Bayesian Monte Carlo Method Research Articles

Estimation of vertical structure of latent heat generated in thunderstorms using CloudSat radar

AbstractThe Earth's atmosphere is highly coupled between the vertical layers and the surface. An understanding of circulations in the atmosphere is important for developing models and improving weather forecasting. The latent heat produced in the atmosphere is one of the key driving forces of these circulations. It is therefore very important to estimate the latent heat in the atmosphere accurately, especially in thunderstorm clouds, which have proved to be one of the major sources of gravity waves in tropical regions. The current space‐based latent heat retrievals are limited to precipitation‐based estimation which cannot define the complete structure of a thunderstorm where precipitation is not the main indicator of the severity. A novel method is proposed in this study which retrieves the latent heat profiles of thunderstorm clouds using CloudSat W‐band radar profiles. A realistic database of simulated thunderstorm events developed using the Regional Atmospheric Modelling System – Cloud Resolving Model (RAMS‐CRM) is compared with observations using the Bayesian Monte Carlo method to derive an estimate with an uncertainty analysis for each estimate. The method is validated in the southeast Asian region with European Centre for Medium‐Range Weather Forecasts driven RAMS‐CRM profiles. The algorithm performance on observation data using linear fit, regression and bias analysis is discussed. A case study retrieval is also performed to demonstrate the retrieval on real CloudSat data.

Gaussian Process Based Expected Information Gain Computation for Bayesian Optimal Design.

Optimal experimental design (OED) is of great significance in efficient Bayesian inversion. A popular choice of OED methods is based on maximizing the expected information gain (EIG), where expensive likelihood functions are typically involved. To reduce the computational cost, in this work, a novel double-loop Bayesian Monte Carlo (DLBMC) method is developed to efficiently compute the EIG, and a Bayesian optimization (BO) strategy is proposed to obtain its maximizer only using a small number of samples. For Bayesian Monte Carlo posed on uniform and normal distributions, our analysis provides explicit expressions for the mean estimates and the bounds of their variances. The accuracy and the efficiency of our DLBMC and BO based optimal design are validated and demonstrated with numerical experiments.

Development of spectral decomposition based on Bayesian information criterion with estimation of confidence interval

ABSTRACT We develop an automatic peak fitting algorithm using the Bayesian information criterion (BIC) fitting method with confidence-interval estimation in spectral decomposition. First, spectral decomposition is carried out by adopting the Bayesian exchange Monte Carlo method for various artificial spectral data, and the confidence interval of fitting parameters is evaluated. From the results, an approximated model formula that expresses the confidence interval of parameters and the relationship between the peak-to-peak distance and the signal-to-noise ratio is derived. Next, for real spectral data, we compare the confidence interval of each peak parameter obtained using the Bayesian exchange Monte Carlo method with the confidence interval obtained from the BIC-fitting with the model selection function and the proposed approximated formula. We thus confirm that the parameter confidence intervals obtained using the two methods agree well. It is therefore possible to not only simply estimate the appropriate number of peaks by BIC-fitting but also obtain the confidence interval of fitting parameters.

Molecular Evolution of the Fusion Protein (F) Gene in Human Respirovirus 3.

To elucidate the evolution of human respirovirus 3 (HRV3), we performed detailed genetic analyses of the F gene (full-length) detected from hundreds of HRV3 strains obtained from various geographic regions. First, we performed time-scaled evolutionary analyses using the Bayesian Markov chain Monte Carlo method. Then, we performed analyses of phylodynamics, similarity, phylogenetic distance, selective pressure, and conformational B-cell epitope with the F-protein structural analyses. Time-scaled phylogenetic tree showed that the common ancestor of HRV3 and bovine respirovirus 3 diverged over 300 years ago and subdivided it into three major clusters and four subclusters during the most recent 100 years. The overall evolutionary rate was approximately 10–3 substitutions/site/year. Indigenous similarity was seen in the present strains, and the mean phylogenetic distance were 0.033. Many negative selection sites were seen in the ectodomain. The conformational epitopes did not correspond to the neutralizing antibody binding sites. These results suggest that the HRV3 F gene is relatively conserved and restricted in this diversity to preserve the protein function, although these strains form many branches on the phylogenetic tree. Furthermore, HRV3 reinfection may be responsible for discordances between the conformational epitopes and the neutralizing antibody binding sites of the F protein. These findings contribute to a better understanding of HRV3 virology.

