Markov Chain Monte Carlo Simulation Research Articles

Bayesian spatial modeling of COVID-19 case-fatality rate inequalities

The ongoing outbreak of COVID-19 challenges the health systems and epidemiological responses of all countries worldwide. Although preventive measures have been globally considered, the spatial heterogeneity of its effectiveness is evident, underscoring global health inequalities. Using Bayesian-based Markov chain Monte Carlo simulations, we identify the spatial association of socioeconomic factors and the risk for dying from COVID-19 in Colombia. We confirm that from March 16 to October 04, 2020, the COVID-19 case-fatality rate and the multidimensional poverty index have a heterogeneous spatial distribution. Spatial analysis reveals that the risk of dying from COVID-19 increases in regions with a higher proportion of poor people with dwelling (RR 1.74 95%CI = 1.54–9.75), educational (RR 1.69 95%CI = 1.36–5.94), childhood/youth (RR 1.35 95%CI = 1.08–4.03), and health (RR 1.16 95%CI = 1.06–2.04) deprivations. These findings evidence the vulnerability of most disadvantaged members of society to dying in a pandemic and assist the spatial planning of preventive strategies focused on vulnerable communities.

Multiple Imputation of Missing Data in Educational Production Functions

Educational production functions rely mostly on longitudinal data that almost always exhibit missing data. This paper contributes to a number of avenues in the literature on the economics of education and applied statistics by reviewing the theoretical foundation of missing data analysis with a special focus on the application of multiple imputation to educational longitudinal studies. Multiple imputation is one of the most prominent methods to surmount this problem. Not only does it account for all available information in the predictors, but it also takes into account the uncertainty generated by the missing data themselves. This paper applies a multiple imputation technique using a fully conditional specification method based on an iterative Markov chain Monte Carlo (MCMC) simulation using a Gibbs sampler algorithm. Previous attempts to use MCMC simulation were applied on relatively small datasets with small numbers of variables. Therefore, another contribution of this paper is its application and comparison of the imputation technique on a large longitudinal English educational study for three iteration specifications. The results of the simulation proved the convergence of the algorithm.

Constraining tidal quality factor using spin period in eclipsing binaries

ABSTRACT Evolution of binary objects under the influence of tides drastically affects the expected observational properties of the system. With the discovery of a large number of close-in hot Jupiter systems and eclipsing binaries from missions such as Kepler and Transiting Exoplanet Survey Satellite, it has become imperative to understand the extent of tidal influence on their formation and observed properties. In the case of binary systems, an efficient tidal dissipation can lead to either spin-up or spin-down of the stars and/or spin–orbit synchronization, depending upon the exchange of angular momentum between the star and the orbit. We combine the eclipsing binary systems from the Kepler mission with stellar and orbital parameters available in the literature to create a catalogue of 41 eclipsing binaries suitable for analysis of tidal dissipation. Empirically, the efficiency of tidal dissipation is parametrized using a modified tidal quality factor ($Q_{\star }^{\prime }$). We find constraints on $Q_{\star }^{\prime }$ using the observed rotation period of the primary star in the eclipsing binary systems. We calculate detailed evolutions of binary systems under the combined influence of tides, stellar evolution, and loss of stellar angular momentum to magnetic winds, and perform Markov chain Monte Carlo simulations to account for the uncertainties in the observed data. Our analysis shows that $\log _{10}{Q^{\prime }_{\star }}=7.818\pm 0.035$ can reproduce the observed primary star spin in almost all systems in our sample.

