Markov Chain Monte Carlo Sampling Research Articles

The future of cosmological likelihood-based inference: accelerated high-dimensional parameter estimation and model comparison

We advocate for a new paradigm of cosmological likelihood-based inference, leveraging recent developments in machine learning and its underlying technology, to accelerate Bayesian inference in high-dimensional settings. Specifically, we combine (i) emulation, where a machine learning model is trained to mimic cosmological observables, e.g. CosmoPower-JAX; (ii) differentiable and probabilistic programming, e.g. JAX and NumPyro, respectively; (iii) scalable Markov chain Monte Carlo (MCMC) sampling techniques that exploit gradients, e.g. Hamiltonian Monte Carlo; and (iv) decoupled and scalable Bayesian model selection techniques that compute the Bayesian evidence purely from posterior samples, e.g. the learned harmonic mean implemented in harmonic. This paradigm allows us to carry out a complete Bayesian analysis, including both parameter estimation and model selection, in a fraction of the time of traditional approaches. First, we demonstrate the application of this paradigm on a simulated cosmic shear analysis for a Stage IV survey in 37- and 39-dimensional parameter spaces, comparing ΛCDM and a dynamical dark energy model ( w0waCDM). We recover posterior contours and evidence estimates that are in excellent agreement with those computed by the traditional nested sampling approach while reducing the computational cost from 8 months on 48 CPU cores to 2 days on 12 GPUs. Second, we consider a joint analysis between three simulated next-generation surveys, each performing a 3x2pt analysis, resulting in 157- and 159-dimensional parameter spaces. Standard nested sampling techniques are simply unlikely to be feasible in this high-dimensional setting, requiring a projected 12 years of compute time on 48 CPU cores; on the other hand, the proposed approach only requires 8 days of compute time on 24 GPUs. All packages used in our analyses are publicly available.

Investigating early and late-time epochs in f(Q) gravity

In the following work, a new hybrid model of the form f(Q)=Q(1+a)+bQ02Q\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ f(Q)=Q(1+a)+b\\frac{Q_0^2}{Q} $$\\end{document} has been proposed and confronted using both early as well as late-time constraints. We first use conditions from the era of Big Bang Nucleosynthesis (BBN) in order to constrain the models which are further used to study the evolution of the Universe through the deceleration parameter. This methodology is employed for the hybrid model as well as a simple model of the form α1Q+α2Q0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\alpha _1 Q+\\alpha _2 Q_0 $$\\end{document} which is found to reduce to Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}CDM. The error bar plot for the Cosmic Chronometer (CC) and Pantheon+SH0ES datasets which includes the comparison with Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}CDM, has been studied for the constrained hybrid model. Additionally, we perform a Monte Carlo Markov Chain (MCMC) sampling of the model against three datasets – CC, Pantheon+SH0ES, and Baryon Acoustic Oscillations (BAO) to find the best-fit ranges of the free parameters. It is found that the constraint range of the model parameter (a) from the BBN study has a region of overlap with the ranges obtained from the MCMC analysis. Finally, we perform a statistical comparison between our model and the Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}CDM model using AIC and BIC method.

Physical model and Bayesian theory based hydraulic component fault diagnosis method

Hydraulic components are integral parts of hydraulic systems, and their failures directly impact the normal operation of hydraulic systems. Due to the dynamic variation of working pressure in hydraulic components with load, it is challenging to diagnose faults of hydraulic components under dynamic pressure conditions using existing methods. This paper focuses on the research of internal leakage faults in hydraulic directional control valves and proposes a fault diagnosis method based on physical model and Bayesian theory for hydraulic components. Firstly, this method investigates the working fault mechanism of hydraulic directional control valves and constructs an internal leakage model. Then, correlation analysis is introduced to select fault feature signals, and principal component analysis is adopted to construct internal leakage features. Finally, based on Bayesian model, Markov chain Monte Carlo sampling, and internal leakage features, the parameters of the internal leakage model are estimated to achieve fault diagnosis of internal leakage in hydraulic directional control valves. Experimental results demonstrate that compared to several traditional fault diagnosis methods, the proposed method exhibits higher adaptability and accuracy under dynamic pressure conditions. This method, based on the internal leakage model and Bayesian theory, realizes fault diagnosis of hydraulic components under dynamic pressure conditions, avoiding the shortcomings of deep learning methods that rely on a large amount of fault data to train fault models.

