Bayesian Markov Chain Monte Carlo Research Articles

Spatial autoregressive models with unknown heteroskedasticity: A comparison of Bayesian and robust GMM approach

Most of the estimators suggested for the estimation of spatial autoregressive models are generally inconsistent in the presence of an unknown form of heteroskedasticity in the disturbance term. The estimators formulated from the generalized method of moments (GMM) and the Bayesian Markov Chain Monte Carlo (MCMC) frameworks can be robust to unknown forms of heteroskedasticity. In this study, the finite sample properties of the robust GMM estimator are compared with the estimators based on the Bayesian MCMC approach for the spatial autoregressive models with heteroskedasticity of an unknown form. A Monte Carlo simulation study provides evaluation of the performance of the heteroskedasticity robust estimators. Our results indicate that the MLE and the Bayesian estimators impose relatively greater bias on the spatial autoregressive parameter when there is negative spatial dependence in the model. In terms of finite sample efficiency, the Bayesian estimators perform better than the robust GMM estimator. In addition, two empirical applications are provided to evaluate relative performance of heteroskedasticity robust estimators.

Are Central Bankers Inflation Nutters? A Bayesian MCMC Estimator of the Long Memory Parameter in a State Space Model

Several central banks have adopted inflation targets. The implementation of these targets is flexible; the central banks aim to meet the target over the long term but allow inflation to deviate from the target in the short-term in order to avoid unnecessary volatility in the real economy. In this paper, we propose modeling the degree of flexibility using an ARFIMA model. Under the assumption that the central bankers control the long-run inflation rates, the fractional integration order captures the flexibility of the inflation targets. A higher integration order is associated with a more flexible target. Several estimators of the fractional integration order have been proposed in the literature. Grassi and Magistris (2011) show that a state-based maximum likelihood estimator is superior to other estimators, but our simulations show that their finding is over-biased for a nearly non-stationary time series. We resolve this issue by using a Bayesian Monte Carlo Markov Chain (MCMC) estimator. Applying this estimator to inflation from six inflation-targeting countries for the period 1999 M1 to 2013 M3, we find that inflation is integrated of order 0.8 to 0.9 depending on the country. The inflation targets are thus implemented with a high degree of flexibility.

The influence of ignoring secondary structure on divergence time estimates from ribosomal RNA genes

Genes coding for ribosomal RNA molecules (rDNA) are among the most popular markers in molecular phylogenetics and evolution. However, coevolution of sites that code for pairing regions (stems) in the RNA secondary structure can make it challenging to obtain accurate results from such loci. While the influence of ignoring secondary structure on multiple sequence alignment and tree topology has been investigated in numerous studies, its effect on molecular divergence time estimates is still poorly known. Here, I investigate this issue in Bayesian Markov Chain Monte Carlo (BMCMC) and penalized likelihood (PL) frameworks, using empirical datasets from dragonflies (Odonata: Anisoptera) and glass sponges (Porifera: Hexactinellida). My results indicate that highly biased inferences under substitution models that ignore secondary structure only occur if maximum-likelihood estimates of branch lengths are used as input to PL dating, whereas in a BMCMC framework and in PL dating based on Bayesian consensus branch lengths, the effect is far less severe. I conclude that accounting for coevolution of paired sites in molecular dating studies is not as important as previously suggested, as long as the estimates are based on Bayesian consensus branch lengths instead of ML point estimates. This finding is especially relevant for studies where computational limitations do not allow the use of secondary-structure specific substitution models, or where accurate consensus structures cannot be predicted. I also found that the magnitude and direction (over- vs. underestimating node ages) of bias in age estimates when secondary structure is ignored was not distributed randomly across the nodes of the phylogenies, a phenomenon that requires further investigation.

