Bayesian Markov Chain Monte Carlo Research Articles

BayesR3 enables fast MCMC blocked processing for largescale multi-trait genomic prediction and QTN mapping analysis

Bayesian methods, such as BayesR, for predicting the genetic value or risk of individuals from their genotypes, such as Single Nucleotide Polymorphisms (SNP), are often implemented using a Markov Chain Monte Carlo (MCMC) process. However, the generation of Markov chains is computationally slow. We introduce a form of blocked Gibbs sampling for estimating SNP effects from Markov chains that greatly reduces computational time by sampling each SNP effect iteratively n-times from conditional block posteriors. Subsequent iteration over all blocks m-times produces chains of length m × n. We use this strategy to solve large-scale genomic prediction and fine-mapping problems using the Bayesian MCMC mixed-effects genetic model, BayesR3. We validate the method using simulated data, followed by analysis of empirical dairy cattle data using high dimension milk mid infra-red spectra data as an example of “omics” data and show its use to increase the precision of mapping variants affecting milk, fat, and protein yields relative to a univariate analysis of milk, fat, and protein.

Bayesian MCMC Approach to Learning About the SIR Model

Abstract: This project aims to study the parameters of the Deterministic SIR(Susceptible → Infected → Recovered) model of COVID-19 in a Bayesian MCMC framework. Several deterministic mathematical models are being developed everyday to forecast the spread of COVID-19 correctly. Here, I have tried to model and study the parameters of the SIR Infectious disease model using the Bayesian Framework and Markov-Chain Monte-Carlo (MCMC) techniques. I have used Bayesian Inference to predict the Basic Reproductive Rate ࢚ࡾ in real time using and following this, demonstrated the process of how the parameters of the SIR Model can be estimated using Bayesian Statistics and Markov-Chain Monte-Carlo Methods. Keywords: COVID-19, Bayesian Inference, Dynamical Systems, SIR Model, Basic Reproductive Rate, Markov-Chain MonteCarlo(MCMC)

The distribution of fitness effects of spontaneous mutations in Chlamydomonas reinhardtii inferred using frequency changes under experimental evolution.

The distribution of fitness effects (DFE) for new mutations is fundamental for many aspects of population and quantitative genetics. In this study, we have inferred the DFE in the single-celled alga Chlamydomonas reinhardtii by estimating changes in the frequencies of 254 spontaneous mutations under experimental evolution and equating the frequency changes of linked mutations with their selection coefficients. We generated seven populations of recombinant haplotypes by crossing seven independently derived mutation accumulation lines carrying an average of 36 mutations in the haploid state to a mutation-free strain of the same genotype. We then allowed the populations to evolve under natural selection in the laboratory by serial transfer in liquid culture. We observed substantial and repeatable changes in the frequencies of many groups of linked mutations, and, surprisingly, as many mutations were observed to increase as decrease in frequency. Mutation frequencies were highly repeatable among replicates, suggesting that selection was the cause of the observed allele frequency changes. We developed a Bayesian Monte Carlo Markov Chain method to infer the DFE. This computes the likelihood of the observed distribution of changes of frequency, and obtains the posterior distribution of the selective effects of individual mutations, while assuming a two-sided gamma distribution of effects. We infer that the DFE is a highly leptokurtic distribution, and that approximately equal proportions of mutations have positive and negative effects on fitness. This result is consistent with what we have observed in previous work on a different C. reinhardtii strain, and suggests that a high fraction of new spontaneously arisen mutations are advantageous in a simple laboratory environment.

