MCMC Estimation Research Articles

Occupied with classification: Which occupational classification scheme better predicts health outcomes?

Health inequalities continue to grow despite continuous policy intervention. Work, one domain of health inequalities, is often included as a component of social class rather than as a determinant in its own right. Many social class classifications are derived from occupation types, but there are other components within them that mean they may not be useful as proxies for occupation. This paper develops the exposome, a life-course exposure model developed by Wild (2005), into the worksome, allowing for the explicit consideration of both physical and psychosocial exposures and effects derived from work and working conditions. The interactions between and within temporal and geographical scales are strongly emphasised, and the interwoven nature of both psychosocial and physical exposures is highlighted. Individuals within an occupational type can be both affected by and effect upon occupation level characteristics and health measures. By using the worksome, occupation types are separated from value-laden social classifications. This paper will empirically examine whether occupation better predicts health measures from the European Working Conditions Survey (EWCS). Logistic regression models using Bayesian MCMC estimation were run for each classification system, for each health measure. Health measures included, for example, whether the respondent felt their work affected their health, their self-rated health, pain in upper or lower limbs, and headaches. Using the Deviance Information Criterion (DIC), a measure of predictive accuracy penalised for model complexity, the models were assessed against one another. The DIC shows empirically which classification system is most suitable for use in modelling. The 2-digit International Standard Classification of Occupations showed the best predictive accuracy for all measures. Therefore, examining the relationship between health and work should be done with classifications specific to occupation or industry rather than socio-economic class classifications. This justifies the worksome, allowing for a conceptual framework to link many forms of work-health research.

Gene selection for microarray gene expression classification using Bayesian Lasso quantile regression

Gene selection has been proven to be an effective way to improve the results of many classification methods. However, existing gene selection techniques in binary classification regression are sensitive to outliers of the data, heteroskedasticity or other anomalies of the latent response. In this paper, we propose a new Bayesian hierarchical model to overcome these problems in a relatively straightforward way. In particular, we propose a new Bayesian Lasso method that employs a skewed Laplace distribution for the errors and a scaled mixture of uniform distribution for the regression parameters, together with Bayesian MCMC estimation. Comprehensive comparisons between our proposed gene selection method and other competitor methods are performed experimentally, depending on four benchmark gene expression datasets. The experimental results prove that the proposed method is very effective for selecting the most relevant genes with high classification accuracy.

Bayesian Analysis of Realized Matrix-Exponential GARCH Models

The paper develops a new realized matrix-exponential GARCH (MEGARCH) model, which uses the information of returns and realized measure of co-volatility matrix simultaneously. The paper also considers an alternative multivariate asymmetric function to develop news impact curves. We consider Bayesian MCMC estimation to allow non-normal posterior distributions. For three US financial assets, we compare the realized MEGARCH models with existing multivariate GARCH class models. The empirical results indicate that the realized MEGARCH models outperform the other models regarding in-sample and out-of-sample performance. The news impact curves based on the posterior densities provide reasonable results.

Threshold stochastic volatility: Properties and forecasting

We analyze the ability of Threshold Stochastic Volatility (TSV) models to represent and forecast asymmetric volatilities. First, we derive the statistical properties of TSV models. Second, we demonstrate the good finite sample properties of a MCMC estimator, implemented in the software package WinBUGS, when estimating the parameters of a general specification, denoted CTSV, that nests the TSV and asymmetric autoregressive stochastic volatility (A-ARSV) models. The MCMC estimator also discriminates between the two specifications and allows us to obtain volatility forecasts. Third, we analyze daily S&P 500 and FTSE 100 returns and show that the estimated CTSV model implies plug-in moments that are slightly closer to the observed sample moments than those implied by other nested specifications. Furthermore, different asymmetric specifications generate rather different European options prices. Finally, although none of the models clearly emerge as best out-of-sample, it seems that including both threshold variables and correlated errors may be a good compromise.

Efficient orbit-aware triad and quad census in directed and undirected graphs

The prevalence of select substructures is an indicator of network effects in applications such as social network analysis and systems biology. Moreover, subgraph statistics are pervasive in stochastic network models, and they need to be assessed repeatedly in MCMC sampling and estimation algorithms. We present a new approach to count all induced and non-induced four-node subgraphs (the quad census) on a per-node and per-edge basis, complete with a separation into their non-automorphic roles in these subgraphs. It is the first approach to do so in a unified manner, and is based on only a clique-listing subroutine. Computational experiments indicate that, despite its simplicity, the approach outperforms previous, less general approaches.By way of the more presentable triad census, we additionally show how to extend the quad census to directed graphs. As a byproduct we obtain the asymptotically fastest triad census algorithm to date.