ANCESTRAL CHARACTER ESTIMATION UNDER THE THRESHOLD MODEL FROM QUANTITATIVE GENETICS

Evolutionary biology is a study of life's history on Earth. In researching this history, biologists are often interested in attempting to reconstruct phenotypes for the long extinct ancestors of living species. Various methods have been developed to do this on a phylogeny from the data for extant taxa. In the present article, I introduce a new approach for ancestral character estimation for discretely valued traits. This approach is based on the threshold model from evolutionary quantitative genetics. Under the threshold model, the value exhibited by an individual or species for a discrete character is determined by an underlying, unobserved continuous trait called "liability." In this new method for ancestral state reconstruction, I use Bayesian Markov chain Monte Carlo (MCMC) to sample the liabilities of ancestral and tip species, and the relative positions of two or more thresholds, from their joint posterior probability distribution. Using data simulated under the model, I find that the method has very good performance in ancestral character estimation. Use of the threshold model for ancestral state reconstruction relies on a priori specification of the order of the discrete character states along the liability axis. I test the use of a Bayesian MCMC information theoretic criterion based approach to choose among different hypothesized orderings for the discrete character. Finally, I apply the method to the evolution of feeding mode in centrarchid fishes.

Bayesian rainfall frequency analysis with extreme value using the informative prior distribution

Determination of the frequency and the magnitude of the extreme rainfall events are very important for water resources management and the designs of the hydraulic structures because the extreme rainfall events and the resulting floods usually cause a lot of damage to life and properties of human society. Recently an increase in the occurrence of extreme events due to global warming has been observed all over the world. Therefore, it is required that the conventional rainfall frequency analysis methods may be reconsidered in two ways. Firstly, the conventional probability distributions used in the frequency analysis should be evaluated again whether the probability distribution can represent the effect of the extreme value or not. Also, the uncertainty in the rainfall frequency analysis should be quantified for the flexible water resources management. Therefore, the comparative study with the Gumbel distribution and the GEV(Generalized Extreme Value) distribution are performed to evaluate the efficiency of the GEV distribution in this article. Also, the Bayesian MCMC(Markov Chain Monte Carlo) scheme and the MLE with a quadratic approximation for parameter estimation are compared to show the advantage of the Bayesian MCMC in the aspect of uncertainty analysis. Especially, the informative prior distributions using the additional information are elicited in the process of the Bayesian MCMC.

Time-dependent reliability analysis using Bayesian MCMC on the reduction of reservoir storage by sedimentation

Currently, an operational strategy for the maintenance of reservoirs is an important issue because of the reduction of reservoir storage from sedimentation. However, relatively few studies have addressed the reliability analysis including uncertainty on the decrease of the reservoir storage by the sedimentation. Therefore, it is necessary that the reduction of the reservoir storage by the sedimentation should be assessed by a probabilistic viewpoint because the natural uncertainty is embedded in the process of the sedimentation. The objective of this study is to advance the maintenance procedures, especially the assessment of future reservoir storage, using the time-dependent reliability analysis with the Bayesian approach. The stochastic gamma process is applied to estimate the reduction of the Soyang dam reservoir storage in South Korea. In estimating the parameters of the stochastic gamma process, the Bayesian Markov chain Monte Carlo (MCMC) scheme using the informative prior distribution through the empirical Bayes method is applied. The Metropolis–Hastings algorithm is constructed and its convergence is checked by the various diagnostics. The range of the expected life time of the Soyang dam reservoir by the Bayesian MCMC is estimated from 111 to 172 years at a 5 % significance level. Finally, it is suggested that improving the assessment strategy in this study can provide valuable information to the decision makers who are in charge of the maintenance of a reservoir or a dam.

