to the softening hyperelasticity model is made by linking a quantified tissue-scale histological characteristic and stiff model parameters using artificial neural networks. The model is applied to skeletal muscle tissue from different species and sites to assess its predictive capabilities for physiological differences. The results show that the approach can achieve reliable predictions of skeletal muscle tissue failure strength. The proposed approach can be extended to different scales to enrich the understanding of structure–property linkages for biomaterials.

A Bayesian approach for estimating the uncertainty on the contribution of nitrogen fixation and calculation of nutrient balances in grain legumes

BackgroundThe proportion of nitrogen (N) derived from the atmosphere (Ndfa) is a fundamental component of the plant N demand in legume species. To estimate the N benefit of grain legumes for the subsequent crop in the rotation, a simplified N balance is frequently used. This balance is calculated as the difference between fixed N and removed N by grains. The Ndfa needed to achieve a neutral N balance (hereafter θ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ heta$$\\end{document}) is usually estimated through a simple linear regression model between Ndfa and N balance. This quantity is routinely estimated without accounting for the uncertainty in the estimate, which is needed to perform formal statistical inference about θ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ heta$$\\end{document}. In this article, we utilized a global database to describe the development of a novel Bayesian framework to quantify the uncertainty of θ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ heta$$\\end{document}. This study aimed to (i) develop a Bayesian framework to quantify the uncertainty of θ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ heta$$\\end{document}, and (ii) contrast the use of this Bayesian framework with the widely used delta and bootstrapping methods under different data availability scenarios.ResultsThe delta method, bootstrapping, and Bayesian inference provided nearly equivalent numerical values when the range of values for Ndfa was thoroughly explored during data collection (e.g., 6–91%), and the number of observations was relatively high (e.g., ≥100\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ge 100$$\\end{document}). When the Ndfa tested was narrow and/or sample size was small, the delta method and bootstrapping provided confidence intervals containing biologically non-meaningful values (i.e. < 0% or > 100%). However, under a narrow Ndfa range and small sample size, the developed Bayesian inference framework obtained biologically meaningful values in the uncertainty estimation.ConclusionIn this study, we showed that the developed Bayesian framework was preferable under limited data conditions ─by using informative priors─ and when uncertainty estimation had to be constrained (regularized) to obtain meaningful inference. The presented Bayesian framework lays the foundation not only to conduct formal comparisons or hypothesis testing involving θ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ heta$$\\end{document}, but also to learn about its expected value, variance, and higher moments such as skewness and kurtosis under different agroecological and crop management conditions. This framework can also be transferred to estimate balances for other nutrients and/or field crops to gain knowledge on global crop nutrient balances.

Fuzzy Bayesian inference for under-five mortality data

Under-five mortality remains a significant global health challenge, with millions of children dying before their fifth birthday each year. This study explores the application of fuzzy Bayesian inference for under-five mortality data using Tanzania as a case study. Fuzzy Bayesian inference has emerged as a promising technique that combines the flexibility of fuzzy set theory with the probabilistic framework of Bayesian inference. The study employs fuzzy sets and membership functions to represent the linguistic terms and their degrees of membership, along with the Poisson distribution to model the mortality rate. The results demonstrate the potential of fuzzy Bayesian inference for analyzing under-five mortality rates. This approach provides a more nuanced understanding of the complex mortality patterns.

Split-and-merge model selection of mixtures of Gaussian processes with RJMCMC

The mixture of Gaussian processes is a powerful statistical learning model that can be effectively applied to curve clustering and prediction. However, the corresponding model selection problem, that is, selecting an appropriate number of components in the mixture, is rather difficult to solve. In our previous work, we established the split-and-merge automatic model selection algorithm for mixtures of Gaussian processes along the output space under the framework of Reversible Jump Markov Chain Monte Carlo (RJMCMC), which can not only determine the number of actual Gaussian processes but also dynamically adjust the Gaussian process components to avoid dependence on parameter initialization and initial partitioning of the dataset during the parameter learning on a given dataset. In this study, we propose two algorithms: Penalized Likelihood RJMCMC and Penalized Prior RJMCMC. The former integrates a penalized term into the likelihood, while the latter incorporates a penalized term into the prior and operates within the full Bayesian inference framework, both aiming to focus more sharply on determining the number of components in the convergence process. Furthermore, we prove the geometric ergodicity of the RJMCMC algorithm for the mixture of Gaussian processes model, ensuring convergence of the posterior distribution with sufficient iterations. The experimental results further demonstrate the robustness of our PP-RJMCMC algorithm in model selection, showing superior performance compared to traditional approaches in curve classification and clustering. Additionally, the prediction performance is comparable to the EM algorithm. Although not directly explored in this study, the RJMCMC results can be used to initialize the EM algorithm, which could potentially improve prediction accuracy and accelerate computation.

Sequential and adaptive probabilistic integration for Bayesian model updating

The present study attempts to introduce a Bayesian perspective to marginal likelihood estimation. For this purpose, the Bayesian marginal likelihood inference (BMLI) framework is first developed, where the posterior statistics of the marginal likelihood are estimated using efficient random process sampling. The sequential and adaptive probabilistic integration (SAPI) method is then proposed within the BMLI framework to efficiently infer the posterior distribution of the model parameters as a result of the marginal likelihood estimation. In this method, an adaptive tempering of the likelihood function is presented to draw samples from a series of intermediate distributions to perform probabilistic integration sequentially, and the samples are finally converged to the target posterior domain. An active learning process is also designed to accelerate the sequential integration with a minimum number of likelihood function observations. Four numerical examples are investigated and the superiority of the SAPI method over other sequential sampling methods is demonstrated.

A mechanistic modeling and estimation framework for environmental pathogen surveillance

Environmental pathogen surveillance is a promising disease surveillance modality that has been widely adopted for SARS-CoV-2 monitoring. The highly variable nature of environmental pathogen data is a challenge for integrating these data into public health response. One source of this variability is heterogeneous infection both within an individual over the course of infection as well as between individuals in their pathogen shedding over time. We present a mechanistic modeling and estimation framework for connecting environmental pathogen data to the number of infected individuals. Infected individuals are modeled as shedding pathogen into the environment via a Poisson process whose rate parameter λt varies over the course of their infection. These shedding curves λt are themselves random, allowing for variation between individuals. We show that this results in a Poisson process for environmental pathogen levels with rate parameter a function of the number of infected individuals, total shedding over the course of infection, and pathogen removal from the environment. Theoretical results include determination of identifiable parameters for the model from environmental pathogen data and simple, explicit formulas for the likelihood for particular choices of individual shedding curves. We give a two step Bayesian inference framework, where the first step corresponds to calibration from data where the number of infected individuals is known, followed by an estimation step from environmental surveillance data when the number of infected individuals is unknown. We apply this modeling and estimation framework to synthetic data, as well as to an empirical case study of SARS-CoV-2 in environmental dust collected from isolation rooms housing university students. Both the synthetic data and empirical case study indicate high inter-individual variation in shedding, leading to wide credible intervals for the number of infected individuals. We examine how uncertainty in estimates of the number of infected individuals from environmental pathogen levels scales with the true number of infected individuals and model misspecification. While credible intervals for the number of infected individuals are wide, our results suggest that distinguishing between no infection and small-to-moderate levels of infection (≈10 infected individuals) may be possible, and that it is broadly possible to differentiate between moderate (≈40) and high (≈200) numbers of infected individuals.