Molecular Evolution of the Protease Region in Norovirus Genogroup II.

Noroviruses are a major cause of viral epidemic gastroenteritis in humans worldwide. The protease (Pro) encoded in open reading frame 1 (ORF1) is an essential enzyme for proteolysis of the viral polyprotein. Although there are some reports regarding the evolutionary analysis of norovirus GII-encoding genes, there are few reports focused on the Pro region. We analyzed the molecular evolution of the Pro region of norovirus GII using bioinformatics approaches. A time-scaled phylogenetic tree of the Pro region constructed using a Bayesian Markov chain Monte Carlo method indicated that the common ancestor of GII diverged from GIV around 1680 CE [95% highest posterior density (HPD), 1607–1749]. The GII Pro region emerged around 1752 CE (95%HPD, 1707–1794), forming three further lineages. The evolutionary rate of GII Pro region was estimated at more than 10–3 substitutions/site/year. The distribution of the phylogenetic distances of each genotype differed, and showed genetic diversity. Mapping of the negative selection and substitution sites of the Pro structure showed that the substitution sites in the Pro protein were mostly produced under neutral selection in positions structurally adjacent to the active sites for proteolysis, whereas negative selection was observed in residues distant from the active sites. The phylodynamics of GII.P4, GII.P7, GII.P16, GII.P21, and GII.P31 indicated that their effective population sizes increased during the period from 2005 to 2016 and the increase in population size was almost consistent with the collection year of these genotypes. These results suggest that the Pro region of the norovirus GII evolved rapidly, but under no positive selection, with a high genetic divergence, similar to that of the RNA-dependent RNA polymerase (RdRp) region and the VP1 region of noroviruses.

Development and uncertainty analysis of radionuclide atmospheric dispersion modeling codes based on Gaussian plume model

It is necessary to assess the radiological consequences of radioactive leakage accident in the planning and operation of a nuclear power plant, especially an atmospheric radioactive material spill that has a rapid and broad impact on public health. Uncertainty analysis of the assessment results will help to reduce the probability of making mistakes in the emergency response after accident. The Gaussian plume model is the most widely used computational model for atmospheric diffusion assessment. Based on this model, the FORTRAN computer language is used to compile Radionuclides Atmosphere Dispersion Codes (RADC). Calculation results based on RADC are compared with HotSpot Health Physics Codes to verify its calculation accuracy. Based on the Bayesian Markov Chain Monte Carlo method, uncertainty of the Gaussian plume model is analysed, and the influence of observation error on the confidence interval is calculated. The results show that the greater the air concentration of radioactivity, the wider the confidence interval; the observation error has a great impact on the confidence interval. Meanwhile, the small observation error will cause a large change in the width of the confidence interval.

Early stage data-based probabilistic wear life prediction and maintenance interval optimization of driving wheels

This study presents an early stage data-based maintenance strategy of driving wheels that have different life distributions depending upon their location. Wear was predicted under the condition that the shape of the contact surface changes over time by an original method of back calculating degradation over time through the establishment of a basic wear model and a recursive function for wear progression. An accurate wear model was established and verified by an experiment. The variation in the profile of a wear-induced wheel was applied to the wear model. Furthermore, the model was combined with a recursive function and used to obtain the time-series degradation data. Subsequently, the factors which have a major influence on wheel production were analyzed, and a meta-model was configured using the response surface method. The degradation function and parameter distribution were estimated using uncertainty propagation, and the wear life distribution was derived using Bayesian inference and Markov chain Monte Carlo method. The reliability of driving wheels was obtained, and the maintenance interval was optimized under each maintenance conditions. Based on this novel method, the early stage data-based maintenance strategy was achieved, and the result of the wear life prediction was validated using the probability distribution analysis.