Optimal Bayesian MCMC based fire brigade non-suppression probability model considering uncertainty of parameters

The fire brigade non-suppression probability model is a major factor that should be considered in evaluating fire-induced risk through fire probabilistic risk assessment (PRA), and also uncertainty is a critical consideration in support of risk-informed performance-based (RIPB) fire protection decision-making. This study developed an optimal integrated probabilistic fire brigade non-suppression model considering uncertainty of parameters based on the Bayesian Markov Chain Monte Carlo (MCMC) approach on electrical fire which is one of the most risk significant contributors. The result shows that the log-normal probability model with a location parameter (μ) of 2.063 and a scale parameter (σ) of 1.879 is best fitting to the actual fire experience data. It gives optimal model adequacy performance with Bayesian information criterion (BIC) of −1601.766, residual sum of squares (RSS) of 2.51E-04, and mean squared error (MSE) of 2.08E-06. This optimal log-normal model shows the better performance of the model adequacy than the exponential probability model suggested in the current fire PRA methodology, with a decrease of 17.3% in BIC, 85.3% in RSS, and 85.3% in MSE. The outcomes of this study are expected to contribute to the improvement and securement of fire PRA realism in the support of decision-making for RIPB fire protection programs.

Reliability framework for characterizing heat wave and cold spell events

Extreme weather events such as heat waves and cold spells affect people’s lives. This study develops a probabilistic framework to evaluate heat waves and cold spells. As case studies, average daily temperatures of meteorological stations of the two cities (Tehran and Vancouver) from 1995 to 2016 are used to identify four main indicators including intensity, average intensity, duration, and the rate of the occurrence. In addition, probabilistic spatial analysis of the events is obtained through MODIS’s land surface temperature product. To include possible uncertainties, the predictive probability distributions of the intensity and duration are derived using a Bayesian scheme and Monte Carlo Markov Chain method. The probability distributions of the indicators show that the most extreme temperature (lowest temperature) occurs during the cold spell. Reliability evaluations indicate that both cities are more likely to be affected by the cold spell than the heat wave. Results of this study can be used as a benchmark for heat wave/cold spell characterization. The developed approach can be applied to characterize other extreme weather events in any location.

The heritability of Nematodirus battus fecal egg counts.

Although Nematodirus battus is a serious threat to the health and survival of young lambs, there are few options to control this parasite. Bayesian Monte Carlo Markov Chain modelling with a zero-inflated Poisson distribution was used to estimate the heritability of egg counts in both June and July for each of five consecutive cohorts of 200 Scottish Blackface lambs. In one of the 10 analyses, the results failed the diagnostic tests. In seven of the analyses, there was no convincing evidence that the variation in egg counts was heritable. In the 2 years of high infection, the heritability was approximately 0.4 in June but the estimates lacked precision and the 95% highest posterior density credible intervals ranged from just above zero to 0.7. Selective breeding for resistance to N. battus will be difficult because genetically resistant or susceptible lambs cannot be consistently identified by phenotypic markers.

Bayesian Convolution for Stochastic Epidemic Model

Dengue Hemorrhagic Fever (DHF) is a tropical disease that always attacks densely populated urban communities. Some factors, such as environment, climate and mobility, have contributed to the spread of the disease. The Aedes aegypti mosquito is an agent of dengue virus in humans, and by inhibiting its life cycle it can reduce the spread of the dengue disease. Therefore, it is necessary to involve the dynamics of mosquito's life cycle in a model in order to obtain a reliable risk map for intervention. The aim of this study is to develop a stochastic convolution susceptible, infective, recovered-susceptible, infective (SIR-SI) model describing the dynamics of the relationship between humans and Aedes aegypti mosquitoes. This model involves temporal trend and uncertainty factors for both local and global heterogeneity. Bayesian approach was applied for the parameter estimation of the model. It has an intrinsic recurrent logic for Bayesian analysis by including prior distributions. We developed a numerical computation and carry out simulations in WinBUGS, an open-source software package to perform Markov chain Monte Carlo (MCMC) method for Bayesian models, for the complex systems of convolution SIR-SI model. We considered the monthly DHF data of the 2016–2018 periods from 10 districts in Kendari-Indonesia for the application as well as the validation of the developed model. The estimated parameters were updated through to Bayesian MCMC. The parameter estimation process reached convergence (or fulfilled the Markov chain properties) after 50000 burn-in and 10000 iterations. The deviance was obtained at 453.7, which is smaller compared to those in previous models. The districts of Wua-Wua and Kadia were consistent as high-risk areas of DHF. These two districts were considered to have a significant contribution to the fluctuation of DHF cases.

