Metropolis-Hastings Markov Chain Research Articles

A Bayesian approach to identifying the role of hospital structure and staff interactions in nosocomial transmission of SARS-CoV-2.

Nosocomial infections threaten patient safety, and were widely reported during the COVID-19 pandemic. Effective hospital infection control requires a detailed understanding of the role of different transmission pathways, yet these are poorly quantified. Using patient and staff data from a large UK hospital, we demonstrate a method to infer unobserved epidemiological event times efficiently and disentangle the infectious pressure dynamics by ward. A stochastic individual-level, continuous-time state-transition model was constructed to model transmission of SARS-CoV-2, incorporating a dynamic staff-patient contact network as time-varying parameters. A Metropolis-Hastings Markov chain Monte Carlo (MCMC) algorithm was used to estimate transmission rate parameters associated with each possible source of infection, and the unobserved infection and recovery times. We found that the total infectious pressure exerted on an individual in a ward varied over time, as did the primary source of transmission. There was marked heterogeneity between wards; each ward experienced unique infectious pressure over time. Hospital infection control should consider the role of between-ward movement of staff as a key infectious source of nosocomial infection for SARS-CoV-2. With further development, this method could be implemented routinely for real-time monitoring of nosocomial transmission and to evaluate interventions.

Source term estimation for continuous plume dispersion in Fusion Field Trial-07: Bayesian inference probability adjoint inverse method

In scenarios involving sudden releases of unidentified gases or concealed pollution emergencies, source control emerges as a critical procedure to safeguard residential air quality. Appropriate inverse source tracking methodology depending on diverse measurement data could be utilized to promptly identify pollutant source parameters. In this study, source term estimation (STE) method, i.e., jointly combining probability adjoint method with the Bayesian inference method, has been proposed. General form of the pollutant inverse transport equation was firstly established. Subsequently, the pollution source information, assumed from single continuous point releases during Fusion Field Trials 2007 under an unsteady wind field, was identified using the Bayesian inference probability adjoint inverse method. Metropolis-Hastings Markov Chain Monte Carlo (MH-MCMC) and Differential Evolution Markov Chain Monte Carlo (DE-MCMC) were then compared as sampling methods for Bayesian inference. Results indicated that the DE-MCMC algorithm has superior convergence and could present higher accuracy of pollutant source information than that of MH-MCMC algorithm, particularly for highly nonlinear and multi-modal distribution systems. Furthermore, the integration of Union standard Adjoint Location Probability (UALP) as prior information into the Bayesian inference probability adjoint inverse method effectively narrowed the sampling range, enhancing both the accuracy and robustness of the proposed approach. Finally, the impact of the covariance matrix on the inverse identification accuracy was explored. Overall, this research has provided insights into the future applicability of this Bayesian inference inversion technique for point source identification.

A rapidly mixing Markov chain from any gapped quantum many-body system

We consider the computational task of sampling a bit string x from a distribution π(x)=|⟨x|ψ⟩|2, where ψ is the unique ground state of a local Hamiltonian H. Our main result describes a direct link between the inverse spectral gap of H and the mixing time of an associated continuous-time Markov Chain with steady state π. The Markov Chain can be implemented efficiently whenever ratios of ground state amplitudes ⟨y|ψ⟩/⟨x|ψ⟩ are efficiently computable, the spectral gap of H is at least inverse polynomial in the system size, and the starting state of the chain satisfies a mild technical condition that can be efficiently checked. This extends a previously known relationship between sign-problem free Hamiltonians and Markov chains. The tool which enables this generalization is the so-called fixed-node Hamiltonian construction, previously used in Quantum Monte Carlo simulations to address the fermionic sign problem. We implement the proposed sampling algorithm numerically and use it to sample from the ground state of Haldane-Shastry Hamiltonian with up to 56 qubits. We observe empirically that our Markov chain based on the fixed-node Hamiltonian mixes more rapidly than the standard Metropolis-Hastings Markov chain.