Data-driven EUR modeling and optimization in the liquid-rich Duvernay Formation, western Canada sedimentary basin, Canada

Estimated Ultimate Recovery (EUR) is one of the focuses of the feasibility assessment for oil and gas development projects. EUR is the utmost recoverable oil and gas volume under the current assumption of technology and economics. Many factors including geology, drilling, completion, operation, and commodity prices influence EUR, which makes the prediction a difficult task. Reservoir numerical simulation and production decline curve analysis (DCA) are two broadly accepted method to calculate EUR. However, the former requires substantial data and resources, while the latter is lack of causative mechanism to associate the fundamentals to productivity. This study proposes a machine learning (ML) procedure in EUR modeling, by which EUR is linked to fundamental variables from available data and the variation in EUR can be explained by various factors so that the results can be applied to optimize future projects. In the proposed procedure, the EUR was estimated using a probabilistic dual flow regime model and Markov Chain Monte Carlo (MCMC) simulation. The resulting EUR in each well was then modeled using a two-level stacked ensemble ML approach, while Shapley value was used to explain feature sensitivity in the trained model. In the last, the EUR is optimized by adjusting the most sensitive factors in the trained model. The trained ML model achieved high accuracy on EUR prediction, and the Shapley value analysis showed that completion length, condensate gas ratio and fracturing fluid volume are among the most important features to EUR. The EUR optimization result showed that there is large room for improvement by adjusting the key features. This proposed approach provides a new perspective to find associations between the fundamental factors and the well EUR which improves the understanding of oil and gas production in unconventional reservoirs.

Predicting the Compressibility Factor of Natural Gas by Using Statistical Modeling and Neural Network

Simulating the phase behavior of a reservoir fluid requires the determination of many parameters, such as gas–oil ratio and formation volume factor. The determination of such parameters requires knowledge of the critical properties and compressibility factor (Z factor). There are many techniques to determine the compressibility factor, such as experimental pressure, volume, and temperature (PVT) tests, empirical correlations, and artificial intelligence approaches. In this work, two different models based on statistical regression and multi-layer-feedforward neural network (MLFN) were developed to predict the Z factor of natural gas by utilizing the experimental data of 1079 samples with a wide range of pseudo-reduced pressure (0.12–25.8) and pseudo reduced temperature (1.3–2.4). The statistical regression model was proposed and trained in R using the “rjags” package and Markov chain Monte Carlo simulation, while the multi-layer-feedforward neural network model was postulated and trained using the “neural net” package. The neural network consists of one input layer with two anodes, three hidden layers, and one output layer. The input parameters are the ratio of pseudo-reduced pressure and the pseudo-reduced temperature of the natural hydrocarbon gas, while the output is the Z factor. The proposed statistical and MLFN models showed a positive correlation between the actual and predicted values of the Z factor, with a correlation coefficient of 0.967 and 0.979, respectively. The results from the present study show that the MLFN can lead to accurate and reliable prediction of the natural gas compressibility factor.

A Bayesian Spatio-Network Model for Multiple Adolescent Adverse Health Behaviours

Abstract The use of alcohol, cigarettes and marijuana among adolescents are major public health concerns, and a number of epidemiological studies have been conducted to understand the drivers of these individual health behaviours. However, there is no literature that jointly models these health behaviours with the aim of understanding the relative importance of individual factors, friendship effects and spatial effects in determining the prevalence of alcohol, cigarette and marijuana use among adolescents. To address this gap in the literature, we propose a novel multivariate spatio-network model for jointly modelling all three of these behaviours, with inference conducted in a Bayesian setting using Markov chain Monte Carlo simulation. The model is motivated by survey data from five schools in Los Angeles, California, and the results indicate the important roles that individual factors and friendship networks play in driving the uptake of these health behaviours.

Bayesian inference of a stochastic diffusion process for the dynamic of HIV in closed heterosexual population with simulations and application to Morocco case

A model of the HIV dynamic in a heterosexual population of fixed size is considered in this paper. We represent the dynamic by a multidimensional SIR model. We formulate the stochastic diffusion approximation process to describe the dynamic of HIV by using strong approximation theorems for density-dependent Markov chains. Our aim is to estimate the parameters of this model; to reach this goal, we use Bayesian inference with Markov chain Monte Carlo (MCMC) simulations. We prove that the posterior distributions of the parameters are shifted Generalized Inverse Gaussian (GIG). The obtained results are well illustrated by simulations and real application of Morocco’s case.