Bayesian confirmatory analysis of multiple response data

This paper proposes a Bayesian confirmatory factor-analytic probit model to reveal the latent utility structure of multiple response data commonly found in marketing surveys. It conditions model formulation on previous knowledge and imposes a parsimonious hierarchical structure involving a measurement model (to define common factors) and a structural model to explain brand choice. The confirmatory model offers some advantages over exploratory models applied to multiple response survey data. First, the model improves model identification and prediction by imposing a simpler structure that accounts for data dependencies without assuming a multivariate distribution. Secondly, using MCMC estimation, the model can easily accommodate many underlying dimensions (J) in the data, which has been challenging to address with other approaches. Lastly, the confirmatory approach offers a practical framework where the analyst has control over the specification of the latent structure of the data via informative priors. This study uniquely applies the model to test and ‘confirm’ previous knowledge and managerial hypotheses about market structures, and how brands are related and compete with one another. The study applies a fully Bayesian estimation and model choice strategy and includes a cross-validatory demarcation between test and validation sub-samples.

Simple confidence intervals for MCMC without CLTs

This short note argues that 95% confidence intervals for MCMC estimates can be obtained even without establishing a CLT, by multiplying their widths by 2.3.

On the Calibration of the 3/2 Model

We consider the problem of calibrating the 3/2 stochastic volatility model to option data. In comparison to the characteristic function of the Heston model, the characteristic function of the 3/2 model can be up to 50 times slower to evaluate. This makes the standard least squares calibration with finite-difference gradients unreasonably slow. To address this problem we derive the analytic gradient of the characteristic function in compact form. We then propose a computational method for the analytic gradient formula which caches intermediate results across the partial derivatives, in addition to the strike dimension and the maturity dimension. Compared to the fastest method of calibrating the 3/2 model which we could find in the literature, the method proposed in this paper is more than 10 times faster. We also discuss the issue of non-convexity in the least squares calibration of the 3/2 model for market data. To tackle it, we propose a regularized calibration where the regularization point is obtained using risk neutral MCMC estimation of the model. We find that this approach is particularly well suited for the calibration problem as it generates naturally a consistent damping matrix for the parameter estimates, in addition to being very fast.

Equation-solving estimator based on Metropolis-Hastings algorithm with delayed rejection

ABSTRACTNumerous works have recently attempted to develop more efficient estimators for MCMC inference than classical ones. In this perspective and approximate nonstandard discrete distributions, Liang and Liu proposed the equation solving estimator as an alternative to the conventional frequency estimator. The specific MCMC method used is the Metropolis-Hastings (M-H) algorithm. In this work, we propose to adapt the equation-solving estimator to the context of simulation using the Metropolis-Hastings algorithm with delayed rejection (MHDR). Developed originally by Mira, this algorithm is considered an improved version of the standard M-H sampler which aims to reduce the variance of MCMC estimators. An application to a Bayesian hypothesis test problem shows the superiority of the equation-solving estimator, based on MHDR sampling, over the one introduced by Liang and Liu.

Alternative Formulations of the Leverage Effect in a Stochastic Volatility Model with Asymmetric Heavy-Tailed Errors

This paper investigates three formulations of the leverage effect in a stochastic volatility model with a skewed and heavy-tailed observation distribu- tion. The first formulation is the conventional one, where the observation and evo- lution errors are correlated. The second is a hierarchical one, where log-volatility depends on the past log-return multiplied by a time-varying latent coefficient. In the third formulation, this coefficient is replaced by a constant. The three models are compared with each other and with a GARCH formulation, using Bayes fac- tors. MCMC estimation relies on a parametric proposal density estimated from the output of a particle smoother. The results, obtained with recent S&P500 and Swiss Market Index data, suggest that the last two leverage formulations strongly dominate the conventional one. The performance of the MCMC method is consis- tent across models and sample sizes, and its implementation only requires a very modest (and constant) number of filter and smoother particles.

Discrete-Time Arbitrage-Free Nelson-Siegel Term Structure Model and Application

We characterize the discrete-time arbitrage-free Nelson-Siegel term structure model, prove the uniqueness of the solution for model identification, make specification analysis on its canonical form, and detail the MCMC estimation method with a fast and reliable prior extraction step. Using the model, we examine how the yield curves of U.S. and China react to exchange rate policy shocks from China in its gradual reform to a more flexible exchange rate regime. Model decomposition reveals that, in U.S. yield responses, changes in risk premia for medium- to long-term yields dominate changes in yield expectation for short- to medium-term yields. The results are helpful to diagnosing market sentiment and exchange rate risk pricing as China further internationalizes its currency.