Stochastic modeling and statistical calibration with model error and scarce data

This paper introduces a procedure to assess the predictive accuracy of stochastic models subject to model error and sparse data. Model error is introduced as uncertainty on the coefficients of appropriate polynomial chaos expansions (PCE). The error associated with finite sample size allows us to conceive of these coefficients as statistics of the data that we describe as random variables whose influence on output quantities of interest is evaluated through the extended polynomial chaos expansion (EPCE). A Bayesian data assimilation scheme is introduced to update these expansions by considering the resulting nested chaos expansion as a hierarchical probabilistic model. Stochastic models of quantities of interest (QoI) are thus constructed and efficiently evaluated. The Metropolis–Hastings Markov chain Monte Carlo procedure is used to sample the posterior. Two illustrative analytical and numerical problems are used to demonstrate the proposed approach.

Collective Monte Carlo updates through tensor network renormalization

We introduce a Metropolis-Hastings Markov chain for Boltzmann distributions of classical spin systems. It relies on approximate tensor network contractions to propose correlated collective updates at each step of the evolution. We present benchmark computations for a wide variety of instances of the two-dimensional Ising model, including ferromagnetic, antiferromagnetic, (fully) frustrated and Edwards-Anderson spin glass instances, and we show that, with modest computational effort, our Markov chain achieves sizeable acceptance rates, even in the vicinity of critical points. In each of the situations we have considered, the Markov chain compares well with other Monte Carlo schemes such as the Metropolis or Wolff’s algorithm: equilibration times appear to be reduced by a factor that varies between 4040 and 20002000, depending on the model and the observable being monitored. We also present an extension to three spatial dimensions, and demonstrate that it exhibits fast equilibration for finite ferro- and antiferromagnetic instances. Additionally, and although it is originally designed for a square lattice of finite degrees of freedom with open boundary conditions, the proposed scheme can be used as such, or with slight modifications, to study triangular lattices, systems with continuous degrees of freedom, matrix models, a confined gas of hard spheres, or to deal with arbitrary boundary conditions.

Bayesian Life Test Acceptance Criteria for Progressively Censored Competing Risks Data Using Copulas

In many practical situations, more than one failure mechanism may contribute to product failure. Many studies assume independence between the different competing risks of failure. Nevertheless, the assumption of independence is not always justified in various practical applications. When the competing risks are assumed dependent, it is important to identify models that describe their dependence structure. Copulas are considered a powerful tool to model such dependence structures. This paper addresses the problem of developing Bayesian life test acceptance criteria through two-sample prediction of future observations based on another independent Weibull progressively Type-II censored sample with binomial random removals. It is assumed that unit failure occurs due to only one of two competing risks. Dependence among the competing risks of failure is modeled using Archimedean copulas with nonconjugate prior distributions. A Metropolis–Hastings Markov chain Monte Carlo algorithm is implemented to derive the prediction intervals that define the proposed acceptance criteria. The derived acceptance criteria enable manufacturers to conform to the required quality specifications and help their clients to properly set their quality expectations. A real data example is provided to illustrate the proposed life test acceptance criteria.

Modeling dragonfly population data with a Bayesian bivariate geometric mixed-effects model

We develop a generalized linear mixed model (GLMM) for bivariate count responses for statistically analyzing dragonfly population data from the Northern Netherlands. The populations of the threatened dragonfly species Aeshna viridis were counted in the years 2015–2018 at 17 different locations (ponds and ditches). Two different widely applied population size measures were used to quantify the population sizes, namely the number of found exoskeletons (‘exuviae’) and the number of spotted egg-laying females were counted. Since both measures (responses) led to many zero counts but also feature very large counts, our GLMM model builds on a zero-inflated bivariate geometric (ZIBGe) distribution, for which we show that it can be easily parameterized in terms of a correlation parameter and its two marginal medians. We model the medians with linear combinations of fixed (environmental covariates) and random (location-specific intercepts) effects. Modeling the medians yields a decreased sensitivity to overly large counts; in particular, in light of growing marginal zero inflation rates. Because of the relatively small sample size (n = 114) we follow a Bayesian modeling approach and use Metropolis-Hastings Markov Chain Monte Carlo (MCMC) simulations for generating posterior samples.