Systemic vs. in-irrigation tranexamic acid in percutaneous nephrolithotomy A systematic review, Bayesian network meta-analysis, and meta-regression.

Percutaneous nephrolithotomy (PCNL) is the gold-standard treatment for large renal stones. One potentially significant complication of PCNL is blood loss, which can result in transfusion requirement and poorer stone-free outcomes. Tranexamic acid (TXA) has emerged as a promising intervention, administered systemically (TXA-S) or as part of irrigation fluid (TXA-I) in endourology. This study aimed to comprehensively analyze existing evidence regarding the applications of TXA in PCNL through a Bayesian network meta-analysis, offering insights into its efficacy and comparative effectiveness. In February 2022, a PRISMA-compliant systematic review (PROSPERO registration number CRD 42021270593) was performed to identify randomized controlled clinical trials (RCT) on TXA as either systemic therapy or in irrigation fluid. Studies in languages other than English and Spanish were not considered. A Bayesian network was built using results from identified studies to create models that were later run through Markov Chain Monte Carlo sampling through 200 000 iterations. Eight RCTs compared TXA-S vs. placebo, one TXA-I vs. placebo, and one TXA-I vs. TXA-S. TXA-I had lower risk of transfusion (relative risk [RR] 0.63 [0.47,0.84], SUCRA 0.950) than TXA-S (RR 0.79 [0.65,0.95], SUCRA 0.545). TXA-I had a lower risk of complications (RR 0.38 [0.21,0.67], SUCRA=0.957) compared to TXA-S (RR 0.55 [0.39, 0.78], SUCRA 0.539). TXA-I had a lower postoperative decrease in hemoglobin (mean difference [MD] -1.2 [1.3, 1.0], SUCRA 0.849) compared to TXA-S (MD -0.97 [-1.0, -0.93], SUCRA 0.646]). TXA, regardless of the route of administration, is an effective intervention in decreasing bleeding, postoperative complications, and risk of transfusion when compared with placebo. Further studies directly comparing TXA-S to TXA-I would be useful to determine the optimal route of delivery.

Using the Bayesian sampling method to estimate corporate loss given default distribution

We use Markov chain Monte Carlo (MCMC) sampling to draw model coefficients to generate LGD distributions. We find that applying this Bayesian method on a sophisticated model, such as the zero-one-inflated beta (ZOIB) model, that accounts for the bi-modal distribution of the LGDs can generate LGD distributions that mimic the observed distributions well. By contrast, applying this Bayesian sampling approach on a simple model such as Tobit cannot capture the bi-modal LGD distributions accurately. Finally, we argue that this Bayesian sampling approach to generate LGD distributions is better fit for the stress testing purpose than the typical approach to estimate LGD model coefficients and then stress the macro variables. The latter approach yields stressed LGDs that may not be conservative enough, even if the macro variables are stressed to their worst historical values.

Power Law f(Q)$f(Q)$ Cosmology with Bulk Viscous Fluid

AbstractIn this work, a power law model is explored, specifically, , along with viscous matter fluid having transport coefficient . The corresponding analytical solution is derived and then confronted with recent cosmic data. The Markov Chain Monte Carlo (MCMC) sampling technique is utilized to estimate the mean value of arbitrary parameters, by incorporating Cosmic Chronometers and recently published Pantheon+Analysis samples. In addition, some cosmological parameters are reconstructed by resampling the chains obtained by emcee, incorporating 6000 samples. It is found that the matter‐energy density depicts the expected positive behavior, whereas the effective pressure indicates the negative behavior that is leading the accelerating expansion, which is further predicted in the effective EoS parameter. Further, the asymptotic nature of the assumed model is investigated by invoking phase‐space analysis. It is concluded that the assumed viscous model successfully predicts an evolution of the universe from decelerated epoch to stable accelerated de‐Sitter epoch.

