Posterior Distribution Of Parameters Research Articles

Combining prior and post‐release data while accounting for dispersal to improve predictions for reintroduction populations

AbstractAttempts to reintroduce species to managed areas may be compromised by dispersal into the surrounding landscape. Therefore, decisions regarding the selection and ongoing management of reintroduction areas require predicting dispersal as well as the survival and reproduction rates of the species to be reintroduced. Dispersal can potentially be measured directly by tracking animals, but this is often impractical. However, dispersal can also be inferred from re‐sighting surveys done within reintroduction areas if such data are available from multiple areas with varying connectivity to the surrounding landscape, allowing apparent survival and recruitment to be modelled as a function of connectivity metrics. Here, we show how data from 10 previous reintroductions of a New Zealand passerine, the toutouwai (Petroica longipes), were used to predict population dynamics at a predator‐controlled reintroduction area with high connectivity, and predictions then updated using post‐release data. Bayesian hierarchical modelling of the previous data produced prior distributions for productivity, adult survival and apparent juvenile survival rates that accounted for random variation among areas as well as rat density and connectivity. The modelling of apparent juvenile survival as a function of connectivity allowed it to be partitioned into estimates of survival and fidelity. Bayesian updating based on post‐release data produced posterior distributions for parameters that were consistent with the priors but much more precise. The prior data also allowed the recruitment rate estimated in the new area to be partitioned into separate estimates for productivity, juvenile survival and juvenile fidelity. Consequently, it was possible to not only estimate population growth under current management, but also predict the consequences of reducing the scale or intensity of predator control, facilitating adaptive management. The updated model could then be used to predict population growth as a function of the connectivity and predator control regime at proposed reintroduction areas while accounting for random variation among areas.

Using machine learning techniques in inverse problems of acoustical oceanography

AbstractThe goal of the work presented here is to study a novel approach for inverting acoustic signals recorded in the marine environment for the estimation of environmental parameters of the water column and/or the seabed. The proposed approach is based on signal feature extraction using a discrete wavelet packet transform, applied to the measured signal, and hidden Markov models that exploit the sequential patterns of the signals. The signal feature is thereafter used in the framework of a mixture density network, which, after training with sets of simulated signals calculated within a predefined search space, provides conditional posterior distributions of the recoverable parameters. The technique is tested with two test cases corresponding to different types of inverse problems. The first case corresponds to a simple problem of geoacoustic inversion, while the second is referred to a, rather unusual, still interesting problem of recovering the shape of a seamount using long‐range acoustic data. Both test cases are based on simulated experiments. The inversion results obtained using the proposed scheme are compared with inversion results using statistical features of the acoustic signal, which is another inversion approach well documented in the literature and is also based on the wavelet packet transform of the measured signal.

Bayesian Inference for Multiple Datasets

Estimating parameters for multiple datasets can be time consuming, especially when the number of datasets is large. One solution is to sample from multiple datasets simultaneously using Bayesian methods such as adaptive multiple importance sampling (AMIS). Here, we use the AMIS approach to fit a von Mises distribution to multiple datasets for wind trajectories derived from a Lagrangian Particle Dispersion Model driven from 3D meteorological data. A posterior distribution of parameters can help to characterise the uncertainties in wind trajectories in a form that can be used as inputs for predictive models of wind-dispersed insect pests and the pathogens of agricultural crops for use in evaluating risk and in planning mitigation actions. The novelty of our study is in testing the performance of the method on a very large number of datasets (>11,000). Our results show that AMIS can significantly improve the efficiency of parameter inference for multiple datasets.

Estimating causal effects from panel data with dynamic multivariate panel models

Panel data are ubiquitous in scientific fields such as social sciences. Various modeling approaches have been presented for observational causal inference based on such data. Existing approaches typically impose restrictive assumptions on the data-generating process such as Gaussian responses or time-invariant effects, or they can only consider short-term causal effects. To surmount these restrictions, we present the dynamic multivariate panel model (DMPM) that supports time-varying, time-invariant, and individual-specific effects, multiple responses across a wide variety of distributions, and arbitrary dependency structures of lagged responses of any order. We formally demonstrate how DMPM facilitates causal inference within the structural causal modeling framework and we take a Bayesian approach for the estimation of the posterior distributions of the model parameters and causal effects of interest. We demonstrate the use of DMPM by applying the approach to both real and synthetic data.

