Markov Chain Monte Carlo Estimation Research Articles

Generalized Method of Moments Estimation of Realized Stochastic Volatility Model

The purpose of this paper is to study the generalized method of moments (GMM) estimation procedures of the realized stochastic volatility model; we give the moment conditions for this model and then obtain the estimation of parameters. Then, we apply these moment conditions to the realized stochastic volatility model to improve the volatility prediction effect. This paper selects the Shanghai Composite Index (SSE) as the original data of model research and completes the volatility prediction under a realized stochastic volatility model. Markov chain Monte Carlo (MCMC) estimation and quasi-maximum likelihood (QML) estimation are applied to the parameter estimation of the realized stochastic volatility model to compare with the GMM method. And the volatility prediction accuracy of these three different methods is compared. The results of empirical research show that the effect of model prediction using the parameters obtained by the GMM method is close to that of the MCMC method, and the effect is obviously better than that of the quasi-maximum likelihood estimation method.

ESPRESSO: topological clustering of single-cell transcriptomics data to reveal informative genes for spatio–temporal architectures of cells

BackgroundBioinformatics capability to analyze spatio–temporal dynamics of gene expression is essential in understanding animal development. Animal cells are spatially organized as functional tissues where cellular gene expression data contain information that governs morphogenesis during the developmental process. Although several computational tissue reconstruction methods using transcriptomics data have been proposed, those methods have been ineffective in arranging cells in their correct positions in tissues or organs unless spatial information is explicitly provided.ResultsThis study demonstrates stochastic self-organizing map clustering with Markov chain Monte Carlo calculations for optimizing informative genes effectively reconstruct any spatio–temporal topology of cells from their transcriptome profiles with only a coarse topological guideline. The method, eSPRESSO (enhanced SPatial REconstruction by Stochastic Self-Organizing Map), provides a powerful in silico spatio–temporal tissue reconstruction capability, as confirmed by using human embryonic heart and mouse embryo, brain, embryonic heart, and liver lobule with generally high reproducibility (average max. accuracy = 92.0%), while revealing topologically informative genes, or spatial discriminator genes. Furthermore, eSPRESSO was used for temporal analysis of human pancreatic organoids to infer rational developmental trajectories with several candidate ‘temporal’ discriminator genes responsible for various cell type differentiations.ConclusionseSPRESSO provides a novel strategy for analyzing mechanisms underlying the spatio–temporal formation of cellular organizations.

A sequential exploratory diagnostic model using a Pólya-gamma data augmentation strategy.

Cognitive diagnostic models provide a framework for classifying individuals into latent proficiency classes, also known as attribute profiles. Recent research has examined the implementation of a Pólya-gamma data augmentation strategy binary response model using logistic item response functions within a Bayesian Gibbs sampling procedure. In this paper, we propose a sequential exploratory diagnostic model for ordinal response data using a logit-link parameterization at the category level and extend the Pólya-gamma data augmentation strategy to ordinal response processes. A Gibbs sampling procedure is presented for efficient Markov chain Monte Carlo (MCMC) estimation methods. We provide results from a Monte Carlo study for model performance and present an application of the model.

Longitudinal joint modeling for assessing parallel interactive development of latent ability and processing speed using responses and response times.

To measure the parallel interactive development of latent ability and processing speed using longitudinal item response accuracy (RA) and longitudinal response time (RT) data, we proposed three longitudinal joint modeling approaches from the structural equation modeling perspective, namely unstructured-covariance-matrix-based longitudinal joint modeling, latent growth curve-based longitudinal joint modeling, and autoregressive cross-lagged longitudinal joint modeling. The proposed modeling approaches can not only provide the developmental trajectories of latent ability and processing speed individually, but also exploit the relationship between the change in latent ability and processing speed through the across-time relationships of these two constructs. The results of two empirical studies indicate that (1) all three models are practically applicable and have highly consistent conclusions in terms of the changes in ability and speed in the analysis of the same data set, and (2) additional analysis of the RT data and acquisition of individual processing speed measurements can reveal the parallel interactive development phenomena that are difficult to detect using RA data alone. Furthermore, the results of our simulation study demonstrate that the proposed Bayesian Markov chain Monte Carlo estimation algorithm can ensure accurate model parameter recovery for all three proposed longitudinal joint models. Finally, the implications of our findings are discussed from the research and practice perspectives.