Systematic approach to estimate non-uniform heat generation rate in heat transfer problems using liquid crystal thermography and inverse methodology

ABSTRACT This paper presents an inverse methodology to estimate the parameters of the non-uniform heat generation (function estimation) within a flat plate assembly using steady-state conjugate heat transfer experiments on the flat plate assembly. Steady-state laminar conjugate forced convection experiments on a flat plate assembly are conducted on a horizontal wind tunnel to estimate the parameters of the non-uniform heat generation within flat plate assembly using the inverse methodology. Bayesian inference based Metropolis Hastings–Markov Chain Monte Carlo (MH–MCMC) algorithm and experimental temperatures are employed in the inverse methodology. The experimental temperatures are measured at convenient locations of the flat plate assembly using liquid crystal thermography. In order to accomplish the retrieval, first, steady-state experiments on only the cork material are conducted to estimate the thermal conductivity of the cork material accurately for use in the estimation of the heat generation rate so that the additional error due to uncertainty in the thermal conductivity of the cork material does not affect our final goal of estimating heat generation rate. Following this, steady-state experiments on the cork setup (consisting of a non-uniform heat generation heater and two symmetric cork plates) are conducted to ascertain the nature of heat generation of the heater using measured temperatures and fundamental rate laws. The priors are generated using coupled artificial neural network (ANN) and Levenberg–Marquardt (LM) algorithm for Bayesian inference. Using the Bayesian inference with priors, the parameters of non-uniform heat generation are then estimated in terms of the mean, maximum a posteriori with standard deviation. Finally, the simulated heat powers and temperatures are estimated with retrieved parameters of the non-uniform heat generation. These compared very well with the measured heat powers and temperatures. Finally, a recipe for solving a practical problem, in which only measured temperatures are available, is provided.

A Bayesian Framework for Addressing the Uncertainty in Production Forecasts of Tight-Oil Reservoirs Using a Physics-Based Two-Phase Flow Model

Summary Extrapolation of history matched single-phase flow solutions is a common practice to forecast production from tight-oil reservoirs. Nonetheless, this approach (a) omits multiphase flow effects that exist below bubblepoint conditions and (b) has not included the quantification of the uncertainty of the estimated ultimate recovery (EUR). This work combines a new two-phase (oil and gas) flow solution within a Bayesian framework to address the uncertainty in the EUR. We illustrate the application of the procedure to tight-oil wells of west Texas. First, we combine the oil and the gas flow equations into a single dimensionless two-phase flow equation. The solution is a dimensionless flow rate model that can be easily scaled using two parameters: hydrocarbon pore volume and characteristic time. Second, this study generates the probabilistic production forecasts using a Bayesian approach in which the parameters of the model are treated as random variables. We construct parallel Markov chains of the parameters using an adaptative Metropolis-Hastings (M-H) Markov chain Monte Carlo (MCMC) for this purpose. Third, we evaluate the robustness of our inferences using posterior predictive checks (PPCs). Finally, we quantify the uncertainty in the EUR percentiles using the bootstrap method. The results of this research are as follows. First, this work shows that EUR estimates based on single-phase flow solutions will consistently underestimate the ultimate oil recovery factors in solution-gas drives where the reservoir pressure is less than the bubblepoint. The degree of underestimation will depend on the reservoir and flowing conditions as well as the fluid properties. Second, the application of parallel Markov chains using an adaptative M-H MCMC scheme that addresses the correlation between the model’s parameters solves the issues of mixing and autocorrelation of Markov chains and, thus, it speeds up speeding up the convergence of the Markov chains. Third, we generate replicated data from our posterior distributions to assess the robustness of our inferences (PPCs). Finally, we use hindcasting to calibrate and strengthen our inferences. To our knowledge, all these approaches are novel in EUR forecasting. Using a Bayesian framework with a low-dimensional (two-parameter) physics-based model provides a fast and reliable technique to quantify the uncertainty in production forecasts. In addition, the use of parallel chains with an adaptative M-H MCMC accelerates the rate of convergence and increases the robustness of the method.