Uncertainty quantification in multivariable regression for material property prediction with Bayesian neural networks

With the increased use of data-driven approaches and machine learning-based methods in material science, the importance of reliable uncertainty quantification (UQ) of the predicted variables for informed decision-making cannot be overstated. UQ in material property prediction poses unique challenges, including multi-scale and multi-physics nature of materials, intricate interactions between numerous factors, limited availability of large curated datasets, etc. In this work, we introduce a physics-informed Bayesian Neural Networks (BNNs) approach for UQ, which integrates knowledge from governing laws in materials to guide the models toward physically consistent predictions. To evaluate the approach, we present case studies for predicting the creep rupture life of steel alloys. Experimental validation with three datasets of creep tests demonstrates that this method produces point predictions and uncertainty estimations that are competitive or exceed the performance of conventional UQ methods such as Gaussian Process Regression. Additionally, we evaluate the suitability of employing UQ in an active learning scenario and report competitive performance. The most promising framework for creep life prediction is BNNs based on Markov Chain Monte Carlo approximation of the posterior distribution of network parameters, as it provided more reliable results in comparison to BNNs based on variational inference approximation or related NNs with probabilistic outputs.

Cyclic behavior of laminated bio-based connections with slotted-in steel plates: Genetic algorithm, deterministic neural network-based model parameter identification, and uncertainty quantification

To support more sustainable construction, this paper experimentally investigates the cyclic behavior of laminated timber (Laminated Veneer Lumber (LVL)) and glubam (Glue Laminated Bamboo) connections with slotted-in steel plates in terms of experimental test, numerical simulations and parameter identification. Experimental tests included eight different configurations: two materials (LVL and glubam), two bolt diameters (8 and 10 mm), and one or two bolts. Two different cyclic-loading protocols were applied for each type of connection: only tension and tension/compression. The observed behavior is then compared to a finite element model developed in OpenSeesPy, which takes into account factors such as sliding, contact, pinching, cyclic stiffness, and strength degradation. To identify the best set of parameters for the model, three different approaches are considered: genetic algorithm, fast deterministic neural network, and probabilistic Bayesian method. First, the model identification is carried out by means of a genetic algorithm-based optimization. The parameter-identification results are evaluated in terms of elastic stiffness, yielding point, and ductility. Next, a sensitivity analysis is performed to determine the significance of the parameters, and an innovative approach combining neural network and sensitivity analysis is proposed for fast and preliminary parameter identification. Then, probabilistic Bayesian identification is employed to calculate the posterior distribution of the model parameters identified and the confidence bounds of the estimated response. Finally, different model identification parameters are compared and suggestions for algorithm selection are provided.

A Bayesian Change Point Model for Dynamic Alternative Transcription Start Site Usage During Cellular Differentiation.

ABSTRACT An alternative transcription start site (ATSS) is a major driving force for increasing the complexity of transcripts in human tissues. As a transcriptional regulatory mechanism, ATSS has biological significance. Many studies have confirmed that ATSS plays an important role in diseases and cell development and differentiation. However, exploration of its dynamic mechanisms remains insufficient. Identifying ATSS change points during cell differentiation is critical for elucidating potential dynamic mechanisms. For relative ATSS usage as percentage data, the existing methods lack sensitivity to detect the change point for ATSS longitudinal data. In addition, some methods have strict requirements for data distribution and cannot be applied to deal with this problem. In this study, the Bayesian change point detection model was first constructed using reparameterization techniques for two parameters of a beta distribution for the percentage data type, and the posterior distributions of parameters and change points were obtained using Markov Chain Monte Carlo (MCMC) sampling. With comprehensive simulation studies, the performance of the Bayesian change point detection model is found to be consistently powerful and robust across most scenarios with different sample sizes and beta distributions. Second, differential ATSS events in the real data, whose change points were identified using our method, were clustered according to their change points. Last, for each change point, pathway and transcription factor motif analyses were performed on its differential ATSS events. The results of our analyses demonstrated the effectiveness of the Bayesian change point detection model and provided biological insights into cell differentiation.