Realized population change for long‐term monitoring: California spotted owl case study

ABSTRACTThe annual rate of population change (λt) is a good metric for evaluating population performance because it summarizes survival and recruitment rates and can be used for open populations. Another measure of population performance, realized population change (Δt) is an encompassing metric of population trend over a period of time; it is the ratio of population size at an end time period relative to the initial population size. Our first goal was to compare mean λ and Δt as summaries of population change over time. Our second goal was to evaluate different methods for estimating these parameters; specifically we wished to compare the value of estimates from fixed effects models, random effects estimates from mixed effects models, and Bayesian Markov chain Monte Carlo (MCMC) methods. Our final goal was to evaluate the use of the posterior distribution of Δt as a means for estimating the probability of population decline retrospectively. To meet these goals, we used California spotted owl (Strix occidentalis occidentalis) data collected on 3 study areas from 1990 to 2011 as a case study. The estimated MCMC median λs for 2 of the study areas were 0.986 and 0.993, indicating declining populations, whereas median λ was 1.014 for the third study area, indicating an increasing population. For 2 of the study areas, estimated MCMC median Δts over the 18‐year monitoring period were 0.78 and 0.89, suggesting 21% and 11% declines in population size, whereas the third study area was 1.22 suggesting a 22% increase. Results from Δt analyses highlight that small differences in mean λ from 1.0 (stationary) can result in large differences in population size over a longer time period; these temporal effects are better depicted by Δt. Fixed effects, random effects, and MCMC estimates of mean and median λ and of Δt were similar (≤9% relative difference). The estimate of temporal process variance was larger for MCMC than the random effects estimates. Results from a Bayesian approach using MCMC simulations indicated that the probabilities of a ≥15% decline over 18 years were 0.69, 0.40, and 0.04 for the 3 study areas, whereas the probabilities the populations were stationary or increasing were 0.07, 0.22, and 0.82. For retrospective analyses of monitored populations, using Bayesian MCMC methods to generate a posterior distribution of Δt is a valuable conservation and management tool for robustly estimating probabilities of specified declines of interest. © 2013 The Wildlife Society.

Rapid quantification of uncertainty in permeability and porosity of oil reservoirs for enabling predictive simulation

One of the most difficult tasks in subsurface flow simulations is the reliable characterization of properties of the subsurface. A typical situation employs dynamic data integration such as sparse (in space and time) measurements to be matched with simulated responses associated with a set of permeability and porosity fields. Among the challenges found in practice are proper mathematical modeling of the flow, persisting heterogeneity in the porosity and permeability, and the uncertainties inherent in them. In this paper we propose a Bayesian framework Monte Carlo Markov Chain (MCMC) simulation to sample a set of characteristics of the subsurface from the posterior distribution that are conditioned to the production data. This process requires obtaining the simulated responses over many realizations. In reality, this can be a prohibitively expensive endeavor with possibly many proposals rejection, and thus wasting the computational resources. To alleviate it, we employ a two-stage MCMC that includes a screening step of a proposal whose simulated response is obtained via an inexpensive coarse-scale model. A set of numerical examples using a two-phase flow problem in an oil reservoir as a benchmark application is given to illustrate the procedure and its use in predictive simulation.

A Bayesian Monte Carlo Markov Chain Method for Parameter Estimation of Fractional Differenced Gaussian Processes

We present a Bayesian Monte Carlo Markov Chain method to simultaneously estimate the spectral index and power amplitude of a fractional differenced Gaussian process at low frequency, in presence of white noise, and a linear trend and periodic signals. This method provides a sample of the likelihood function and thereby, using Monte Carlo integration, all parameters and their uncertainties are estimated simultaneously. We test this method with simulated and real Global Positioning System height time series and propose it as an alternative to optimization methods currently in use. Furthermore, without any mathematical proof, the results from the simulations suggest that this method is unaffected by the stationary regime and hence, can be used to check whether or not a time series is stationary.

BSEM estimation of network effect and customer orientation empowerment on trust in social media and network environment

This paper presents a stochastic model that identifies network effect and customer orientation empowerment as strong antecedents of trustworthiness and trust in social media network environment. As Trust is emerging as a critical influencer of consumer behavior in organizations, social media has become the facilitator or the enabler of this influence. This paper aims to explore and examine the relationships amongst the antecedents of trust in the context of the social media network environment via Bayesian estimation and testing of the structural equation model. In facilitating the estimation of the stochastic model, a survey was conducted on 255 social media users. A series of statistical analyses were conducted prior to the estimation using Bayesian Markov Chain Monte Carlo (MCMC). Results showed that network effect and customer orientation empowerment were significant predictors of trustworthiness and trust. Bayesian MCMC results confirmed that the findings were consistent with the literature.