Bayesian Estimation of the Shape Parameters of Mcdonald Generalized Beta-Binomial Distribution

The paper explores and establishes a unique Bayesian framework for estimating three shape parameters of the McDonald generalized beta-binomial distribution. The mixture distribution is used in modelling overdispersed binomial data. Foundations of the framework have been enriched by knowledge of Bayesian statistics and Markov Chain Monte Carlo methods. A Metropolis within Gibbs Monte Carlo method to sample from the unknown posterior form of the distribution was used. The shape parameters (α, β and γ) were assigned flat gamma priors to ensure equal probabilities for all the values. McDonald generalized beta-binomial variables were simulated with fixed shape parameters set at (α,β,γ)=(0.5,0.5,0.5) respectively and samples generated were used to estimate the parameters, to evaluate if the method recovers estimates close to the true parameter values. Standard errors were also computed for the simulated data and real data. Further, credible regions and highest probability density intervals (HPD) were computed and their corresponding lengths. To evaluate the marginal posterior samples for every shape parameter generated trace plots presented, their respective correlation plots were also presented and the histograms to show the distributions assumed by every parameter. Bayesian framework provides a direct and flexible method of computation for a mixture distribution whose complexity may pose challenges of integration when using the classical methods of estimation.

Monitoring of velocity changes based on seismic ambient noise: A brief review and perspective

Over the past two decades, the development of the ambient noise cross-correlation technology has spawned the exploration of underground structures. In addition, ambient noise-based monitoring has emerged because of the feasibility of reconstructing the continuous Green’s functions. Investigating the physical properties of a subsurface medium by tracking changes in seismic wave velocity that do not depend on the occurrence of earthquakes or the continuity of artificial sources dramatically increases the possibility of researching the evolution of crustal deformation. In this article, we outline some state-of-the-art techniques for noise-based monitoring, including moving-window cross-spectral analysis, the stretching method, dynamic time wrapping, wavelet cross-spectrum analysis, and a combination of these measurement methods, with either a Bayesian least-squares inversion or the Bayesian Markov chain Monte Carlo method. We briefly state the principles underlying the different methods and their pros and cons. By elaborating on some typical noise-based monitoring applications, we show how this technique can be widely applied in different scenarios and adapted to multiples scales. We list classical applications, such as following earthquake-related co- and postseismic velocity changes, forecasting volcanic eruptions, and tracking external environmental forcing-generated transient changes. By monitoring cases having different targets at different scales, we point out the applicability of this technology for disaster prediction and early warning of small-scale reservoirs, landslides, and so forth. Finally, we conclude with some possible developments of noise-based monitoring at present and summarize some prospective research directions. To improve the temporal and spatial resolution of passive-source noise monitoring, we propose integrating different methods and seismic sources. Further interdisciplinary collaboration is indispensable for comprehensively interpreting the observed changes.

Incorporating Contact Network Uncertainty in Individual Level Models of Infectious Disease using Approximate Bayesian Computation.

Infectious disease transmission between individuals in a heterogeneous population is often best modelled through a contact network. However, such contact network data are often unobserved. Such missing data can be accounted for in a Bayesian data augmented framework using Markov chain Monte Carlo (MCMC). Unfortunately, fitting models in such a framework can be highly computationally intensive. We investigate the fitting of network-based infectious disease models with completely unknown contact networks using approximate Bayesian computation population Monte Carlo (ABC-PMC) methods. This is done in the context of both simulated data, and data from the UK 2001 foot-and-mouth disease epidemic. We show that ABC-PMC is able to obtain reasonable approximations of the underlying infectious disease model with huge savings in computation time when compared to a full Bayesian MCMC analysis.

Insight into the origin of chikungunya virus in Malaysian non-human primates via sequence analysis