Derivation of a Human In Vivo Benchmark Dose for Bisphenol A from ToxCast In Vitro Concentration Response Data Using a Computational Workflow for Probabilistic Quantitative In Vitro to In Vivo Extrapolation.

A computational workflow which integrates physiologically based kinetic (PBK) modelling; global sensitivity analysis (GSA), Approximate Bayesian Computation (ABC), Markov Chain Monte Carlo (MCMC) simulation and the Virtual Cell Based Assay (VCBA) for the estimation of the active, free in vitro concentration of chemical in the reaction medium was developed to facilitate quantitative in vitro to in vivo extrapolation (QIVIVE). The workflow was designed to estimate parameter and model uncertainty within a computationally efficient framework. The workflow was tested using a human PBK model for bisphenol A (BPA) and high throughput screening (HTS) in vitro concentration-response data, for estrogen and pregnane X receptor activation determined in human liver and kidney cell lines, from the ToxCast/Tox21 database. In vivo benchmark dose 10% lower confidence limits (BMDL10) for oral uptake of BPA (ng/kg BW/day) were calculated from the in vivo dose-responses and compared to the human equivalent dose (HED) BMDL10 for relative kidney weight change in the mouse derived by European Food Safety Authority (EFSA). Three from four in vivo BMDL10 values calculated in this study were similar to the EFSA values whereas the fourth was much smaller. The derivation of an uncertainty factor (UF) to accommodate the uncertainties associated with measurements using human cell lines in vitro, extrapolated to in vivo, could be useful for the derivation of Health Based Guidance Values (HBGV).

A Bayesian approach with urban-scale energy model to calibrate building energy consumption for space heating: A case study of application in Beijing

Urban-scale energy model can be a crucial tool for evaluating and in turn propelling the implementation of energy efficiency and low carbon programs for buildings and cites. A variety of disputes on integrity and correctness lie in basic statistical data of China's building energy use. Inadequate information and performance gap caused by input uncertainties are the common obstacles to produce reliable energy modelling results. This paper develops a bottom-up approach to depict energy use intensity (EUI) for space heating of building in the urban level accurately, even if the data resource is inadequate and imprecise or the data are influenced by uncertain issues. A hybrid probability model is developed and the model parameters are calibrated by Bayesian inference and Markov Chain Monte Carlo simulation using data set of meter reading from 2062 stochastic-sampled heating substations in Beijing. Preparation and simulation efforts of using this energy model are discussed, following this framework and adjusting according to local climate conditions, typological building characteristics and morphological urban-scale parameters. The results show that the approach is reliable and efficient to calibrate parameters in building energy models. The urban-scale benchmarks of EUI for space heating in Beijing is successfully performed to demonstrate the proposed methodology.

Economic premiums associated with Mycobacterium avium ssp. paratuberculosis-negative replacement purchases in major dairy-producing regions

Johne's disease, or paratuberculosis, is an infectious disorder of the intestines that can affect domestic and wild ruminants that is caused by an infection with Mycobacterium avium ssp. paratuberculosis (MAP). Although the economic losses due to Johne's disease in dairy cattle herds and the benefits and costs of various potential control practices have been estimated before, little is known about the economic value of purchasing MAP-negative dairy replacements in major dairy-producing regions. This study used Markov Chain Monte Carlo simulation techniques to compare 2 sets of MAP-negative and MAP-positive herds across a comprehensive selection of regions: herds purchasing MAP-negative replacement animals and herds purchasing replacement animals with unknown MAP infection status. The economic benefits per MAP-negative replacement purchased were then estimated over a 10-yr horizon, and the additional value of MAP-negative replacements when compared with unknown status replacements were calculated as a percentage premium of the average aggregated dairy replacement price in each region. An average benefit of US$76 per MAP-negative replacement purchase was estimated in major dairy-producing regions, equivalent to a premium of 13%, with higher premiums in regions characterized by below-average replacement prices and on-average farm-gate prices. It was also estimated that the greatest benefits from MAP-negative replacement purchases are associated with MAP-negative herds that successfully remain uninfected.