Estimation of evolutionary parameters using short, random and partial sequences from mixed samples of anonymous individuals.

BackgroundOver the last decade, next generation sequencing (NGS) has become widely available, and is now the sequencing technology of choice for most researchers. Nonetheless, NGS presents a challenge for the evolutionary biologists who wish to estimate evolutionary genetic parameters from a mixed sample of unlabelled or untagged individuals, especially when the reconstruction of full length haplotypes can be unreliable. We propose two novel approaches, least squares estimation (LS) and Approximate Bayesian Computation Markov chain Monte Carlo estimation (ABC-MCMC), to infer evolutionary genetic parameters from a collection of short-read sequences obtained from a mixed sample of anonymous DNA using the frequencies of nucleotides at each site only without reconstructing the full-length alignment nor the phylogeny.ResultsWe used simulations to evaluate the performance of these algorithms, and our results demonstrate that LS performs poorly because bootstrap 95 % Confidence Intervals (CIs) tend to under- or over-estimate the true values of the parameters. In contrast, ABC-MCMC 95 % Highest Posterior Density (HPD) intervals recovered from ABC-MCMC enclosed the true parameter values with a rate approximately equivalent to that obtained using BEAST, a program that implements a Bayesian MCMC estimation of evolutionary parameters using full-length sequences. Because there is a loss of information with the use of sitewise nucleotide frequencies alone, the ABC-MCMC 95 % HPDs are larger than those obtained by BEAST.ConclusionWe propose two novel algorithms to estimate evolutionary genetic parameters based on the proportion of each nucleotide. The LS method cannot be recommended as a standalone method for evolutionary parameter estimation. On the other hand, parameters recovered by ABC-MCMC are comparable to those obtained using BEAST, but with larger 95 % HPDs. One major advantage of ABC-MCMC is that computational time scales linearly with the number of short-read sequences, and is independent of the number of full-length sequences in the original data. This allows us to perform the analysis on NGS datasets with large numbers of short read fragments. The source code for ABC-MCMC is available at https://github.com/stevenhwu/SF-ABC.

Some remarks on MCMC estimation of spectra of integral operators

We prove a law of large numbers for empirical approximations of the spectrum of a kernel integral operator by the spectrum of random matrices based on a sample drawn from a Markov chain, which complements the results by V. Koltchinskii and E. Gin\'{e} for i.i.d. sequences. In a special case of Mercer's kernels and geometrically ergodic chains, we also provide exponential inequalities, quantifying the speed of convergence.

Revisiting the 4-Parameter Item Response Model: Bayesian Estimation and Application.

There has been renewed interest in Barton and Lord's (An upper asymptote for the three-parameter logistic item response model (Tech. Rep. No. 80-20). Educational Testing Service, 1981) four-parameter item response model. This paper presents a Bayesian formulation that extends Béguin and Glas (MCMC estimation and some model fit analysis of multidimensional IRT models. Psychometrika, 66 (4):541-561, 2001) and proposes a model for the four-parameter normal ogive (4PNO) model. Monte Carlo evidence is presented concerning the accuracy of parameter recovery. The simulation results support the use of less informative uniform priors for the lower and upper asymptotes, which is an advantage to prior research. Monte Carlo results provide some support for using the deviance information criterion and [Formula: see text] index to choose among models with two, three, and four parameters. The 4PNO is applied to 7491 adolescents' responses to a bullying scale collected under the 2005-2006 Health Behavior in School-Aged Children study. The results support the value of the 4PNO to estimate lower and upper asymptotes in large-scale surveys.

Bayesian Estimation of Time-Changed Default Intensity Models

We estimate a reduced-form model of credit risk that incorporates stochastic volatility in default intensity via stochastic time-change. Our Bayesian MCMC estimation method overcomes nonlinearity in the measurement equation and state-dependent volatility in the state equation. We implement on firm-level time-series of CDS spreads, and find strong in-sample evidence of stochastic volatility in this market. Relative to the widely-used CIR model for the default intensity, we find that stochastic time-change offers modest benefit in fitting the cross-section of CDS spreads at each point in time, but very large improvements in fitting the time-series, i.e., in bringing agreement between the moments of the default intensity and the model-implied moments. Finally, we obtain model-implied out-of-sample density forecasts via auxiliary particle filter, and find that the time-changed model strongly outperforms the baseline CIR model.