Bayesian inference of the spatial distribution of steel corrosion in reinforced concrete structures using corrosion-induced crack width

Observations of corrosion-induced crack widths offer crucial information about the corrosion states of steel reinforcements in reinforced concrete (RC) structures, enabling a cost-effective method for inferring corrosion states through inverse analysis. However, the uncertainty associated with the relationship between corrosion-induced cracking and steel weight loss necessitates a probabilistic inference method, especially when considering the spatial distributions of steel weight loss, which provides important information to estimate the load-bearing capacity loss of corroded RC structures. This paper proposes a Bayesian framework to infer the steel weight loss distribution in RC structures based on the observed corrosion-induced crack width. To reduce the dimensions of the Bayesian inference, a Karhunen-Loève transform is applied to extract the principal distribution features of the steel weight loss. The forward model of the Bayesian inference adopts a data-driven sequence-to-sequence transduction approach to predict corrosion-induced crack width from steel weight loss. This model incorporates a novel nonlinear convolution kernel for input encoding and a sparse polynomial chaos expansion for decoding, which proves more accurate and efficient than finite element simulations. The Hamiltonian Markov chain Monte Carlo (HMCMC) sampler is used to efficiently sample from the posterior distribution of the Bayesian inference. The case study of the proposed method demonstrated that Bayesian inference provides robust range estimation for the steel weight loss distribution, with its 95% confidence interval encompassing most observations. Additionally, the method efficiently inferred high-dimensional steel weight loss sequences up to 61 dimensions, taking advantage of the dimension reduction technique and the gradient-informed HMCMC sampler.

Joint modeling of varying-disease-state longitudinal ordinal data and time-to-event data with application to alzheimer’s disease

Joint models are routinely used in clinical trials to fit longitudinal and survival data simulta- neously in an integrated fashion. We propose a joint model that incorporates state-specific trajectories for fitting the longitudinal ordinal response and time-to-event data, focusing on its application to Alzheimer’s Disease (AD). The proposed joint model effectively captures the fluctuating cognitive conditions observed before and after the transition between two disease states. By integrating longitudinal data into the survival sub-model through shared trajectories, we can improve the fit of the survival data. A Markov chain Monte Carlo (MCMC) sampling algorithm is developed to carry out Bayesian computation. A variation of the Deviance Information Criterion is developed to assess the fit of each component of the joint model as well as the contribution of the longitudinal data in fitting the survival data. A variation of the concordance (C) index is further derived to assess the discriminatory and predictive performance of the longitudinal sub-model. An in-depth analysis of the real data from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) database is carried out to demonstrate the applicability of the proposed methodology. Journal of Statistical Research 2024, Vol. 58, No. 1, pp. 49-73.

Bayesian analysis of multivariate mixed longitudinal ordinal and continuous data

SummaryMultivariate longitudinal ordinal and continuous data exist in many scientific fields. However, it is a rigorous task to jointly analyse them due to the complicated correlated structures of those mixed data and the lack of a multivariate distribution. The multivariate probit model, assuming there is a multivariate normal latent variable for each multivariate ordinal data, becomes a natural modeling choice for longitudinal ordinal data especially for jointly analysing with longitudinal continuous data. However, the identifiable multivariate probit model requires the variances of the latent normal variables to be fixed at 1, thus the joint covariance matrix of the latent variables and the continuous multivariate normal variables is restricted at some of the diagonal elements. This constrains to develop both the classical and Bayesian methods to analyse mixed ordinal and continuous data. In this investigation, we proposed three Markov chain Monte Carlo (MCMC) methods: Metropolis–Hastings within Gibbs algorithm based on the identifiable model, and a Gibbs sampling algorithm and parameter‐expanded data augmentation based on the constructed non‐identifiable model. Through simulation studies and a real data application, we illustrated the performance of these three methods and provided an observation of using non‐identifiable model to develop MCMC sampling methods.