Globally Centered Autocovariances in MCMC

Autocovariances are a fundamental quantity of interest in Markov chain Monte Carlo (MCMC) simulations with autocorrelation function (ACF) plots being an integral visualization tool for performance assessment. Unfortunately, for slow-mixing Markov chains, the empirical autocovariance can highly underestimate the truth. For multiple-chain MCMC sampling, we propose a globally centered estimator of the autocovariance function (G-ACvF) that exhibits significant theoretical and empirical improvements. We show that the bias of the G-ACvF estimator is smaller than the bias of the current state-of-the-art. The impact of this improved estimator is evident in three critical output analysis applications: (a) ACF plots, (b) estimates of the Monte Carlo asymptotic covariance matrix, and (c) estimates of the effective sample size. Under weak conditions, we establish strong consistency of our improved asymptotic covariance estimator, and obtain its large-sample bias and variance. The performance of the new estimators is demonstrated through various examples. Supplementary materials for this article are available online.

Analysing the impact of migration on HIV/AIDS cases using epidemiological modelling to guide policy makers.

In this paper, we present the impact of migration on the spread of HIV and AIDS cases. A simple model for HIV and AIDS that incorporates migration and addresses its contributions to the spread of HIV and AIDS cases was constructed. The model was calibrated to HIV and AIDS incidence data from Malaysia. We explore the use of Markov chain Monte Carlo (MCMC) simulation method to estimate uncertainty in all the unknown parameters incorporated in our proposed model. Among the migrant population, 1.5572e-01 were susceptible to HIV transmission, which constituted 67,801 migrants. A proportion of migrants, 6.3773e-04, were estimated to be HIV infected, constituting 278 migrants. There were 72 (per 10,000) migrants estimated to have had AIDS, representing a proportion of 1.6611e-08. The result suggests that the disease-free steady state was unstable since the estimated basic reproduction number was 2.0906 and 2.3322 for the models without and with migration, respectively. This is not a good indicator from the public health point of view, as the aim is to stabilize the epidemic at the disease-free equilibrium. The advantage of introduction of migration to the simple model validated the true and the transmission rate associated with HIV and AIDS epidemic disease in Malaysia. It also indicates an approximately 12 percentage points increase in the rate of HIV infection with migration.

An Empirical Method for Causal Inference of Constructs for QoE in Haptic–Audiovisual Communications

This article proposes an empirical method for inferring causal directions in multidimensional Quality of Experience (QoE) in multimedia communications, noting that causation in QoE is perceptual. As an example for modeling framework, we pick up a Bayesian structural equation model (SEM) previously built for haptic audiovisual interactive communications. The SEM includes three constructs (Audiovisual quality, Haptic quality, and User experience quality), which are latent variables each representing a group of observed variables with similar characteristics. In the SEM, the causal directions of the constructs were assumed by resorting to the domain knowledge. This article aims at proposing a methodology for inferring causal directions of constructs in general by verifying the assumption of causal directions in the SEM through their observed data alone. For that purpose, we compare six SEMs each with different causal directions of constructs, one of which is the one from the domain knowledge. The proposed method is based on QoE prediction by a Bayesian approach with Markov chain Monte Carlo (MCMC) simulation. Setting observed scores to the indicators of exogenous variables in each SEM, we predict values of all the indicators; we then assess the mean square error (MSE) between predicted QoE and mean opinion score (MOS) from observed scores and estimate the probability distribution of the MSE in each SEM. We can compare any two SEMs to find which is more plausible by examining the probability that the MSE for one SEM is smaller than or equal to that for the other. These probabilities are estimated with MCMC simulation. The method indicates that the causal directions thus inferred for the haptic audiovisual interactive communications adequately support the original ones drawn from the domain knowledge. In addition, we demonstrate that QoE can behave like the “impact-perceive-adapt” model of the effects of delayed haptic and visual feedback on performance in a collaborative environment, which Jay, Glencross, and Hubbold proposed in 2007, and that it accompanies reversal of plausible causal directions like a flip–flop.