A Bayesian Nonparametric Latent Space Approach to Modeling Evolving Communities in Dynamic Networks

The evolution of communities in dynamic (time-varying) network data is a prominent topic of interest. A popular approach to understanding these dynamic networks is to embed the dyadic relations into a latent metric space. While methods for clustering with this approach exist for dynamic networks, they all assume a static community structure. This paper presents a Bayesian nonparametric model for dynamic networks that can model networks with evolving community structures. Our model extends existing latent space approaches by explicitly modeling the additions, deletions, splits, and mergers of groups with a hierarchical Dirichlet process hidden Markov model. Our proposed approach, the hierarchical Dirichlet process latent position cluster model (HDP-LPCM), incorporates transitivity, models both individual and group level aspects of the data, and avoids the computationally expensive selection of the number of groups required by most popular methods. We provide a Markov chain Monte Carlo estimation algorithm and demonstrate its ability to detect evolving community structure in a network of military alliances during the Cold War and a narrative network constructed from the Game of Thrones television series.

An empirical analysis of participation in international environmental agreements

This study investigates the determinants of participation in environmental agreements, with a special focus on lobbying and regional agreements. To this end, we collated the largest ratification dataset in the literature and identified all countries eligible for membership in each agreement. This feature allows to correct the identification bias associated with the misidentification of the risk set when regional agreements are included in the regression sample. We also improve the treatment of unobserved heterogeneity by using a multilevel survival approach and Markov Chain Monte Carlo (MCMC) estimator. Overall, we find that countries’ participation choices are interrelated and primarily driven by the agreements’ characteristics. Our findings indicate that regional agreements are two and half times more likely to be ratified than global agreements and that environmental lobbying positively affects participation in environmental agreements, while the effect of industrial lobbying is statistically insignificant. This result is robust to changes in specification and proxies used. Our results motivate several policy suggestions. We emphasise regional agreements’ capacity to deliver higher participation than global agreements and the importance of securing the early ratification of key players.

Dependence Modelling of Lifetimes in Egyptian Families

In this study, we analyse a large sample of Egyptian social pension data which covers, by law, the policyholder’s spouse, children, parents and siblings. This data set uniquely enables the study and comparison of pairwise dependence between multiple familial relationships beyond the well-known husband and wife case. Applying Bayesian Markov Chain Monte Carlo (MCMC) estimation techniques with the two-step inference functions for margins (IFM) method, we model dependence between lifetimes in spousal, parent–child and child–parent relationships, using copulas to capture the strength of association. Dependence is observed to be strongest in child–parent relationships and, in comparison to the high-income countries of data sets previously studied, of lesser significance in the husband and wife case, often referred to as broken-heart syndrome. Given the traditional use of UK mortality tables in the modelling of mortality in Egypt, the findings of this paper will help to inform appropriate mortality assumptions specific to the unique structure of the Egyptian scheme.

Lindley procedure and MCMC technique in Bayesian estimation for Kumaraswamy Weibull distribution

In this study, a comparison between three methods for estimating unknown parameters of the Kumaraswamy Weibull distribution for different sample sizes of type II censoring data is presented. Specifically, we compare the behaviors of maximum likelihood estimates, Lindley and Markov chain Monte Carlo (MCMC) estimates as Bayesian estimates. We have not found any work on this topic after reviews of the literature except one with little information about the inference of this important distribution. The simplest form for Lindley approximation of the posterior mean is proposed and approximate closed forms of acceptable Bayes estimates for the models of multi-parameters such as Kumaraswamy Weibull distribution is derived. A Monte Carlo simulation is conducted to investigate the performances of the proposed estimators. Finally, three real data examples are analyzed to illustrate the application possibility of the different proposed estimation methods. The results reveal that, although, good performance of the approximate forms of Lindley estimators, the estimators resulting in the MCMC technique are better in the sense of the mean squared errors.

Genome-Wide Association with Uncertainty in the Genetic Similarity Matrix.