Quantum dynamical Hamiltonian Monte Carlo

One of the open challenges in quantum computing is to find meaningful and practical methods to leverage quantum computation to accelerate classical machine-learning workflows. A ubiquitous problem in machine-learning workflows is sampling from probability distributions that we only have access to via their log probability. To this end, we extend the well-known Hamiltonian Monte Carlo (HMC) method for Markov chain Monte Carlo (MCMC) sampling to leverage quantum computation in a hybrid manner as a proposal function. Our new algorithm, Quantum Dynamical Hamiltonian Monte Carlo (QD-HMC), replaces the classical symplectic integration proposal step with simulations of quantum-coherent continuous-space dynamics on digital or analog quantum computers. We show that QD-HMC maintains key characteristics of HMC, such as maintaining the detailed balanced condition with momentum inversion, while also having the potential for polynomial speedups over its classical counterpart in certain scenarios. As sampling is a core subroutine in many forms of probabilistic inference, and MCMC in continuously parametrized spaces covers a large class of potential applications, this work widens the areas of applicability of quantum devices. Published by the American Physical Society 2024

Statistical data analysis of x-ray spectroscopy data enabled by neural network accelerated Bayesian inference.

Bayesian inference applied to x-ray spectroscopy data analysis enables uncertainty quantification necessary to rigorously test theoretical models. However, when comparing to data, detailed atomic physics and radiation transfer calculations of x-ray emission from non-uniform plasma conditions are typically too slow to be performed in line with statistical sampling methods, such as Markov Chain Monte Carlo sampling. Furthermore, differences in transition energies and x-ray opacities often make direct comparisons between simulated and measured spectra unreliable. We present a spectral decomposition method that allows for corrections to line positions and bound-bound opacities to best fit experimental data, with the goal of providing quantitative feedback to improve the underlying theoretical models and guide future experiments. In this work, we use a neural network (NN) surrogate model to replace spectral calculations of isobaric hot-spots created in Kr-doped implosions at the National Ignition Facility. The NN was trained on calculations of x-ray spectra using an isobaric hot-spot model post-processed with Cretin, a multi-species atomic kinetics and radiation code. The speedup provided by the NN model to generate x-ray emission spectra enables statistical analysis of parameterized models with sufficient detail to accurately represent the physical system and extract the plasma parameters of interest.

Bayesian neural network and Bayesian physics-informed neural network via variational inference for seismic petrophysical inversion

Bayesian neural network via variational inference (BNN-VI) aims to estimate probability distribution of the training parameters of the neural network, which are difficult to compute with traditional methods, by proposing a family of densities and finding the candidates that are close to the target. Variational inference is a Bayesian method that provides a faster tool than Markov chain Monte Carlo sampling algorithms. However, to provide an accurate estimation of the most likely models, BNN-VI requires sufficient training data, which is not always available in geophysical inverse problems. We propose a method that combines a Bayesian approach with a physics-informed neural networks algorithms via variational inference, namely Bayesian physics-informed neural networks via variational inference (BPINN-VI) and apply it to a geophysical inverse problem for the estimation of petrophysical properties from seismic data. The method is based on a Bayesian network approach in which the objective function is defined by the Kullback–Leibler (KL) divergence. In addition, the physical relations between data (seismic measurements) and model variables (petrophysical properties) are embedded into neural networks through a physics-dependent loss term. We tested the proposed method on a pre-stack seismic dataset from the North Sea with limited direct measurements of the target petrophysical properties from well logs. The outcome is the most likely model of petrophysical properties. Compared to BNN-VI, the BPINN-VI results show higher correlation and R2 coefficients, and lower mean square error as well as lower uncertainty and higher lateral continuity.