Unifying Consensus and Covariance Intersection for Efficient Distributed State Estimation Over Unreliable Networks

This article presents and studies a recursive information consensus filter for decentralized dynamic state estimation under circumstances in which the communication network is unreliable. Local estimators are assumed to have access only to local information, and no structure is assumed about the topology of the communication network, which need not be connected at all times. The filter is a hybrid approach: it uses iterative covariance intersection to reach consensus over priors, which might become correlated, while consensus over new information is handled using weights based on a Metropolis–Hastings Markov chain. We establish bounds for estimation performance and show that this hybrid method produces unbiased conservative estimates that are better than covariance intersection. The performance of the hybrid method is evaluated extensively, including comparisons with competing algorithms, with a hypothetical “full history” yardstick, and centralized performance. We conduct an assessment on a realistic atmospheric dispersion problem and also on more carefully crafted settings to help characterize particular aspects of the performance.

Maximum—A Posteriori Estimation of Linear Time-Invariant State-Space Models via Efficient Monte-Carlo Sampling

Abstract This article addresses maximum-a-posteriori (MAP) estimation of linear time-invariant state-space (LTI-SS) models. The joint posterior distribution of the model matrices and the unknown state sequence is approximated by using Rao-Blackwellized Monte-Carlo sampling algorithms. Specifically, the conditional distribution of the state sequence given the model parameters is derived analytically, while only the marginal posterior distribution of the model matrices is approximated using a Metropolis-Hastings Markov Chain Monte-Carlo sampler. From the joint distribution, MAP estimates of the unknown model matrices as well as the state sequence are computed. The performance of the proposed algorithm is demonstrated on a numerical example and on a real laboratory benchmark dataset of a hair dryer process.

Constraining Einstein’s equivalence principle with multiwavelength polarized astrophysical sources

ABSTRACTThe observed time delays between photons with different circular polarizations from an astrophysical object provide a new, interesting way of testing the Einstein Equivalence Principle (EEP). In this paper, we constrain the EEP by considering both Shapiro time delay and Faraday rotation effects. We continue to search for astronomical sources that are suitable for testing the EEP accuracy, and obtain 60 extragalactic radio sources with multiwavelength polarization angles in three different radio bands (20, 8.6, and 4.8 GHz) and 29 brightest stars within our own Milky Way galaxy with multicolour linear polarimetric data in five optical bands (UBVRI). We apply the Metropolis–Hastings Markov Chain to simulate the fit parameters. The final results show that the values of the parametrized post-Newtonian parameter γ discrepancy (Δγp) are constrained to be in the range of 10−26 − 10−23 for 60 radio sources and in the range of 10−23 − 10−20 for 29 optical polarization stars. Compared to previous EEP tests that based on the single polarization measurement in the gamma-ray band, our results have profound superiority that nearly a few tens of astrophysical sources with multiwavelength polarization observations commonly in the optical and radio bands are available. It ensures that these sources can give more significantly robust bounds on the EEP. Although the presented method is straightforward, the resulting constraints on the EEP should be taken as upper limits as other more complex astrophysical effects affecting a polarization rotation are hardly considered.

Rao-Blackwellized sampling for batch and recursive Bayesian inference of Piecewise Affine models

This paper addresses batch (offline) and recursive (online) Bayesian inference of Piecewise Affine (PWA) regression models. By exploiting the particular structure of PWA models, efficient Rao-Blackwellized Monte Carlo sampling algorithms are developed to approximate the joint posterior distribution of the model parameters. Only the marginal posterior of the parameters used to describe the regressor-space partition is approximated, either in a batch mode using a Metropolis–Hastings Markov-Chain Monte Carlo (MCMC) sampler, or sequentially using particle filters, while the conditional distribution of the other model parameters is computed analytically. Probability distributions for the predicted outputs given new test inputs are derived and modifications of the proposed approaches to address maximum-a-posteriori estimate are discussed. The performance of the proposed algorithms is shown via a numerical example and through a benchmark case study on data-driven modelling of the electronic component placement process in a pick-and-place machine.