Genome-wide association studies (GWASs) are often confounded by population stratification and structure. Linear mixed models (LMMs) are a powerful class of methods for uncovering genetic effects, while controlling for such confounding. LMMs include random effects for a genetic similarity matrix, and they assume that a true genetic similarity matrix is known. However, uncertainty about the phylogenetic structure of a study population may degrade the quality of LMM results. This may happen in bacterial studies in which the number of samples or loci is small, or in studies with low-quality genotyping. In this study, we develop methods for linear mixed models in which the genetic similarity matrix is unknown and is derived from Markov chain Monte Carlo estimates of the phylogeny. We apply our model to a GWAS of multidrug resistance in tuberculosis, and illustrate our methods on simulated data.

Implicit Copula Variational Inference

Key to effective generic, or “black-box,” variational inference is the selection of an approximation to the target density that balances accuracy and speed. Copula models are promising options, but calibration of the approximation can be slow for some choices. Smith, Loaiza-Maya, and Nott (2020) suggest using tractable and scalable “implicit copula” models that are formed by element-wise transformation of the target parameters. We propose an adjustment to these transformations that make the approximation invariant to the scale and location of the target density. We also show how a sub-class of elliptical copulas have a generative representation that allows easy application of the re-parameterization trick and efficient first order optimization. We demonstrate the estimation methodology using two statistical models as examples. The first is a mixed effects logistic regression, and the second is a regularized correlation matrix. For the latter, standard Markov chain Monte Carlo estimation methods can be slow or difficult to implement, yet our proposed variational approach provides an effective and scalable estimator. We illustrate by estimating a regularized Gaussian copula model for income inequality in U.S. states between 1917 and 2018. An Online Appendix and MATLAB code to implement the method are available as supplementary materials.

A Bayesian Pipe Failure Prediction for Optimizing Pipe Renewal Time in Water Distribution Networks

The sustainable management of the water supply system requires methodologies to monitor, repair, or replace the aging infrastructure, but more importantly, it must be able to assess the condition of the networks and predict their behavior over time. Among other infrastructure systems, the water distribution network is one of the essential civil infrastructure systems; therefore, the effective maintenance and renewal of the infrastructure’s physical assets are essential. This article aims to determine pipe failure prediction to optimize pipe renewal time. This research methodology investigates the most appropriate parameters for predicting pipe failure in the optimization. In particular, the non-homogeneous Poisson process (NHPP) with the Markov chain Monte Carlo (MCMC) approach is presented for Bayesian inference, while maximum likelihood (ML) is applied for frequentist inference as a comparison method. It is concluded that the two estimations are relatively appropriate for predicting failures, but MCMC estimation is closer to the total observed data. Based on life-cycle cost (LCC) analysis, the MCMC estimation generates flatter LCC curves and lower LCC values than the ML estimation, which affects the decision making of optimum pipe renewal in water distribution networks.

Bayesian inference in spatial GARCH models: an application to US house price returns

ABSTRACT In this paper we consider a high-order spatial generalized autoregressive conditional heteroskedasticity (GARCH) model to account for the volatility clustering patterns observed over space. The model consists of a log-volatility equation that includes the high-order spatial lags of the log-volatility term and the squared outcome variable. We use a transformation approach to turn the model into a mixture of normals model, and then introduce a Bayesian Markov chain Monte Carlo (MCMC) estimation approach coupled with a data-augmentation technique. Our simulation results show that the Bayesian estimator has good finite sample properties. We apply a first-order version of the spatial GARCH model to US house price returns at the metropolitan statistical area level over the period 2006Q1–2013Q4 and show that there is significant variation in the log-volatility estimates over space in each period.

Radar analysis algorithm for determining meteor head echo parameter probability distributions

ABSTRACT We present an automated radar data analysis algorithm developed to calculate probability distributions of meteor- and meteoroid parameters for head echoes detected with the Middle and Upper atmosphere (MU) radar in Shigaraki, Japan. The algorithm utilizes direct Monte Carlo simulations of uncertainties, with Bayesian Markov-chain Monte Carlo estimation of meteor model parameters and N-body propagation of distributions to perform orbit determination. The implementation has been validated using raw data simulations and a comparison with previous analysis methods. The concepts are applicable on a wide range of possible head echo measurements with other radar systems. The generated probability distributions provide quantitative reliability, which enables improved statistical studies and investigating the origins of detected meteoroids. The methodology section is highly detailed in order for the methods to be reproducible and provide a solid reference foundation for future studies. One such study is presented in a companion paper called ‘High-altitude meteors detected by the interferometric MU radar’.