GammaBayes: a Bayesian pipeline for dark matter detection with CTA

We present GammaBayes, a Bayesian Python package for dark matter detection with the Cherenkov Telescope Array (CTA).GammaBayes takes as input the CTA measurements of gamma rays and a user-specified dark-matter particle model.It outputs the posterior distribution for parameters of the dark-matter model including the velocity-averaged cross section for dark-matter self interactions 〈σv〉 and the dark-matter mass mχ .It also outputs the Bayesian evidence, which can be used for model selection.We demonstrate GammaBayes using 525 hours of simulated data, corresponding to 108 observed gamma-ray events.The vast majority of this simulated data consists of noise, but 100000 events arise from the annihilation of scalar singlet dark matter with mχ = 1 TeV.We recover the dark matter mass within a 95% credible interval of mχ ∼ 0.96–1.07 TeV.Meanwhile, the velocity averaged cross section is constrained to 〈σv〉 ∼ 1.4–2.1 × 10-25 cm3 s-1 (95% credibility).This is equivalent to measuring the number of dark-matter annihilation events to be NS ∼ 1.1-0.2 +0.2 × 105.The no-signal hypothesis 〈σv〉 = 0 is ruled out with about 5σ credibility.We discuss how GammaBayes can be extended to include more sophisticated signal and background models and the computational challenges that must be addressed to facilitate these upgrades.The source code is publicly available here.

Investigating Model Dependencies for Obscured Active Galactic Nuclei: A Case Study of NGC 3982

Abstract X-ray spectroscopy of heavily obscured active galactic nuclei (AGN) offers a unique opportunity to study the circumnuclear environment of accreting supermassive black holes. However, individual models describing the obscurer have unique parameter spaces that give distinct parameter posterior distributions when fit to the same data. To assess the impact of model-specific parameter dependencies, we present a case study of the nearby heavily obscured low-luminosity AGN NGC 3982, which has a variety of column density estimations reported in the literature. We fit the same broadband XMM-Newton+NuSTAR spectra of the source with five unique obscuration models and generate posterior parameter distributions for each. By using global parameter exploration, we traverse the full prior-defined parameter space to accurately reproduce complex posterior shapes and inter-parameter degeneracies. The unique model posteriors for the line-of-sight column density are broadly consistent, predicting Compton-thick N H > 1.5 × 1024 cm−2 at the 3σ confidence level. The posterior median intrinsic X-ray luminosity in the 2–10 keV band was found to differ substantially, however, with values in the range log L 2–10 keV/ erg s−1 = 40.9–42.1 for the individual models. We additionally show that the posterior distributions for each model occupy unique regions of their respective multidimensional parameter spaces and how such differences can propagate into the inferred properties of the central engine. We conclude by showcasing the improvement in parameter inference attainable with the High Energy X-ray Probe, with its uniquely broad, simultaneous, and high-sensitivity bandpass of 0.2–80 keV.

Stochastic inversion of fracture networks using the reversible jump Markov chain Monte Carlo algorithm

Characterization of fracture networks is essential in the production optimization or storage calculation for enhanced geothermal systems or geologic carbon storage. A novel inversion approach is proposed for estimating the fracture networks in this research. The discrete fracture network technique is adopted to probabilistically describe various fracture parameters such as trace length, midpoint position or azimuthal angle. The reversible jump Markov chain Monte Carlo algorithm is applied to explore the target posterior distribution of model parameters of differing dimensionality, in which the number of fractures is assumed to be unknown. More specifically, the birth-death strategy is utilized to perturb the fracture number iteratively in the sampling process. The proposed methodology is applied with two different types of observational datasets, namely the head records from steady-state flow simulation and the acoustic impedance obtained from seismic inversion. The sampling results can successfully recover the fracture geometry in the observed domain, and the number of fractures in the system can be retrieved as well. Benchmarked on multiple Markov chain trials, the technique of parallel tempering can greatly improve the convergence efficiency and increase the diversity of sampled posterior models, through the random swapping of model states across the whole temperature ladder.