Are patients who return for 10-year follow-up after AIS surgery different from those who do not?

To evaluate the impact of patients lost to follow-up on outcomes of surgery for adolescent idiopathic scoliosis (AIS) at 10-year postoperative. Preoperative, 2-year, and 5-year postoperative demographic, radiographic, and SRS-22 data from a prospective multi-center registry were compared between patients with a 10-year follow-up visit versus those without. A second analysis utilized variables that were different between the groups, along with SRS scores, in a cohort of patients with preoperative, 2-, 5-, and 10-year postoperative SRS scores (complete cohort) to impute missing 10-year data (imputed cohort) utilizing Markov chain Monte Carlo simulation. 250 patients had 10-year follow-up (21%). Those with 10-year follow-up had a greater percentage of patients who underwent anterior procedures (p < 0.05). Radiographically, the groups were similar at all three time points. SRS-22 scores demonstrated slightly worse pain and function preoperatively and at 2year in those lost to follow-up (effect size eta = 0.11-0.12), with no differences at 5year. Imputed data analysis demonstrated similar trends over time in SRS-22 scores compared to the complete cohort for total score and all domains except pain. There was no significant difference in imputed versus complete 10-year SRS-22 scores (p > 0.05). This study identified early differences between patients with 10-year follow-up and those without, though effect sizes were small and non-existent at 5years. SRS-22 scores at 10year between the complete and imputed data sets did not differ. Clinically relevant outcomes of the subset who followed-up at 10year are likely generalizable to the entire eligible AIS population.

Dark energy interactions near the Galactic Center

We investigate scalar-tensor theories, motivated by dark energy models, in the strong gravity regime around the black hole at the centre of our galaxy. In such theories general relativity is modified since the scalar field couples to matter. We consider the most general conformal and disformal couplings of the scalar field to matter to study the orbital behavior of the nearby stars around the galactic star center $Sgr A^{*}$. Markov Chain Monte Carlo (MCMC) simulation yields a bound on the parameters of the couplings of the scalar field to matter. Using Bayesian Analysis yields the first constraints on such theories in the strong gravity regime.

Coefficients of association between nominal and fully ranked ordinal variables with applications to ecological network analysis

A central issue of ecological data analysis is the pairwise comparison of variables describing biological entities and the environment. Difficulties arise with calculations if the measurement scales of the variables differ. In particular, no method is available for measuring the association between a nominal and a fully ranked ordinal variable. Here two coefficients are suggested by reducing this problem to the evaluation of pattern in string representations. The first one is a topological measure that counts the number of other types of elements occurring between pairs of elements of a given state along the entire length of the string, thus providing a global coefficient of aggregation/segregation. The second coefficient is based on counting the number of different elements within substrings generated from the complete string with the moving window technique. Thus, it is a local measure. There is no compact and general formula for calculating these measures, and heuristics are involved for finding the possible minimum and maximum values by algorithmic approximation and Markov Chain Monte Carlo simulation. An R function is provided for computations. The methods are applied to the comparison of nominal variables (biological traits) categorizing marine food web nodes with fully ranked variables describing major graph theory properties of the same nodes in the network. The most descriptive traits (mobility, major functional group) significantly associated with network metrics (weighted indices) were identified from a variety of combinations across three marine ecosystems. These coefficients thus provide an objective, statistically-sound method for identifying ecologically meaningful traits.