Modeling Rapid Guessing Behaviors in Computer-Based Testlet Items.

In traditional test models, test items are independent, and test-takers slowly and thoughtfully respond to each test item. However, some test items have a common stimulus (dependent test items in a testlet), and sometimes test-takers lack motivation, knowledge, or time (speededness), so they perform rapid guessing (RG). Ignoring the dependence in responses to testlet items can negatively bias standard errors of measurement, and ignoring RG by fitting a simpler item response theory (IRT) model can bias the results. Because computer-based testing captures response times on testlet responses, we propose a mixture testlet IRT model with item responses and response time to model RG behaviors in computer-based testlet items. Two simulation studies with Markov chain Monte Carlo estimation using the JAGS program showed (a) good recovery of the item and person parameters in this new model and (b) the harmful consequences of ignoring RG (biased parameter estimates: overestimated item difficulties, underestimated time intensities, underestimated respondent latent speed parameters, and overestimated precision of respondent latent estimates). The application of IRT models with and without RG to data from a computer-based language test showed parameter differences resembling those in the simulations.

Cross-sector comovements and policy impact in the COVID-19 stock market: A dynamic factor approach

This study investigates the remarkable comovements in U.S. equity returns during the COVID-19 pandemic. It constructs a dynamic factor model (DFM) to illuminate the sources of the comovements and their implications. Using the Markov Chain Monte Carlo (MCMC) estimation method, the study finds that the comovements had a weak daily oscillation pattern during the pandemic. With that pattern, the study also finds significant monetary policy effects on the equity returns of several key sectors. In addition, it estimates the impact of news shocks, including monetary policy news, fiscal stimulus news, and unemployment news, on cross-sector equity returns. For any given sector, the conventional and unconventional monetary policy news shocked the sector in opposite directions. Among the positive monetary news shocks, the strongest were from interest rate policy surprises. Conversely, fiscal stimulus news had the most substantial positive impact and triggered all sectors to rebound from the bear market at the end of March 2020. Furthermore, by applying Natural Language Processing (NLP) sentiment analysis, this study sheds light on the positive correlation between comovements and news sentiment.

Rater characteristics, response content, and scoring contexts: Decomposing the determinates of scoring accuracy.

Raters may introduce construct-irrelevant variance when evaluating written responses to performance assessments, threatening the validity of students’ scores. Numerous factors in the rating process, including the content of students’ responses, the characteristics of raters, and the context in which the scoring occurs, are thought to influence the quality of raters’ scores. Despite considerable study of rater effects, little research has examined the relative impacts of the factors that influence rater accuracy. In practice, such integrated examinations are needed to afford evidence-based decisions of rater selection, training, and feedback. This study provides the first naturalistic, integrated examination of rater accuracy in a large-scale assessment program. Leveraging rater monitoring data from an English language arts (ELA) summative assessment program, I specified cross-classified, multilevel models via Bayesian (i.e., Markov chain Monte Carlo) estimation to decompose the impact of response content, rater characteristics, and scoring contexts on rater accuracy. Results showed relatively little variation in accuracy attributable to teams, items, and raters. Raters did not collectively exhibit differential accuracy over time, though there was significant variation in individual rater’s scoring accuracy from response to response and day to day. I found considerable variation in accuracy across responses, which was in part explained by text features and other measures of response content that influenced scoring difficulty. Some text features differentially influenced the difficulty of scoring research and writing content. Multiple measures of raters’ qualification performance predicted their scoring accuracy, but general rater background characteristics including experience and education did not. Site-based and remote raters demonstrated comparable accuracy, while evening-shift raters were slightly less accurate, on average, than day-shift raters. This naturalistic, integrated examination of rater accuracy extends previous research and provides implications for rater recruitment, training, monitoring, and feedback to improve human evaluation of written responses.

Interrater reliability for multilevel data: A generalizability theory approach.