Improved hierarchical Bayesian modeling framework with arbitrary polynomial chaos for probabilistic model updating

Bayesian finite element model updating techniques have found widespread application in the structural health monitoring. The conventional Bayesian modeling framework (CBMF) identifies the posterior distribution of structural parameters using data from a single experiment. However, structural parameters exhibit variability due to changes in environmental or experimental conditions, an aspect overlooked by CBMF. In recent years, the hierarchical Bayesian modeling framework (HBMF) has gradually attracted attention. This framework incorporates an additional layer of hyperparameters and utilizes multiple sets of experimental data to describe the variability in structural parameters caused by changes in experimental conditions. Unfortunately, the increase in hyperparameters and data size leads the HBMF to face the dilemma of exceedingly high computational costs. To address this issue, this study proposes an improved hierarchical Bayesian modeling framework (IHBMF). To enhance the computational efficiency of IHBMF, the importance sampling method is employed to simplify the computation of the likelihood function for hyperparameters. Subsequently, a surrogate model based on arbitrary polynomial chaos expansion is introduced to further reduce the computational cost of IHBMF. The framework's accuracy and efficiency were validated through analysis of a simply supported beam and a steel pedestrian bridge. The results demonstrate that IHBMF not only delivers a more accurate quantification of structural parameter uncertainty than CBMF but also exhibits higher computational efficiency compared to HBMF, showcasing its superior capability in structural health monitoring applications.

2-D probabilistic inversion of MT data and uncertainty quantification using the Hamiltonian Monte Carlo method

SUMMARY Bayesian methods provide a valuable framework for rigorously quantifying the model uncertainty arising from the inherent non-uniqueness in the magnetotelluric (MT) inversion. However, widely used Markov chain Monte Carlo (MCMC) sampling approaches usually require a significant number of model samples for accurate uncertainty estimates, making their applications computationally challenging for 2-D or 3-D MT problems. In this study, we explore the applicability of the Hamiltonian Monte Carlo (HMC) method for 2-D probabilistic MT inversion. The HMC provides a mechanism for efficient exploration in high-dimensional model space by making use of gradient information of the posterior probability distribution, resulting in a substantial reduction in the number of samples needed for reliable uncertainty quantification compared to the conventional MCMC methods. Numerical examples with synthetic data demonstrate that the HMC method achieves rapid convergence to the posterior probability distribution of model parameters with a limited number of model samples, indicating the computational advantages of the HMC in high-dimensional model space. Finally, we applied the developed approach to the COPROD2 field data set. The statistical models derived from the HMC approach agree well with previous results obtained by 2-D deterministic inversions. Most importantly, the probabilistic inversion provides valuable quantitative model uncertainty information associated with the resistivity structures derived from the observed data, which facilitates model interpretation.

Bayesian federated inference for estimating statistical models based on non-shared multicenter data sets.

Identifying predictive factors for an outcome of interest via a multivariable analysis is often difficult when the data set is small. Combining data from different medical centers into a single (larger) database would alleviate this problem, but is in practice challenging due to regulatory and logistic problems. Federated learning (FL) is a machine learning approach that aims to construct from local inferences in separate data centers what would have been inferred had the data sets been merged. It seeks to harvest the statistical power of larger data sets without actually creating them. The FL strategy is not always efficient and precise. Therefore, in this paper we refine and implement an alternative Bayesian federated inference (BFI) framework for multicenter data with the same aim as FL. The BFI framework is designed to cope with small data sets by inferring locally not only the optimal parameter values, but also additional features of the posterior parameter distribution, capturing information beyond what is used in FL. BFI has the additional benefit that a single inference cycle across the centers is sufficient, whereas FL needs multiple cycles. We quantify the performance of the proposed methodology on simulated and real life data.

A Bayesian Structural Modal Updating Method Based on Sparse Grid and Ensemble Kalman Filter

This study presents a sparse grid interpolation and ensemble Kalman filter (EnKF)-based Markov Chain Monte Carlo (MCMC) method (SG-EnMCMC). Initiating with the formulation of a recursive equation for the state space vector, derived from the structural dynamic equation, this study adopts a dimensionality reduction strategy. This approach involves a separation of physical parameters and the state space vector. The acquisition of physical parameters is accomplished through sampling, utilizing sample moments to substitute population moments, thereby mitigating the need for computationally high-dimensional covariance matrix calculations. To further streamline the recursive equation of the state space vector, a sparse grid method is employed for interpolation. This step simplifies the process while ensuring superior accuracy compared to the Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF). Subsequent to this, acceptance rates and the final parameter posterior distribution within the MCMC framework are derived. The efficiency of the proposed method is assessed through validation in two shaking table experiments.