Probabilistic models of concrete compressive strength and elastic modulus with rubber aggregates

The disposal of waste rubber products is a significant issue globally and it poses a serious threat to the environment creating long-term ecological problems. The possible use of rubber aggregates in concrete is a valid alternative to obtain a green construction material. This paper develops probabilistic models for the concrete Strength Reduction Factor (SRF) and Elastic modulus Reduction Factor (ERF) accounting for the amount of rubber aggregates as well as several variables defining the mix design. Three different rubber aggregate types are considered, namely fine and coarse replaced individually and fine and coarse replaced simultaneously. A total of 644 sets of concrete compressive strength and elastic modulus tests are collected from the literature for the model calibration. The paper presents a discussion about the formulation of the models, variance stabilizing transformations, model calibration, and model selection. Once formulated, we calibrate the probabilistic models using data from experimental tests. The unknown model parameters are estimated using a Bayesian approach implemented using A Markov Chain Monte Carlo (MCMC) simulation method. The proposed probabilistic models are used to evaluate the reliability of rubberized concrete structures. As an illustration, the proposed probabilistic models are used to estimate the reliability of an example column made of rubberized concrete under compressive axial force and of an example one-way slab made of rubberized concrete under distributed load.

Genetic characterization of Italian and Spanish wild and domesticated chestnut trees

The only native species of the Castanea genus in Europe is Castanea sativa Mill., a widespread and important multipurpose tree species in the Mediterranean area that provides fruit, wood and shelter for hives. With the aim of expanding the knowledge of the genetic variability of the chestnut species (wild trees and varieties) and promoting the traceability of local products, an analysis based on 16 SSRs was carried out on 630 single trees from Italy and Spain. 319 unique genotypes were identified. A Bayesian approach combined with the Markov Chain Monte Carlo (MCMC) simulation method revealed the existence of two genetically distinct groups of chestnuts: Cluster 1 (Spain) and Cluster 2 (Italy), with a clear separation between the cultivars from (northern and southern) Spain and from Italy. The results also confirmed a common genetic structure between chestnut populations from southern Spain and southern Italy, which is the result of historical events and long-term human impact. The results showed no genetic differentiation between chestnut cultivars (grafted trees) and wild chestnut trees, probably as a consequence of the proximity of orchards and natural populations, which resulted in a gene flow between them.

An automated prior robustness analysis in Bayesian model comparison

SummaryIt is well‐known that the marginal likelihood, the gold standard for Bayesian model comparison, can be sensitive to prior hyperparameter choices. However, most models require computationally intense simulation‐based methods to evaluate the typically high‐dimensional integral of the marginal likelihood expression. Hence, despite the recognition that prior sensitivity analysis is important in this context, it is rarely done in practice. We develop efficient and feasible methods to compute the sensitivities of the marginal likelihood, obtained via two common simulation‐based methods, with respect to any prior hyperparameter, alongside the Markov chain Monte Carlo (MCMC) estimation algorithm. Our approach builds on automatic differentiation (AD), which has only recently been introduced to the more computationally intensive MCMC simulation setting. We illustrate our approach with two empirical applications in the context of widely used multivariate time series models.

Inference of Onset Age of Preclinical State and Sojourn Time for Breast Cancer.

Accurate estimation of the three key parameters (sensitivity, time duration in disease-free state and sojourn time in preclinical state) in cancer screening are critical. Likelihood method with a new link function was applied to the Health Insurance Plan of Greater New York (HIP) breast cancer screening data, to estimate the onset age of preclinical state and the sojourn time in the preclinical state for breast cancer. A new link function to model sensitivity as a function of time in the preclinical state and the sojourn time was adopted. Markov Chain Monte Carlo simulations were used to obtain posterior samples and make inference on the three key parameters. Maximum likelihood estimate was also used for comparison. The onset age of the preclinical state has a wide range for breast cancer; the peak onset age was 65.07 years (95% credible interval [C.I.], 55.76 to 73.02). The mean sojourn time was 2.00 years (95% C.I., 0.85 to 2.95). The 95 % C.I. for the sojourn time was 0.16 to 5.53 years. Sensitivity at onset of the preclinical state was 0.75 (95% C.I., 0.54 to 0.88); and sensitivity at the end of the preclinical state was 0.84 (95% C.I., 0.67 to 0.88). The HIP study was the oldest breast cancer mass screening. The estimates reflect key parameters in those days with lower screening sensitivity. However, it is helpful to know other parameters in the planning for future breast cancer screening.