Uncertainty analysis on extreme value analysis of significant wave height at eastern coast of Korea

In this study, we considered the problem of estimating long-term predictions of design wave height based on the observation data collected over 10–15 years along the eastern-coast of the Korean peninsula. We adopted a method that combines Bayesian method and extreme value theory. The conventional frequency analysis methods must be reconsidered in two ways. First, the conventional probability distributions used in the frequency analysis should be evaluated to determine whether they can accurately model the variation in extreme values. Second, the uncertainty in the frequency analysis should also be quantified. Therefore, we performed a comparative study of the Gumbel distribution and GEV distribution to show the higher efficiency of the latter. Further, we compared the Bayesian MCMC (Markov Chain Monte Carlo) scheme and the MLE (Maximum Likelihood Estimation) with asymptotic normal approximation for parameter estimation to confirm the advantage of the Bayesian MCMC with respect to uncertainty analysis.

Bayesian Markov Chain Monte Carlo Model for Determining Optimum Tender Price in Multifamily Housing Projects

AbstractThis study presents a strategy model for determining the optimum tender price that reflects appropriate profit and risk contingencies in competitive tendering according to the Bayesian Markov Chain Monte Carlo (BMCMC) model. The BMCMC approach is known to be theoretically optimal for handling tender-price problems. The BMCMC model provides a practical solution that can reflect not only objective information but also subjective experience and knowledge. The BMCMC model allows contractors to estimate the tender price more accurately by reflecting the prior distribution function on key factors. Conclusively, this model was found to improve decision-making processes for setting an optimum tender price. An applied example showed that the proposed methods are feasible.

The estimation of lower refractivity uncertainty from radar sea clutter using the Bayesian—MCMC method

The estimation of lower atmospheric refractivity from radar sea clutter (RFC) is a complicated nonlinear optimization problem. This paper deals with the RFC problem in a Bayesian framework. It uses the unbiased Markov Chain Monte Carlo (MCMC) sampling technique, which can provide accurate posterior probability distributions of the estimated refractivity parameters by using an electromagnetic split-step fast Fourier transform terrain parabolic equation propagation model within a Bayesian inversion framework. In contrast to the global optimization algorithm, the Bayesian—MCMC can obtain not only the approximate solutions, but also the probability distributions of the solutions, that is, uncertainty analyses of solutions. The Bayesian—MCMC algorithm is implemented on the simulation radar sea-clutter data and the real radar sea-clutter data. Reference data are assumed to be simulation data and refractivity profiles are obtained using a helicopter. The inversion algorithm is assessed (i) by comparing the estimated refractivity profiles from the assumed simulation and the helicopter sounding data; (ii) the one-dimensional (1D) and two-dimensional (2D) posterior probability distribution of solutions.

A clustering approach for estimating parameters of a profile hidden Markov model

A Profile Hidden Markov Model (PHMM) is a standard form of a Hidden Markov Models used for modeling protein and DNA sequence families based on multiple alignment. In this paper, we implement Baum-Welch algorithm and the Bayesian Monte Carlo Markov Chain (BMCMC) method for estimating parameters of small artificial PHMM. In order to improve the prediction accuracy of the estimation of the parameters of the PHMM, we classify the training data using the weighted values of sequences in the PHMM then apply an algorithm for estimating parameters of the PHMM. The results show that the BMCMC method performs better than the Maximum Likelihood estimation.