Spectral induced polarization tomography inversion: Hybridizing homotopic continuation with Bayesian inversion

Induced polarization tomography offers the potential to better characterize the subsurface structures by considering spectral content from data acquisition over a broad frequency range. Spectral induced polarization (SIP) tomography is generally defined as a nonlinear inverse problem commonly solved through deterministic gradient-based methods. To this end, the spectral parameters, i.e., direct current resistivity, chargeability, relaxation time, and frequency exponent, are resolved by individually or simultaneously inverting all frequency data, followed by fitting a generalized Cole-Cole model to the inverted complex resistivities. Due to the high correlation between the Cole-Cole model parameters and a lack of knowledge about the initial approximation of the spectral parameters, using the classical least-squares methods may lead to inaccurate solutions and impede reliable uncertainty analysis. To cope with these limitations, we introduce a new approach based on a hybrid application of a globally convergent homotopic continuation method and a Bayesian inference to reconstruct the distribution of the subsurface spectral parameters. The homotopic optimization, owing to its fast and global convergence, is first implemented to invert multifrequency SIP data sets aimed at retrieving the complex-valued resistivity. Then, Bayesian inversion based on a Markov chain Monte Carlo (MCMC) sampling method, along with a priori information including the lower and upper bounds of the prior distributions, is used to invert the complex resistivity for the Cole-Cole model parameters. By applying the MCMC inversion algorithm, a full nonlinear uncertainty appraisal can be provided. We numerically evaluate the performance of our method using synthetic and real data examples in the presence of topographical effects. Numerical results prove that the homotopic continuation method outperforms the classic, smooth inversion algorithm in the sense of approximation accuracy and computational efficiency. In addition, we determine that our hybrid inversion strategy provides reliable representations of the main features and structure of the earth’s subsurface in terms of the spectral parameters.

Group lasso priors for Bayesian accelerated failure time models with left-truncated and interval-censored data.

An important task in health research is to characterize time-to-event outcomes such as disease onset or mortality in terms of a potentially high-dimensional set of risk factors. For example, prospective cohort studies of Alzheimer's disease (AD) typically enroll older adults for observation over several decades to assess the long-term impact of genetic and other factors on cognitive decline and mortality. The accelerated failure time model is particularly well-suited to such studies, structuring covariate effects as "horizontal" changes to the survival quantiles that conceptually reflect shifts in the outcome distribution due to lifelong exposures. However, this modeling task is complicated by the enrollment of adults at differing ages, and intermittent follow-up visits leading to interval-censored outcome information. Moreover, genetic and clinical risk factors are not only high-dimensional, but characterized by underlying grouping structures, such as by function or gene location. Such grouped high-dimensional covariates require shrinkage methods that directly acknowledge this structure to facilitate variable selection and estimation. In this paper, we address these considerations directly by proposing a Bayesian accelerated failure time model with a group-structured lasso penalty, designed for left-truncated and interval-censored time-to-event data. We develop an R package with a Markov chain Monte Carlo sampler for estimation. We present a simulation study examining the performance of this method relative to an ordinary lasso penalty and apply the proposed method to identify groups of predictive genetic and clinical risk factors for AD in the Religious Orders Study and Memory and Aging Project prospective cohort studies of AD and dementia.

Computationally Efficient Emulation of Spheroidal Elastic Deformation Sources Using Machine Learning Models: A Gaussian‐Process‐Based Approach

AbstractElastic continuum mechanical models are widely used to compute deformations due to pressure changes in buried cavities, such as magma reservoirs. In general, analytical models are fast but can be inaccurate as they do not correctly satisfy boundary conditions for many geometries, while numerical models are slow and may require specialized expertise and software. To overcome these limitations, we trained supervised machine learning emulators (model surrogates) based on parallel partial Gaussian processes which predict the output of a finite element numerical model with high fidelity but >1,000× greater computational efficiency. The emulators are based on generalized nondimensional forms of governing equations for finite non‐dipping spheroidal cavities in elastic halfspaces. Either cavity volume change or uniform pressure change boundary conditions can be specified, and the models predict both surface displacements and cavity (pore) compressibility. Because of their computational efficiency, using the emulators as numerical model surrogates can greatly accelerate data inversion algorithms such as those employing Bayesian Markov chain Monte Carlo sampling. The emulators also permit a comprehensive evaluation of how displacements and cavity compressibility vary with geometry and material properties, revealing the limitations of analytical models. Our open‐source emulator code can be utilized without finite element software, is suitable for a wide range of cavity geometries and depths, includes an estimate of uncertainties associated with emulation, and can be used to train new emulators for different source geometries.