Comparisons of frequentist and Bayesian inferences for interval estimation on process yield

Process yield has been a standard metric for measuring the capability and performance of manufacturing processes. Process capability index Spk, a concise unit-less gauge with yield-sensitive functionality, communicates succinctly the genuine process yield for normally distributed processes. However, in frequentist statistics, the exact sampling distribution of Spk’s natural estimator is intractable. Various frequentist approaches have attempted to address its wide-scale accuracy in statistical inference. Among them, the approach of generalized confidence interval (GCI) has been demonstrated superiority. In this paper, we incorporate Markov chain Monte Carlo (MCMC) algorithms to introduce a Bayesian-type approach. Extensive simulations in comparison of accuracy and precision performances between the Spk’s frequentist and Bayesian inferences are conducted. Concerning coverage rates and average interval widths of the inferential criteria, Spk’s Bayesian MCMC credibility intervals perform better than frequentist GCIs in most cases, particularly, the cases with only a few samples of information acquired from the manufacturing process.

Gaussian Process based Remaining useful life Prediction for Electric Energy Metering Equipment

Electric energy metering equipment (EEME) will fail in advance not as designed running in extreme environments. A multi-kernel Gaussian process regression model using measurement error data to perceive remaining useful life (RUL) for EEME is proposed. Firstly, the gauss kernel and periodic kernel are used to match the health index trend of EEME under a variety of typical environmental stresses. Furthermore, the Bayesian method and Monte Carlo Markov chain method are used to solve the model, and the Weibull distribution is used to fit the posterior trajectory to get the probability density estimation of the RUL.

Revisiting estimation methods for spatial econometric interaction models

This article develops improved calculation techniques for estimating the spatial econometric interaction model of LeSage and Pace (2008) by maximum likelihood (MLE), Bayesian Markov Chain Monte Carlo (MCMC) and spatial two-stage least-squares (S2SLS). The refined estimation methods derive the parameter estimates and their standard errors exclusively from moment matrices with low dimensions. For the computation of these moments, we exploit efficiency gains linked to a matrix formulation of the model, which we generalize to make more flexible use of the exogenous variables. To improve the MLE we restructure the Hessian matrix and the quadratic term in the likelihood function. We also derive a moment based formulation of the Bayesian MCMC estimator from the same likelihood restructuring. Finally, the S2SLS estimator presented in this article is the first one to exploit the efficiency gains of the matrix formulation and also solves the problem of collinearity among spatial instruments. Several benchmarks show that these moment based estimators scale very well to large samples and can be used to estimate models with 100 million flows in just a few minutes. In addition to the improved estimation methods, this article presents a new way to define a feasible parameter space for the spatial econometric interaction model, which allows to verify the models consistency with a minimal computational burden. All of these developments indicate that the spatial econometric extension of the traditional gravity model has become an increasingly mature alternative and should eventually be considered a standard modeling approach for origin-destination flows.

Bayesian LSTM With Stochastic Variational Inference for Estimating Model Uncertainty in Process‐Based Hydrological Models

AbstractSignificant attention has recently been paid to deep learning as a method for improved catchment modeling. Compared with process‐based models, deep learning is often criticized for its lack of interpretability. One solution is to combine a process‐based hydrological model with a residual error model based on deep learning to give full scope to their respective advantages. In classical residual error models, Bayesian inference via Markov chain Monte Carlo (MCMC) is commonly used to provide an estimation of the uncertainty. However, deep neural networks tend to have excessively large numbers of parameters, making MCMC an unsuitable approach. Here, we introduce an alternative to Bayesian MCMC sampling called stochastic variational inference (SVI) which has recently been developed for Bayesian deep learning in Natural Language Processing. We implement SVI in a Long Short‐Term Memory (LSTM) network and construct residual error models in process‐based hydrological models. This approach is examined in the contrasting geographical and climatic characteristics of two catchments from China, the Tangnaihai catchment and the Shiquan catchment. Compared with the Bayesian linear regression model, the Bayesian LSTM provides better uncertainty estimates. Specifically, the proposed method improves the Continuous Ranked Probability Score (CRPS) by over 10% in both two catchments. In the Tangnaihai catchment, it provides more than 10% narrower uncertainty intervals in terms of Sharpness with slightly superior Reliability. In the Shiquan catchment, it provides comparable uncertainty intervals with better Reliability. Further, our study highlights the scalability of SVI to high‐dimensional parameter spaces in hydrological applications (e.g., distributed hydrological models, groundwater models).