Evaluation of a soil greenhouse gas emission model based on Bayesian inference and MCMC: Model uncertainty

We combined the Bayesian inference and the Markov Chain Monte Carlo (MCMC) technique to quantify uncertainties in the process-based soil greenhouse gas (GHG) emission models. The Metropolis–Hastings sampling was examined by comparing four univariate proposal distributions (UPDs: symmetric/asymmetric uniform and symmetric/asymmetric normal) and one multinormal proposal distribution (MPD). Almost all the posterior parameter ranges from the MPD could be reduced to 1 order of magnitude. The simulation errors in CO2 fluxes were much greater than those in N2O fluxes, which resulted in a greater importance in model structure than in model parameters for CO2 simulations. We suggested deriving the covariance matrix of parameters for MPD from the sampling results of a UPD; and generating a Markov chain by updating a single parameter rather than updating all parameters at each time. The method addressed in this paper can be used to evaluate uncertainties in other GHG emission models.

Assessment of brain glucose metabolism with input function determined from brain PET images by means of Bayesian ICA and MCMC methods

Positron emission tomography (PET) imaging has the capability to produce regional or parametric images of physiological aspects in a tissue of interest. Apart from the acquired PET data, the concentration of the radiotracer supplied to the tissue through the vascularization has to be known as the input function (IF). IF can be obtained by manual or automatic blood sampling and cross calibrated with PET. These procedures are cumbersome, invasive and generate uncertainties. In the present work, we determine IF from internal artery in fluorodeoxyglucose (18F-FDG) brain images by means of Independent Component Analysis (ICA) based on Bayesian theory and Monte Carlo Markov Chain (MCMC) sampling method (BICA, Bayesian ICA). Dynamic brain images were decomposed with BICA into image sequences of blood and tissue components. A region of interest was drawn around the internal artery in the blood image to determine BICA-IF. BICA-IF was therefore corrected for spillover of radioactivity emission from tissue, then it was normalized with three plasma samples to correct for partial volume and blood to plasma radioactivity ratio. BICA-IF was found comparable to IF determined by blood sampling, and rCMRG values in several brain structures obtained with BICA-IF and sampled IF showed a bias of 6.4% which was attributed to the difference in the time sampling of 4s for sampled IF versus 15s for BICA-MC-IF at early times. In conclusion, BICA is a strong approach in image decomposition to extract blood curves in a noninvasive way.

Genetic variability of Hepatitis C Virus in Moroccan population

Hepatitis C virus (HCV) evolution is a highly dynamic process. There is little information about molecular epidemiology of HCV isolates in Morocco, an area known for an intermediate prevalence of HCV infection. The primary aim of this study was to determine the subgenotype distribution of HCV strains in patients with chronic HCV infection in Morocco and an eventual association between HCV subgenotypes and liver cancer. The secondary aim was to estimate the prevalence of amino acid substitutions in the HCV core region in treatment-naive patients from Morocco and an eventual association between amino acid substitutions and liver cancer. Serum samples from a total of 185 anti-HCV positive patients were included in this study (81 males and 104 females). The identification of HCV genotype and subtype was respectively performed by sequencing of the 5’UTR and core regions and phylogenetic analysis of the NS5B region. HCV demographic history was inferred using a Bayesian Monte Carlo Markov chain analysis. Of the 174 patients with detectable viremia, the core and the NS5B regions were amplified in 152 (87.4%) and 141 (81.0%) patients respectively. Phylogenetic analysis based on NS5B region revealed that most HCV strains were classified into subtypes 1b (75.2%) followed by subtypes 2i (19.1%), 2k (2.8%). Subtypes 2a, 1a, and 4a were found in a single patient. HCV subtype 1b had an even higher prevalence in liver cancer cases (84.4% vs 67.5% in chronic hepatitis, P= 0.031). Using a Bayesian approach, the mean date of appearance of the most recent common ancestor was estimated to be 1910 for HCV-1b and 1854 for HCV-2i. Based on core region, mutations at R70Q or L91M were detected in more than one fourth of patients infected with HCV 1b.