Probabilistic risk assessment for reinforced concrete frame structures subject to mainshock‐aftershock sequences

AbstractRecent earthquakes have highlighted that aftershocks can considerably increase the structural demand and seismic risk of engineering structures. This study presents a probabilistic approach to assess the seismic risk of reinforced concrete (RC) frame structures subjected to mainshock‐aftershock sequences. In this approach, a predictive fragility method is used to evaluate the probabilities of structural damage under sequential excitations. The Bayes theorem is employed to generate posterior distributions of unknown model parameters. Then, a practical seismic hazard assessment method is used to conduct mainshock‐aftershock hazard analysis. The Copula technique is employed to develop a joint distribution model of the mainshock and aftershock intensity measures. Finally, the seismic risk is evaluated using the classical risk integration equation with the mainshock‐aftershock fragilities and hazard surfaces. Confidence bounds for fragilities and seismic risks are also obtained to account for the uncertainties of model parameters caused by aftershocks. The proposed approach is demonstrated by considering a seismic‐designed RC frame building. It can be concluded that aftershocks can significantly increase the seismic risk throughout the entire structural service life. The additional uncertainties caused by aftershocks result in wider confidence bounds for seismic risk.

Encoding the Latent Posterior of Bayesian Neural Networks for Uncertainty Quantification.

Bayesian Neural Networks (BNNs) have long been considered an ideal, yet unscalable solution for improving the robustness and the predictive uncertainty of deep neural networks. While they could capture more accurately the posterior distribution of the network parameters, most BNN approaches are either limited to small networks or rely on constraining assumptions, e.g., parameter independence. These drawbacks have enabled prominence of simple, but computationally heavy approaches such as Deep Ensembles, whose training and testing costs increase linearly with the number of networks. In this work we aim for efficient deep BNNs amenable to complex computer vision architectures, e.g., ResNet-50 DeepLabv3+, and tasks, e.g., semantic segmentation and image classification, with fewer assumptions on the parameters. We achieve this by leveraging variational autoencoders (VAEs) to learn the interaction and the latent distribution of the parameters at each network layer. Our approach, called Latent-Posterior BNN (LP-BNN), is compatible with the recent BatchEnsemble method, leading to highly efficient (in terms of computation and memory during both training and testing) ensembles. LP-BNNs attain competitive results across multiple metrics in several challenging benchmarks for image classification, semantic segmentation, and out-of-distribution detection.

CHEX-MATE: CLUster Multi-Probes in Three Dimensions (CLUMP-3D). I. Gas analysis method using X-ray and Sunyaev–Zel’dovich effect data

Galaxy clusters are the products of structure formation through myriad physical processes that affect their growth and evolution throughout cosmic history. As a result, the matter distribution within galaxy clusters, or their shape, is influenced by cosmology and astrophysical processes, in particular the accretion of new material due to gravity. We introduce an analysis method for investigating the three-dimensional triaxial shapes of galaxy clusters from the Cluster HEritage project with -- Mass Assembly and Thermodynamics at the Endpoint of structure formation (CHEX-MATE). In this paper, the first in a CHEX-MATE triaxial analysis series, we focus on utilizing X-ray data from and Sunyaev-Zel'dovich (SZ) effect maps from and the Atacama Cosmology Telescope to obtain a three-dimensional triaxial description of the intracluster medium (ICM) gas. We present the forward modeling formalism of our technique, which projects a triaxial ellipsoidal model for the gas density and pressure, to be compared directly with the observed two-dimensional distributions in X-rays and the SZ effect. A Markov chain Monte Carlo is used to estimate the posterior distributions of the model parameters. Using mock X-ray and SZ observations of a smooth model, we demonstrate that the method can reliably recover the true parameter values. In addition, we applied the analysis to reconstruct the gas shape from the observed data of one CHEX-MATE galaxy cluster, PSZ2 G313.33+61.13 (Abell 1689), to illustrate the technique. The inferred parameters are in agreement with previous analyses for the cluster, and our results indicate that the geometrical properties, including the axial ratios of the ICM distribution, are constrained to within a few percent. With a much better precision than previous studies, we thus further establish that Abell 1689 is significantly elongated along the line of sight, resulting in its exceptional gravitational lensing properties.