Chikungunya virus (CHIKV) is maintained in the sylvatic cycle in West Africa and is transmitted by Aedes mosquito species to monkeys. In 2006, four verified CHIKV isolates were obtained during a survey of arboviruses in monkeys (Macaca fascicularis) in Pahang state, Peninsular Malaysia. RNA was extracted from the CHIKV isolates and used in reverse transcription polymerase chain reactions (RT-PCR) to amplify PCR fragments for sequencing. Nucleic acid primers were designed to generate overlapping PCR fragments that covered the whole viral sequence. A total of 11,238 base pairs (bp) corresponding to open reading frames (ORFs) from our isolates and 47 other registered isolates in the National Center for Biotechnology Information (NCBI) were used to elucidate sequences, amino acids, and phylogenetic relationships and to estimate divergence times by using MEGA 7.0 and the Bayesian Markov chain Monte Carlo method. Phylogenetic analysis revealed that all CHIKV isolates could be classified into the Asian genotype and clustered with Bagan Panchor clades, which are associated with the chikungunya outbreak reported in 2006, with sequence and amino acid similarities of 99.9% and 99.7%, respectively. Minor amino acid differences were found between human and non-human primate isolates. Amino acid analysis showed a unique amino acid at position 221 in the nsP1region, at which a glycine (G) was found only in monkey isolates, whereas arginine (R) was found at the same position only in human isolates. The time to the most recent common ancestor (MRCA) estimation indicated that CHIKV probably started to diverge from human to non-human primates in approximately 2004 in Malaysia. The results suggested that CHIKV in non-human primates probably resulted from the spillover of the virus from humans. The study will be helpful in understanding the movement and evolution of CHIKV in Malaysia and globally.

Semi-parametric dynamic asymmetric Laplace models for tail risk forecasting, incorporating realized measures

This paper extends the joint Value-at-Risk (VaR) and expected shortfall (ES) quantile regression model of Taylor (2019), by incorporating a realized measure to drive the tail risk dynamics, as a potentially more efficient driver than daily returns. Furthermore, we propose and test a new model for the dynamics of the ES component. Both a maximum likelihood and an adaptive Bayesian Markov chain Monte Carlo method are employed for estimation, the properties of which are compared in a simulation study. The results favour the Bayesian approach, which is employed subsequently in a forecasting study of seven financial market indices. The proposed models are compared to a range of parametric, non-parametric and semi-parametric competitors, including GARCH, realized GARCH, the extreme value theory method and the joint VaR and ES models of Taylor (2019), in terms of the accuracy of one-day-ahead VaR and ES forecasts, over a long forecast sample period that includes the global financial crisis in 2007–2008. The results are favorable for the proposed models incorporating a realized measure, especially when employing the sub-sampled realized variance and the sub-sampled realized range.

Optimal Monte Carlo integration on closed manifolds

The worst case integration error in reproducing kernel Hilbert spaces of standard Monte Carlo methods with n random points decays as n^{-1/2}. However, the re-weighting of random points, as exemplified in the Bayesian Monte Carlo method, can sometimes be used to improve the convergence order. This paper contributes general theoretical results for Sobolev spaces on closed Riemannian manifolds, where we verify that such re-weighting yields optimal approximation rates up to a logarithmic factor. We also provide numerical experiments matching the theoretical results for some Sobolev spaces on the sphere {mathbb {S}}^2 and on the Grassmannian manifold {mathcal {G}}_{2,4}. Our theoretical findings also cover function spaces on more general sets such as the unit ball, the cube, and the simplex.

Topological analysis in Monte Carlo simulation for uncertainty propagation

Abstract. This paper proposes and demonstrates improvements for the Monte Carlo simulation for uncertainty propagation (MCUP) method. MCUP is a type of Bayesian Monte Carlo method aimed at input data uncertainty propagation in implicit 3-D geological modeling. In the Monte Carlo process, a series of statistically plausible models is built from the input dataset of which uncertainty is to be propagated to a final probabilistic geological model or uncertainty index model. Significant differences in terms of topology are observed in the plausible model suite that is generated as an intermediary step in MCUP. These differences are interpreted as analogous to population heterogeneity. The source of this heterogeneity is traced to be the non-linear relationship between plausible datasets' variability and plausible model's variability. Non-linearity is shown to mainly arise from the effect of the geometrical rule set on model building which transforms lithological continuous interfaces into discontinuous piecewise ones. Plausible model heterogeneity induces topological heterogeneity and challenges the underlying assumption of homogeneity which global uncertainty estimates rely on. To address this issue, a method for topological analysis applied to the plausible model suite in MCUP is introduced. Boolean topological signatures recording lithological unit adjacency are used as n-dimensional points to be considered individually or clustered using the density-based spatial clustering of applications with noise (DBSCAN) algorithm. The proposed method is tested on two challenging synthetic examples with varying levels of confidence in the structural input data. Results indicate that topological signatures constitute a powerful discriminant to address plausible model heterogeneity. Basic topological signatures appear to be a reliable indicator of the structural behavior of the plausible models and provide useful geological insights. Moreover, ignoring heterogeneity was found to be detrimental to the accuracy and relevance of the probabilistic geological models and uncertainty index models. Highlights. Monte Carlo uncertainty propagation (MCUP) methods often produce topologically distinct plausible models. Plausible models can be differentiated using topological signatures. Topologically similar probabilistic geological models may be obtained through topological signature clustering.