Rare and widespread: integrating Bayesian MCMC approaches, Sanger sequencing and Hyb-Seq phylogenomics to reconstruct the origin of the enigmatic Rand Flora genus Camptoloma.

Genera that are widespread, with geographically discontinuous distributions and represented by few species, are intriguing. Is their achieved disjunct distribution recent or ancient in origin? Why are they species-poor? The Rand Flora is a continental-scale pattern in which closely related species appear codistributed in isolated regions over the continental margins of Africa. Genus Camptoloma (Scrophulariaceae) is the most notable example, comprising three species isolated from each other on the northwest, eastern, and southwest Africa. We employed Sanger sequencing of nuclear and plastid markers, together with genomic target sequencing of 2190 low-copy nuclear genes, to infer interspecies relationships and the position of Camptoloma within Scrophulariaceae by using supermatrix and multispecies-coalescent approaches. Lineage divergence times and ancestral ranges were inferred with Bayesian Markov chain Monte Carlo (MCMC) approaches. The population history was estimated with phylogeographic coalescent methods. Camptoloma rotundifolium, restricted to Southern Africa, was shown to be a sister species to the disjunct clade formed by C. canariense, endemic to the Canary Islands, and C. lyperiiflorum, distributed in the Horn of Africa-Southern Arabia. Camptoloma was inferred to be sister to the mostly South African tribes Teedieae and Buddlejeae. Stem divergence was dated in the Late Miocene, while the origin of the extant disjunction was inferred as Early Pliocene. The current disjunct distribution of Camptoloma across Africa was likely the result of fragmentation and extinction and/or population bottlenecking events associated with historical aridification cycles during the Neogene; the pattern of species divergence, from south to north, is consistent with the "climatic refugia" Rand Flora hypothesis.

A comparison of Bayesian Markov chain Monte Carlo methods in a multilevel scenario

Multilevel modeling is a modern approach to deal with hierarchical or a nested data structure which can assess the variability between clusters. Bayesian Markov Chain Monte Carlo (MCMC) methods of estimations are advanced methods applicable for estimating multilevel models. However, these estimation methods are not as yet tested to identify its’ performances as well as the properties associated with these estimation methods. This study targets to conduct a comparison of Bayesian MCMC methods which are developed for multilevel models where the response is normally distributed. The comparison is based upon extensive simulations and an application to a real-life dataset. The performance of Gibbs sampling (GS) and Metropolis Hastings (MH) methods are compared using a simulation study and additionally the factors which can affect the performance of both MCMC methods are identified. Practicality of these methods in real world scenario is confirmed through the application of MCMC method to a dataset. In the simulations though the Metropolis Hastings (MH) shows slightly better performance than Gibbs, there is no evidence to indicate that significant differences exist between these methods except for small samples where MH is superior. The results from the example are not as clear as from the simulations.

The effect of human mobility restrictions on the COVID-19 transmission network in China.

COVID-19 poses a severe threat worldwide. This study analyzes its propagation and evaluates statistically the effect of mobility restriction policies on the spread of the disease. We apply a variation of the stochastic Susceptible-Infectious-Recovered model to describe the temporal-spatial evolution of the disease across 33 provincial regions in China, where the disease was first identified. We employ Bayesian Markov Chain Monte-Carlo methods to estimate the model and to characterize a dynamic transmission network, which enables us to evaluate the effectiveness of various local and national policies. The spread of the disease in China was predominantly driven by community transmission within regions, which dropped substantially after local governments imposed various lockdown policies. Further, Hubei was only the epicenter of the early epidemic stage. Secondary epicenters, such as Beijing and Guangdong, had already become established by late January 2020. The transmission from these epicenters substantially declined following the introduction of mobility restrictions across regions. The spatial transmission network is able to differentiate the effect of the local lockdown policies and the cross-region mobility restrictions. We conclude that both are important policy tools for curbing the disease transmission. The coordination between central and local governments is important in suppressing the spread of infectious diseases.