Dynamic Exploration-Exploitation Trade-Off in Active Learning Regression with Bayesian Hierarchical Modeling

Active learning provides a framework to adaptively query the most informative experiments towards learning an unknown black-box function. Various approaches of active learning have been proposed in the literature, however, they either focus on exploration or exploitation in the design space. Methods that do consider exploration-exploitation simultaneously employ fixed or ad-hoc measures to control the trade-off that may not be optimal. In this paper, we develop a Bayesian hierarchical approach, referred as BHEEM, to dynamically balance the exploration-exploitation trade-off as more data points are queried. To sample from the posterior distribution of the trade-off parameter, We subsequently formulate an approximate Bayesian computation approach based on the linear dependence of queried data in the feature space. Simulated and real-world examples show the proposed approach achieves at least 21 % and 11 % average improvement when compared to pure exploration and exploitation strategies respectively. More importantly, we note that by optimally balancing the trade-off between exploration and exploitation, BHEEM performs better or at least as well as either pure exploration or pure exploitation.

Normalizing Flow-Based Distribution Estimation of Pharmacokinetic Parameters in Dynamic Contrast-Enhanced Magnetic Resonance Imaging.

The pharmacokinetic (PK) parameters estimated from dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) provide valuable information for clinical research and diagnosis. However, these estimated PK parameters suffer from many sources of variability. Thus, the estimation of the posterior distributions of these PK parameters could provide a way to simultaneously quantify the values and uncertainties of the PK parameters. Our objective is to develop an efficient and flexible method to more closely approximate and estimate the underlying posterior distributions of the PK parameters. The normalizing flow model-based parameters distribution estimation neural network (FPDEN) is proposed to adaptively learn and estimate the posterior distributions of the PK parameters. The maximum likelihood estimation (MLE) loss is directly constructed based on the parameter distributions learned by the normalizing flow model, rather than pre-defined distributions. Experimental analysis shows that the proposed method can improve parameter estimation accuracy. Moreover, the uncertainty derived from the parameter distribution constitutes an effective indicator to exclude unreliable parametric results. A successful demonstration is the improved classification performance of the glioma World Health Organization (WHO) grading task, specifically in terms of distinguishing between low and high grades, as well as between Grade III and Grade IV. The FPDEN method offers improved accuracy for estimation of PK parameters and boosts the performance of the glioma grading task. By enhancing the precision and reliability of DCE-MRI, the proposed method promotes its further applications in clinical practice.

KiDS-1000 cosmology: Combined second- and third-order shear statistics

Aims. In this work, we perform the first cosmological parameter analysis of the fourth release of Kilo Degree Survey (KiDS-1000) data with second- and third-order shear statistics. This paper builds on a series of studies aimed at describing the roadmap to third-order shear statistics. Methods. We derived and tested a combined model of the second-order shear statistic, namely, the COSEBIs and the third-order aperture mass statistics 〈ℳap3〉 in a tomographic set-up. We validated our pipeline with N-body mock simulations of the KiDS-1000 data release. To model the second- and third-order statistics, we used the latest version of HMCODE2020 for the power spectrum and BIHALOFIT for the bispectrum. Furthermore, we used an analytic description to model intrinsic alignments and hydro-dynamical simulations to model the effect of baryonic feedback processes. Lastly, we decreased the dimension of the data vector significantly by considering only equal smoothing radii for the 〈ℳap3〉 part of the data vector. This makes it possible to carry out a data analysis of the KiDS-1000 data release using a combined analysis of COSEBIs and third-order shear statistics. Results. We first validated the accuracy of our modelling by analysing a noise-free mock data vector, assuming the KiDS-1000 error budget, finding a shift in the maximum of the posterior distribution of the matter density parameter, ΔΩm < 0.02 σΩm, and of the structure growth parameter, ΔS8 < 0.05 σS8. Lastly, we performed the first KiDS-1000 cosmological analysis using a combined analysis of second- and third-order shear statistics, where we constrained Ωm = 0.248−0.055+0.062 and S8 = σ8√(Ωm/0.3 )= 0.772 ± 0.022. The geometric average on the errors of Ωm and S8 of the combined statistics decreases, compared to the second-order statistic, by a factor of 2.2.