Isolation and phylogenetic analysis of a new Porcine parvovirus strain GD2013 in China

Porcine parvovirus (PPV), a causative agent of an infectious reproductive disorder causing stillbirth, mummification, embryonic death and infertility (SMEDI) syndrome in swine, is a threat to both domestic pigs and wild boars regardless of age and gender. Recent studies found that the observed average substitution rate in the PPV genome was close to those of the RNA viruses and new strains showing serological neutralization activities different from that of the vaccine strain NADL-2 have been reported. These observations have increased the need for the development of new commercial vaccine strains.In this study, a new PPV strain, GD2013, was isolated from Guangdong, China, and its entire genome sequenced. A phylogenetic tree based on the complete coding region of the genomes of 32 PPV strains was constructed using the Bayesian Markov Chain Monte Carlo (MCMC) method. The results showed that strain GD2013 fell into the same phylogenetic cluster as the classical vaccine strains NADL-2 and POVCAP, suggesting a close relationship to the vaccine strains. Multiple sequence alignments and amino acid mutation analyses of the PPV VP2 gene revealed a new amino acid polymorphism site at Thr45 on VP2 that could be used to identify low virulence strains as vaccine candidates. Selective pressure analysis of the NS1 and VP2 genes by calculating the mean rates of non-synonymous substitutions (dN) over synonymous substitutions (dS) implied that both of these genes were under negative selection. Therefore, by using phylogenetic and amino acid mutation analyses, a likely candidate strain suitable for evaluation as an attenuated vaccine strain was identified.

Panchromatic characterisation of accreting black holes in dusty star-forming galaxies

AbstractAlthough AGN do not typically dominate the bolometric emission of dusty star forming galaxies, large AGN fractions (sometimes > 40%) have been observed in various sub-millimeter surveys. These diagnostics have been however mostly based on X-ray counterpart selections and a complete multiwavength census of the fraction of AGN hosts is needed. I will present new advances in the modelling of panchromatic spectral energy distributions (SEDs) of active galactic nuclei (AGN), based on our publicly available code AGNfitter (Calistro-Rivera et al.2016). AGNfitter implements a fully Bayesian Markov Chain Monte Carlo method to fit the spectral energy distributions of AGNs pushing the wavelengths frontiers from the radio to the X-rays. I will present a recent application of AGNfitter on dusty star forming galaxies in the ALESS submillimeter survey to obtain an unbiased multiwavelength characterisation of the nuclear activity buried in dusty star formation. Our method reveals a significantly larger contribution of AGN activity to the emission in these galaxies than previously observed based on X-rays diagnostics. Our method represents a unique tool to potentially characterise an unbiased accretion history of the Universe when applied to larger populations of star-forming galaxies.

Rasch Versus Classical Equating in the Context of Small Sample Sizes

Equating and scaling in the context of small sample exams, such as credentialing exams for highly specialized professions, has received increased attention in recent research. Investigators have proposed a variety of both classical and Rasch-based approaches to the problem. This study attempts to extend past research by (1) directly comparing classical and Rasch techniques of equating exam scores when sample sizes are small (N≤ 100 per exam form) and (2) attempting to pool multiple forms' worth of data to improve estimation in the Rasch framework. We simulated multiple years of a small-sample exam program by resampling from a larger certification exam program's real data. Results showed that combining multiple administrations' worth of data via the Rasch model can lead to more accurate equating compared to classical methods designed to work well in small samples. WINSTEPS-based Rasch methods that used multiple exam forms' data worked better than Bayesian Markov Chain Monte Carlo methods, as the prior distribution used to estimate the item difficulty parameters biased predicted scores when there were difficulty differences between exam forms.