Bayesian analysis for estimating statistical parameter distributions of elasto-viscoplastic material models

High temperature design methods rely on constitutive models for inelastic deformation and failure typically calibrated against the mean of experimental data without considering the associated scatter. Variability may arise from the experimental data acquisition process, from heat-to-heat material property variations, or both and need to be accurately captured to predict parameter bounds leading to efficient component design. Applying the Bayesian Markov Chain Monte Carlo (MCMC) method to produce statistical models capturing the underlying uncertainty in the experimental data is an area of ongoing research interest. This work varies aspects of the Bayesian MCMC method and explores their effect on the posterior parameter distributions for a uniaxial elasto-viscoplastic damage model using synthetically generated reference data. From our analysis with the uniaxial inelastic model we determine that an informed prior distribution including different types of test conditions results in more accurate posterior parameter distributions. The parameter posterior distributions, however, do not improve when increasing the number of similar experimental data. Additionally, changing the amount of scatter in the data affects the quality of the posterior distributions, especially for the less sensitive model parameters. Moreover, we perform a sensitivity study of the model parameters against the likelihood function prior to the Bayesian analysis. The results of the sensitivity analysis help to determine the reliability of the posterior distributions and reduce the dimensionality of the problem by fixing the insensitive parameters. The comprehensive study described in this work demonstrates how to efficiently apply the Bayesian MCMC methodology to capture parameter uncertainties in high temperature inelastic material models. Quantifying these uncertainties in inelastic models will improve high temperature engineering design practices and lead to safer, more effective component designs.

BEDE: Bayesian estimates of dust evolution for nearby galaxies

ABSTRACT We build a rigorous statistical framework to provide constraints on the chemical and dust evolution parameters for nearby late-type galaxies with a wide range of gas fractions ($3{{\ \rm per\ cent}}\lt f_g\lt 94{{\ \rm per\ cent}}$). A Bayesian Monte Carlo Markov Chain framework provides statistical constraints on the parameters used in chemical evolution models. Nearly a million one-zone chemical and dust evolution models were compared to 340 galaxies. Relative probabilities were calculated from the χ2 between data and models, marginalized over the different time-steps, galaxy masses, and star formation histories. We applied this method to find ‘best-fitting’ model parameters related to metallicity, and subsequently fix these metal parameters to study the dust parameters. For the metal parameters, a degeneracy was found between the choice of initial mass function, supernova metal yield tables, and outflow prescription. For the dust parameters, the uncertainties on the best-fitting values are often large except for the fraction of metals available for grain growth, which is well constrained. We find a number of degeneracies between the dust parameters, limiting our ability to discriminate between chemical models using observations only. For example, we show that the low dust content of low-metallicity galaxies can be resolved by either reducing the supernova dust yields and/or including photofragmentation. We also show that supernova dust dominates the dust mass for low-metallicity galaxies and grain growth dominates for high-metallicity galaxies. The transition occurs around 12 + log (O/H) = 7.75, which is lower than found in most studies in the literature.

Estimasi Jumlah Penghuni Ruangan Berdasarkan Konsentrasi CO2 Dengan Metode Bayesian MCMC

<span lang="PT-BR">The number of occupants in the building is important information for building management because it is related to security issues, evacuation, and energy saving. This article focuses on estimating the number of occupants using the Bayesian Monte Carlo Markov chain (MCMC) method based on indoor CO<sub>2</sub> levels. Probability theory underlies the Bayesian MCMC principle, where the mass balance equation of indoor CO<sub>2</sub> is used as a physical model of estimation calculations. Determination of the variables in the mass balance equation is investigated to obtain the effect on the accuracy of the estimated number of occupants. It found that the higher the standard deviation of the input variable on the physical model, the higher the error estimation produced. In addition, the Bayesian MCMC algorithm is tested in a real-time scheme of test</span><span lang="IN">-</span><span lang="PT-BR">chamber. The result shows an estimated error of 39%. Rapid changes influence estimation errors in actual occupants relative to the sample interval and the time delay of the estimation.</span>