Current interrater reliability (IRR) coefficients ignore the nested structure of multilevel observational data, resulting in biased estimates of both subject- and cluster-level IRR. We used generalizability theory to provide a conceptualization and estimation method for IRR of continuous multilevel observational data. We explain how generalizability theory decomposes the variance of multilevel observational data into subject-, cluster-, and rater-related components, which can be estimated using Markov chain Monte Carlo (MCMC) estimation. We explain how IRR coefficients for each level can be derived from these variance components, and how they can be estimated as intraclass correlation coefficients (ICC). We assessed the quality of MCMC point and interval estimates with a simulation study, and showed that small numbers of raters were the main source of bias and inefficiency of the ICCs. In a follow-up simulation, we showed that a planned missing data design can diminish most estimation difficulties in these conditions, yielding a useful approach to estimating multilevel interrater reliability for most social and behavioral research. We illustrated the method using data on student-teacher relationships. All software code and data used for this article is available on the Open Science Framework: https://osf.io/bwk5t/. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Modeling the evolution of competitive market structure via competitive group dynamics

PurposeThis paper aims to examine the evolution of a competitive market structure over time through the lens of competitive group membership dynamics.Design/methodology/approachA new hidden Markov modeling approach is devised that accounts for the three sources of competitive heterogeneity involving managerial strategy, corporate performance and the impact of strategy on performance. In addition, some observed “entry” and “exit” states are considered to model firms’ entry into and exit from the market. The proposed model is illustrated with an investigation of the US banking industry based on a data set created from the COMPUSTAT database. This paper estimated the model within the Bayesian framework and devised a reversible jump Markov chain Monte Carlo estimation procedure to determine the number of latent competitive groups and uncover the characteristics of each group.FindingsThis paper shows that the US banking industry, contrary to the prior findings of having a relatively stable structure, has, in fact, gone through dramatic changes in the past number of decades.Originality/valueContrary to prior work that has primarily focused on managerial strategy to study market evolutions, the competitive groups perspective accounts for all three sources of intra-industry competitive heterogeneity. In addition, unlike prior research, the analysis is not limited to firms remaining in the panel of study for the entire observation period. Such limitation results in missing the various changes that occur in the competitive market structure because of the new entrants or the struggling firms that do not survive in the market.

Bayesian Inference of Seismogenic Stress for the 2016 Mw 7.8 Kaikōura, New Zealand, Earthquake

ABSTRACT We use a Bayesian Markov chain Monte Carlo estimation strategy to estimate the state of pre-earthquake stress from eight published coseismic slip models (CSMs) of the 2016 Mw 7.8 Kaikōura, New Zealand, earthquake. Our estimation relies on the Wallace–Bott assumption, which equates the direction of slip and the orientation of maximum shear stress along a fault plane, and is analogous to methods that infer stress from focal mechanisms. We infer the orientations and relative magnitudes of the principal components of tensorial stress preceding the 2016 Mw 7.8 Kaikōura, New Zealand, earthquake as stress posterior probability density functions (PDFs). We find that the orientations of the principal stresses are well resolved, with weaker to no resolution of the relative magnitudes of the principal stresses. We form a nonmutually exclusive composite posterior PDF as an aggregate of the individual posterior PDFs estimated from each CSM, which allows for the true coseismic slip to be included in any or all of the CSMs. We find that the Kaikōura earthquake can be described by a homogeneous pre-earthquake tensorial stress, despite the complex pattern of slip on multiple fault segments. This state of crustal stress is best represented by an Andersonian thrust regime with a west-northwest–east-southeast trending, horizontal most compressive stress. In addition to describing the state of pre-earthquake stress, the nonmutually exclusive composite posterior PDF allows for the evaluation of the mechanical consistency of the features within CSMs, both individually and as an ensemble. The estimated stress posteriors allow for testing of the CSMs for consistency with known slip mechanisms on the Hope fault, as well as arbitration between differences in inferred slip presented by the CSMs.

Content and computing outline of two undergraduate Bayesian courses: Tools, examples, and recommendations

Undergraduate Bayesian education is an area that has started getting attention lately. As many educational innovations and articles are published and increasingly more teaching and learning materials are shared, statistics educators might be interested in incorporating Bayesian statistics in their undergraduate statistics and data science curriculum. In this paper, we share a succinct overview of two undergraduate Bayesian courses we have been teaching, with a comparison analysis to present the similarities and differences in our approaches. We dive deeper into various choices of Markov chain Monte Carlo estimation methods of Bayesian models with a working example and discuss their pros and cons for different learning objectives of computing that aspiring Bayesian educators might have in mind. Furthermore, we share challenges and opportunities for course development and curriculum design. The paper is suitable for aspiring Bayesian educators who are interested in learning ways to introduce Bayesian statistics to undergraduate students.