WISDOM project – V. Resolving molecular gas in Keplerian rotation around the supermassive black hole in NGC 0383

ABSTRACT As part of the mm-Wave Interferometric Survey of Dark Object Masses (WISDOM), we present a measurement of the mass of the supermassive black hole (SMBH) in the nearby early-type galaxy NGC 0383 (radio source 3C 031). This measurement is based on Atacama Large Millimeter/sub-millimeter Array (ALMA) cycle 4 and 5 observations of the 12CO(2–1) emission line with a spatial resolution of 58 × 32 pc2 (0.18 arcsec × 0.1 arcsec). This resolution, combined with a channel width of 10 km s−1, allows us to well resolve the radius of the black hole sphere of influence (measured as RSOI = 316 pc = 0.98 arcsec), where we detect a clear Keplerian increase of the rotation velocities. NGC 0383 has a kinematically relaxed, smooth nuclear molecular gas disc with weak ring/spiral features. We forward model the ALMA data cube with the Kinematic Molecular Simulation (KinMS) tool and a Bayesian Markov Chain Monte Carlo method to measure an SMBH mass of (4.2 ± 0.7) × 109 M⊙, a F160W-band stellar mass-to-light ratio that varies from 2.8 ± 0.6 M⊙/L$_{\odot ,\, \mathrm{F160W}}$ in the centre to 2.4 ± 0.3 M⊙$/\rm L_{\odot ,\, \mathrm{F160W}}$ at the outer edge of the disc and a molecular gas velocity dispersion of 8.3 ± 2.1 km s−1(all 3σ uncertainties). We also detect unresolved continuum emission across the full bandwidth, consistent with synchrotron emission from an active galactic nucleus. This work demonstrates that low-J CO emission can resolve gas very close to the SMBH ($\approx 140\, 000$ Schwarzschild radii) and hence that the molecular gas method is highly complimentary to megamaser observations, as it can probe the same emitting material.

A Two-Level Alternating Direction Model for Polytomous Items With Local Dependence

The chiropractic clinical competency examination uses groups of items that are integrated by a common case vignette. The nature of the vignette items violates the assumption of local independence for items nested within a vignette. This study examines via simulation a new algorithmic approach for addressing the local independence violation problem using a two-level alternating directions testlet model. Parameter values for item difficulty, discrimination, test-taker ability, and test-taker secondary abilities associated with a particular testlet are generated and parameter recovery through Markov Chain Monte Carlo Bayesian methods and generalized maximum likelihood estimation methods are compared. To aid with the complex computational efforts, the novel so-called TensorFlow platform is used. Both estimation methods provided satisfactory parameter recovery, although the Bayesian methods were found to be somewhat superior in recovering item discrimination parameters. The practical significance of the results are discussed in relation to obtaining accurate estimates of item, test, ability parameters, and measurement reliability information.

Aging trajectory prediction for lithium-ion batteries via model migration and Bayesian Monte Carlo method

This paper develops a new prediction method for the aging trajectory of lithium-ion batteries with significantly reduced experimental tests. This method is driven by data collected from two types of battery operation modes. The first type is accelerated aging tests that are performed under stress factors, such as overcharging, over-discharging and large current rates, and cover most of the battery lifespan. In the second operation mode, the same kinds of cells are aged at normal speeds to generate a partial aging profile. An accelerated aging model is developed based on the first type of data and is then migrated as a new model to describe the normal-speed aging behavior. Under the framework of Bayesian Monte Carlo algorithms, the new model is parameterized based on the second type of data and is used for prediction of the remaining battery aging trajectory. The proposed prediction method is validated on three types of commercial batteries and also compared with two benchmark algorithms. The sensitivity of results to the number of cycles is investigated for both modes. Illustrative results demonstrate that based on the normal-speed aging data collected in the first 30 cycles, the proposed method can predict the entire aging trajectories (up to 500 cycles) at a root-mean-square error of less than 2.5% for all considered scenarios. When only using the first five-cycle data for model training, such a prediction error is bounded by 5% for aging trajectories of all the tested batteries.