Did Noise Pollution Really Improve during COVID-19? Evidence from Taiwan

Background and objectives: The impacts of COVID-19 are like two sides of one coin. During 2020, there were many research papers that proved our environmental and climate conditions were improving due to lockdown or large-scale restriction regulations. In contrast, the economic conditions deteriorated due to disruption in industry business activities and most people stayed at home and worked from home, which probably reduced the noise pollution. Methods: To assess whether there were differences in noise pollution before and during COVID-19. In this paper, we use various statistical methods following odds ratios, Wilcoxon and Fisher’s tests and Bayesian Markov chain Monte Carlo (MCMC) with various comparisons of prior selection. The outcome of interest for a parameter in Bayesian inference is complete posterior distribution. Roughly, the mean of the posterior will be clear with point approximation. That being said, the median is an available choice. Findings: To make the Bayesian MCMC work, we ran the sampling from the conditional posterior distributions. It is straightforward to draw random samples from these distributions if they have regular shapes using MCMC. The case of over-standard noise per time frame, number of noise petition cases, number of industry petition cases, number of motorcycles, number of cars and density of vehicles are significant at α = 5%. In line with this, we prove that there were differences of noise pollution before and during COVID-19 in Taiwan. Meanwhile, the decreased noise pollution in Taiwan can improve quality of life.

Uncertainty Quantification of Water Level Predictions from Radar‐based Areal Rainfall Using an Adaptive MCMC Algorithm

This study proposes an approach for the uncertainty quantification at each stage of a single hydrological process of water level predictions based on different sources of mean areal precipitation (MAP) forecasts by using an adaptive Bayesian Markov chain Monte Carlo (MCMC) approach. The MAP forecasts are derived from the McGill Algorithm for Precipitation Nowcasting by Lagrangian Extrapolation (MAPLE) system and a long short-term memory (LSTM) network. The predicted water levels at two stations in the Gangnam catchment, Seoul, South Korea, are processed with a coupled 1D/2D urban hydrological model (1D/2D-UHM) forced by MAPLE MAP forecasts and LSTM-corrected MAP forecasts of five heavy rainfall events. The proposed Bayesian approach using the delayed rejection and adaptive Metropolis (DRAM) algorithm was compared with the Metropolis-Hastings (MH) algorithm in the uncertainty estimation of Weibull distribution parameters. The uncertainty contributions of the stages and sources in the related process were analyzed, including quantitative precipitation estimation (QPE) inputs, MAP inputs and 1D/2D-UHM. The results indicate that the uncertainty contribution of the MAPLE MAP forecasting is the highest in the 3-hour forecasting time. The uncertainty contribution of the QPE input for MAPLE MAP forecasting is the smallest and that of two sources, including the LSTM-corrected MAP source, and MAP and the coupled model is more significant than that of the QPE input. This research showed that the adaptive Bayesian MCMC method using the DRAM algorithm might be a robust option in quantitative uncertainty analyses of a single hydrological process, especially for urban flood management.

Emulation‐based inference for spatial infectious disease transmission models incorporating event time uncertainty

AbstractMechanistic models of infectious disease spread are key to inferring spatiotemporal infectious disease transmission dynamics. Ideally, covariate data and the infection status of individuals over time would be used to parameterize such models. However, in reality, complete data are rarely available; for example, infection times are almost never observed. Bayesian data‐augmented Markov chain Monte Carlo (MCMC) methods are commonly used to allow us to infer such missing or censored data. However, for large disease systems, these methods can be highly computationally expensive. In this paper, we propose two methods of approximate inference for such situations based on so‐called emulation techniques. Here, both methods are set in a Bayesian MCMC framework but replace the computationally expensive likelihood function by a Gaussian process‐based likelihood approximation. In the first method, we build an emulator of the discrepancy between summary statistics of simulated and observed epidemic data. In the second method, we develop an emulator of an importance sampling‐based likelihood approximation. We show how both methods offer substantial computational efficiency gains over standard Bayesian MCMC‐based method, and can be used to infer the transmission of complex infectious disease systems. We also show that importance sampling‐based methods tend to perform more satisfactorily.