Bayesian inversion for steady flow in fractured porous media with contact on fractures and hydro-mechanical coupling

The paper is motivated by a strong interest in numerical analysis of flow in fractured porous media, e.g., rocks in geo-engineering applications. It follows the conception of porous media as a continuum with fractures which are represented as lower dimensional objects. In the paper, the finite element discretization of the flow in coupled continuum and fractures is used; fluid pressures serve as the basic unknowns. In many applications, the flow is connected with deformations of the porous matrix; therefore, the hydro-mechanical coupling is also considered. The fluid pressure is transferred to the mechanical load in both pores and fractures and the considered mechanical model involves elastic deformations of the porous matrix and opening/closing of the fractures with the non-penetration constraint. The mechanical model with this constraint is implemented via the technique of the Lagrange multipliers, duality formulation, and combination with a suitable domain decomposition method. There is usually lack of information about problem parameters and they undergo many uncertainties coming e.g. from the heterogeneity of rock formations and complicated realization of experiments for parameter identification. These experiments rarely provide some of the asked parameters directly but require solving inverse problems. The stochastic (Bayesian) inversion is natural due to the mentioned uncertainties. In this paper, the implementation of the Bayesian inversion is realized via Metropolis-Hastings Markov chain Monte Carlo approach. For the reduction of computational demands, the sampling procedure uses the delayed acceptance of samples based on a surrogate model which is constructed during a preliminary sampling process. The developed hydro-mechanical model and the implemented Bayesian inversion are tested on two types of model inverse problems.

Constraining the Einstein equivalence principle with multi-wavelength observations of polarized blazars

ABSTRACT In this paper, we present a novel method to test the Einstein equivalence principle (EEP) using (simultaneous) multi-wavelength radio observations of polarized blazars. We analyse simultaneous multi-wavelength polarization observations of 3C 279 at 22, 43, and 86 GHz obtained by two antennas of the Korean VLBI Network. We obtained 15 groups of polarization data, and applied the Metropolis–Hastings Markov chain (MHMC) to simulate the parameters when considering the EEP effect and the simplest form of Faraday rotation (single external Faraday screen). The final results show the constraint of the parametrized post-Newtonian (PPN) parameter γ discrepancy as Δγp = (1.91 ± 0.34) × 10−20. However, the single external Faraday screen is an oversimplification for blazars because there are numerous observations showing complex Faraday rotation behaviour for blazars due to internal/external Faraday dispersion, beam depolarization, etc. The Δγp results of this paper can only be considered as upper limits. Only if all other effects are revealed and considered should the result be taken as a direct measurement of the violation of the EEP.

Individual-Level Modelling of Infectious Disease Data: EpiILM

In this article, we introduce the R package EpiILM, which provides tools for simulation from, and inference for, discrete-time individual-level models of infectious disease transmission proposed by Deardon et al. (2010). The inference is set in a Bayesian framework and is carried out via Metropolis-Hastings Markov chain Monte Carlo (MCMC). For its fast implementation, key functions are coded in Fortran. Both spatial and contact network models are implemented in the package and can be set in either susceptible-infected (SI) or susceptible-infected-removed (SIR) compartmental frameworks. The use of the package is demonstrated through examples involving both simulated and real data.

Which Firms Require More Governance? Evidence from Mutual Funds' Revealed Preferences

This paper estimates mutual funds’ preferences for governance structures, using data on proxy vote records. I elicit funds’ revealed preferences by studying the differences in their votes on the same issue across their portfolio firms’ shareholder proposals, and develop funds’ preference rankings by implementing the Metropolis-Hastings Markov chain Monte Carlo algorithm. Funds prefer firms with low board independence, high insider ownership, and high abnormal compensation to adopt certain governance provisions that increase shareholder rights. Contrary to the view that the net benefits of takeover defenses are higher for young and small firms, funds are not enthusiastic about large and mature firms increasing shareholder rights. Large and mature firms are disproportionately targeted by shareholder proposals, suggesting the possibility that investors vote down worthless proposals submitted to such firms. I find a mixed relation between fund preferences and firm performance. Active and passive funds have similar preferences. Fund preferences are moderately correlated with overall vote support on relevant shareholder proposals.