A Diffusion‐Based Uncertainty Quantification Method to Advance E3SM Land Model Calibration

AbstractCalibrating land surface models and accurately quantifying their uncertainty are crucial for improving the reliability of simulations of complex environmental processes. This, in turn, advances our predictive understanding of ecosystems and supports climate‐resilient decision‐making. Traditional calibration methods, however, face challenges of high computational costs and difficulties in accurately quantifying parameter uncertainties. To address these issues, we develop a diffusion‐based uncertainty quantification (DBUQ) method. Unlike conventional generative diffusion methods, which are computationally expensive and memory‐intensive, DBUQ innovates by formulating a parameterized generative model and approximates this model through supervised learning, which enables quick generation of parameter posterior samples to quantify its uncertainty. DBUQ is effective, efficient, and general‐purpose, making it suitable for site‐specific ecosystem model calibration and broadly applicable for parameter uncertainty quantification across various earth system models. In this study, we applied DBUQ to calibrate the Energy Exascale Earth System Model land model at the Missouri Ozark AmeriFlux forest site. Results indicated that DBUQ produced accurate parameter posterior distributions similar to those from Markov Chain Monte Carlo sampling but with 30 times less computing time. This significant improvement in efficiency suggests that DBUQ can enable rapid, site‐level model calibration at a global scale, enhancing our predictive understanding of climate impacts on terrestrial ecosystems.

SECRET: Statistical Emulation for Computational Reverse Engineering and Translation with applications in healthcare

There have been impressive advances in the physical and mathematical modelling of complex physiological systems in the last few decades, with the potential to revolutionise personalised healthcare with patient-specific evidence-based diagnosis, risk assessment and treatment decision support using digital twins. However, practical progress and genuine clinical impact hinge on successful model calibration, parameter estimation and uncertainty quantification, which calls for novel innovative adaptions and methodological extensions of contemporary state-of-the-art inference techniques from Statistics and Machine Learning. In the present study, we focus on two computational fluid-dynamics (CFD) models of the blood systemic and pulmonary circulation. We discuss state-of-the-art emulation techniques based on deep learning and Gaussian processes, which are coupled with established inference techniques based on greedy optimisation, simulated annealing, Markov Chain Monte Carlo, History Matching and rejection sampling for computationally fast inference of unknown parameters of the CFD models from blood flow and pressure data. The inference task was set as a competitive challenge which the participants had to conduct within a limited time frame representative of clinical requirements. The performance of the methods was assessed independently and objectively by the challenge organisers, based on a ground truth that was unknown to the method developers. Our results indicate that for the systemic challenge, in which an idealised case of noise-free data was considered, the relative deviation from the ground-truth in parameter space ranges from 10−5% (highest-performing method) to 3% (lowest-performing method). For the pulmonary challenge, for which noisy data was generated, the performance ranges from 0.9% to 7% deviation for the parameter posterior mean, and from 35% to 570% deviation for the parameter posterior variance.

Identification of illicit discharges in sewer networks by an SWMM-Bayesian coupled approach.