Portfolio value-at-risk by Bayesian conditional EVT-copula models: taking an Asian index portfolio for example

Portfolio VaR (Value-at-Risk) is an important but difficult issue in risk management. Traditional approaches deal with single asset and usually fail to accurately estimate the threshold value under given probability level. This study proposed a new model which estimates portfolio VaR (Value-at-Risk) using a Bayesian conditional EVT (extreme value theory)-Copula based approach. First, GJR-GARCH model is used to model the time structure of each asset. Second, EVT is employed for modeling the residuals after GJR-GARCH. This study constructs the semi-parametric empirical marginal CDF (cumulative distribution function) for each residual using a Gaussian kernel estimate for the interior and a generalized Pareto distribution (GPD) estimate for the upper and lower tails. Our approach focuses on the entire distribution rather than the tail distribution only. Finally, a Student’s copula is fitted to the data and used to induce correlation between the simulated residuals of each asset. By using Bayesian MCMC (Markov chain Monte Carlo) to fit the GPD, our estimations do not rely on asymptotics; namely, our estimation gets rid of the influence of limited sample size of extreme events. In order to test the effectiveness of this model we backtest the estimated VaRs over a time period. Empirical results demonstrate that the Bayesian CEVT- Copula based approach outperforms traditional methods such as historical simulation (overestimate) or conditional normal (underestimate) model.

An introduction to generalized linear models—third edition

- Introduces GLMs in a way that enables readers to understand the unifying structure that underpins them. - Discusses common concepts and principles of advanced GLMs, including nominal and ordinal regression, survival analysis, and longitudinal analysis. - Connects Bayesian analysis and MCMC methods to fit GLMs. - Contains numerous examples from business, medicine, engineering, and the social sciences. - Provides the example code for R, Stata, and WinBUGS to encourage implementation of the methods. - Offers the data sets and solutions to the exercises online. Continuing to emphasize numerical and graphical methods, An Introduction to Generalized Linear Models, Third Edition provides a cohesive framework for statistical modeling. This new edition of a bestseller has been updated with Stata, R, and WinBUGS code as well as three new chapters on Bayesian analysis. Like its predecessor, this edition presents the theoretical background of generalized linear models (GLMs) before focusing on methods for analyzing particular kinds of data. It covers normal, Poisson, and binomial distributions; linear regression models; classical estimation and model fitting methods; and frequentist methods of statistical inference. After forming this foundation, the authors explore multiple linear regression, analysis of variance (ANOVA), logistic regression, log-linear models, survival analysis, multilevel modeling, Bayesian models, and Markov chain Monte Carlo (MCMC) methods. Using popular statistical software programs, this concise and accessible text illustrates practical approaches to estimation, model fitting, and model comparisons. It includes examples and exercises with complete data sets for nearly all the models covered.

ASTROMETRY AND RADIAL VELOCITIES OF THE PLANET HOST M DWARF GJ 317: NEW TRIGONOMETRIC DISTANCE, METALLICITY, AND UPPER LIMIT TO THE MASS OF GJ 317b

We have obtained precision astrometry of the planet hosting M dwarf GJ 317 in the framework of the Carnegie Astrometric Planet Search project. The new astrometric measurements give a distance determination of 15.3 pc, 65% further than previous estimates. The resulting absolute magnitudes suggest it is metal rich and more massive than previously assumed. This result strengthens the correlation between high metallicity and the presence of gas giants around low mass stars. At 15.3 pc, the minimal astrometric amplitude for planet candidate GJ 317b is 0.3 milliarcseconds (edge-on orbit), just below our astrometric sensitivity. However, given the relatively large number of observations and good astrometric precision, a Bayesian Monte Carlo Markov Chain analysis indicates that the mass of planet b has to be smaller than twice the minimum mass with a 99% confidence level, with a most likely value of 2.5 Mjup. Additional RV measurements obtained with Keck by the Lick-Carnegie Planet search program confirm the presence of an additional very long period planet candidate, with a period of 20 years or more. Even though such an object will imprint a large astrometric wobble on the star, its curvature is yet not evident in the astrometry. Given high metallicity, and the trend indicating that multiple systems are rich in low mass companions, this system is likely to host additional low mass planets in its habitable zone that can be readily detected with state-of-the-art optical and near infrared RV measurements.