Bayesian Approach for Recovering Piecewise Constant Viscoelasticity from MRE Data

This paper deals with an inverse problem for recovering the piecewise constant viscoelasticity of a living body from MRE (Magnetic Resonance Elastography) data. Based on a scalar partial differential equation whose solution can approximately simulate MRE data, our inverse coefficient problem is considered as a statistical inverse problem of reconstructing the posterior distribution of unknown viscoelastic modulus. For sampling this distribution, one usually can use the Metropolis-Hastings Markov chain Monte Carlo (MH-MCMC) algorithm. However, without an appropriate “proposal” distribution given artificially, the MH-MCMC algorithm is hard to draw samples efficiently. To avoid this, a so-called slice sampling algorithm is introduced in this paper and applied for solving our problem. The performance of these statistical inversion algorithms is numerically tested basing on simulated data.

Hierarchical Bayesian Model for Probabilistic Analysis of Electric Vehicle Battery Degradation

This article proposes a hierarchical Bayesian model for probabilistic estimation of the electric vehicle (EV) battery capacity fade. Deterministic estimation of the EV battery degradation is not reliable, as its aging factors are mostly external and varies by time, location, and the driver’s usage pattern, while probabilistic models can address the observations uncertainties and provide more accurate estimations. We have developed a comprehensive Bayesian network model that incorporates two main aspects of the EV battery aging: hierarchy and variety of external effectual factors. Multiple levels of hierarchical relationship with intermediate hidden variables connect the external factors, such as driving behavior and habits, charging options, and grid services to the battery capacity fade. The mathematical expression of the model is extracted based on Bayes’ theorem, the probability distributions for all variables are carefully chosen, and the Metropolis–Hastings Markov chain Monte Carlo sampling method is applied to generate the posterior distributions. The model is trained with a subset of experimental data (85%) and tested with the other 15% of data to prove its accuracy. Also, three case studies for different drivers, different grid services’ repetitions, and different climates are explored to show model’s flexibility with different input data.

A Hybrid Inversion Scheme Combining Markov Chain Monte Carlo and Iterative Methods for Determining Optical Properties of Random Media

Near-infrared spectroscopy (NIRS) including diffuse optical tomography is an imaging modality which makes use of diffuse light propagation in random media. When optical properties of a random medium are investigated from boundary measurements of reflected or transmitted light, iterative inversion schemes such as the Levenberg–Marquardt algorithm are known to fail when initial guesses are not close enough to the true value of the coefficient to be reconstructed. In this paper, we investigate how this weakness of iterative schemes is overcome using Markov chain Monte Carlo. Using time-resolved measurements performed against a polyurethane-based phantom, we present a case that the Levenberg–Marquardt algorithm fails to work but the proposed hybrid method works well. Then, with a toy model of diffuse optical tomography we illustrate that the Levenberg–Marquardt method fails when it is trapped by a local minimum but the hybrid method can escape from local minima by using the Metropolis–Hastings Markov chain Monte Carlo algorithm until it reaches the valley of the global minimum. The proposed hybrid scheme can be applied to different inverse problems in NIRS which are solved iteratively. We find that for both numerical and phantom experiments, optical properties such as the absorption and reduced scattering coefficients can be retrieved without being trapped by a local minimum when Monte Carlo simulation is run only about 100 steps before switching to an iterative method. The hybrid method is compared with simulated annealing. Although the Metropolis–Hastings MCMC arrives at the steady state at about 10,000 Monte Carlo steps, in the hybrid method the Monte Carlo simulation can be stopped way before the burn-in time.