Illicit discharges into sewer systems are a widespread concern within China's urban drainage management. They can result in unforeseen environmental contamination and deterioration in the performance of wastewater treatment plants. Consequently, pinpointing the origin of unauthorized discharges in the sewer network is crucial. This study aims to evaluate an integrative method that employs numerical modeling and statistical analysis to determine the locations and characteristics of illicit discharges. The Storm Water Management Model (SWMM) was employed to track water quality variations within the sewer network and examine the concentration profiles of exogenous pollutants under a range of scenarios. The identification technique employed Bayesian inference fused with the Markov chain Monte Carlo sampling method, enabling the estimation of probability distributions for the position of the suspected source, the discharge magnitude, and the commencement of the event. Specifically, the cases involving continuous release and multiple sources were examined. For single-point source identification, where all three parameters are unknown, concentration profiles from two monitoring sites in the path of pollutant transport and dispersion are necessary and sufficient to characterize the pollution source. For the identification of multiple sources, the proposed SWMM-Bayesian strategy with improved sampling is applied, which significantly improves the accuracy.

Modelling the lymphatic metastatic progression pathways of OPSCC from multi-institutional datasets

The elective clinical target volume (CTV-N) in oropharyngeal squamous cell carcinoma (OPSCC) is currently based mostly on the prevalence of lymph node metastases in different lymph node levels (LNLs) for a given primary tumor location. We present a probabilistic model for ipsilateral lymphatic spread that can quantify the microscopic nodal involvement risk based on an individual patient’s T-category and clinical involvement of LNLs at diagnosis. We extend a previously published hidden Markov model (HMM), which models the LNLs (I, II, III, IV, V, and VII) as hidden binary random variables (RVs). Each represents a patient’s true state of lymphatic involvement. Clinical involvement at diagnosis represents the observed binary RVs linked to the true state via sensitivity and specificity. The primary tumor and the hidden RVs are connected in a graph. Each edge represents the conditional probability of metastatic spread per abstract time-step, given disease at the edge’s starting node. To learn these probabilities, we draw Markov chain Monte Carlo samples from the likelihood of a dataset (686 OPSCC patients) from three institutions. We compute the model evidence using thermodynamic integration for different graphs to determine which describes the data best.The graph maximizing the model evidence connects the tumor to each LNL and the LNLs I through V in order. It predicts the risk of occult disease in level IV is below 5% if level III is clinically negative, and that the risk of occult disease in level V is below 5% except for advanced T-category (T3 and T4) patients with clinical involvement of levels II, III, and IV. The provided statistical model of nodal involvement in OPSCC patients trained on multi-institutional data may guide the design of clinical trials on volume-deescalated treatment of OPSCC and contribute to more personal guidelines on elective nodal treatment.

Leveraging the ETAS model to forecast mining microseismicity

SUMMARY Mining operations result in changes of the subsurface stress field that can lead to the occurrence of microseismic events. The development of strategies for forecasting and avoidance of significant events is crucial for safe and efficient operations of mines. One such example, discussed here is the observed induced microseismicity in soft rock potash mines. It is primarily driven by the rock excavations but can also be triggered by preceding events or can result from the delayed effects of plastic creep of soft rocks. Therefore, it is important from seismic hazard assessment and risk mitigation points of view to understand the statistical aspects of microseismicity in potash or other types of mines. In this study, the temporal evolution of the induced microseismicity from a potash mine in Saskatchewan is analysed and modelled. Specifically, the epidemic type aftershock sequence model is used to approximate the occurrence rate of the induced mining microseismicity. The estimated parameters signify that the microseismicity displays swarm-type characteristics with limited inter-event triggering. Moreover, the Bayesian predictive framework is used to compute the probabilities of the occurrences of the largest expected events above a certain magnitude for prescribed forecasting time intervals during the evolution of the sequence. This approach for computing the probabilities allows one to incorporate fully the uncertainties of the model parameters. The Markov Chain Monte Carlo sampling of the posterior distribution are used to generate parameter chains to quantify their variability. Furthermore, several statistical tests are conducted to assess the credibility of the obtained retrospective forecasts compared to the observed microseismicity. The obtained results show that the developed approach can accurately forecast the number of events and intensity of the sequence. It also provides a framework for computing the probabilities for the largest expected events.