Bayesian Estimation of Time-Changed Default Intensity Models

We estimate a reduced-form model of credit risk that incorporates stochastic volatility in default intensity via stochastic time-change. Our Bayesian MCMC estimation method overcomes nonlinearity in the measurement equation and state-dependent volatility in the state equation. We implement on firm-level time-series of CDS spreads, and find strong in-sample evidence of stochastic volatility in this market. Relative to the widely used CIR model for the default intensity, we find that stochastic time-change offers modest benefit in fitting the cross-section of CDS spreads at each point in time, but very large improvements in fitting the time-series, i.e., in bringing agreement between the moments of the default intensity and the model-implied moments. Finally, we obtain model-implied out-of-sample density forecasts via auxiliary particle filter, and find that the time-changed model strongly outperforms the baseline CIR model.

Estimating Stochastic Volatility and Jumps Using High-Frequency Data and Bayesian Methods

We are comparing two approaches for stochastic volatility and jumps estimation in the EUR/USD time series - the non-parametric power-variation approach using high-frequency returns, and the parametric Bayesian approach (MCMC estimation of SVJD models) using daily returns. We find that both of the methods do identify continuous stochastic volatility similarly, but they do not identify similarly the jump component. Firstly - the jumps estimated using the non-parametric high-frequency estimators are much more numerous than in the case of the Bayesian method using daily data. More importantly - we find that the probabilities of jump occurrences assigned to every day by both of the methods are virtually no rank-correlated (Spearman rank correlation is 0.0148) meaning that the two methods do not identify jumps at the same days. Actually the jump probabilities inferred using the non-parametric approach are not much correlated even with the daily realized variance and the daily squared returns, indicating that the discontinuous price changes (jumps) observed on high-frequencies may not be distinguishable (from the continuous volatility) on the daily frequency. As an additional result we find strong evidence for jump size dependence and jump clustering (based on the self-exciting Hawkes process) of the jumps identified using the non-parametric method (the shrinkage estimator).

Bayesian procedures as a numerical tool for the estimation of an intertemporal discrete choice model

Discrete choice models usually require a general specification of unobserved heterogeneity. In this paper, we apply Bayesian procedures as a numerical tool for the estimation of a female labor supply model based on a sample size that is typical for common household panels. We provide two important results for the practitioner: First, for a specification with a multivariate normal distribution for the unobserved heterogeneity, the Bayesian MCMC estimator yields almost identical results as a classical maximum simulated likelihood (MSL) estimator. Second, we show that when imposing distributional assumptions that are consistent with economic theory, e.g., log-normally distributed consumption preferences, the Bayesian method performs well and provides reasonable estimates, while the MSL estimator does not converge. These results indicate that Bayesian procedures can be a beneficial tool for the estimation of intertemporal discrete choice models.

Bayesian Estimation of Time-Changed Default Intensity Models

We estimate a reduced-form model of credit risk that incorporates stochastic volatility in default intensity via stochastic time-change. Our Bayesian MCMC estimation method overcomes nonlinearity in the measurement equation and state-dependent volatility in the state equation. We implement on firm-level time-series of CDS spreads, and find strong in-sample evidence of stochastic volatility in this market. Relative to the widely-used CIR model for the default intensity, we find that stochastic time-change offers modest benefit in fitting the cross-section of CDS spreads at each point in time, but very large improvements in fitting the time-series, i.e., in bringing agreement between the moments of the default intensity and the model-implied moments. Finally, we obtain model-implied out-of-sample density forecasts via auxiliary particle filter, and find that the time-changed model strongly outperforms the baseline CIR model.

Applying species-tree analyses to deep phylogenetic histories: Challenges and potential suggested from a survey of empirical phylogenetic studies

Coalescent-based methods for species-tree estimation are becoming a dominant approach for reconstructing species histories from multi-locus data, with most of the studies examining these methodologies focused on recently diverged species. However, deeper phylogenies, such as the datasets that comprise many Tree of Life (ToL) studies, also exhibit gene-tree discordance. This discord may also arise from the stochastic sorting of gene lineages during the speciation process (i.e., reflecting the random coalescence of gene lineages in ancestral populations). It remains unknown whether guidelines regarding methodologies and numbers of loci established by simulation studies at shallow tree depths translate into accurate species relationships for deeper phylogenetic histories. We address this knowledge gap and specifically identify the challenges and limitations of species-tree methods that account for coalescent variance for deeper phylogenies. Using simulated data with characteristics informed by empirical studies, we evaluate both the accuracy of estimated species trees and the characteristics associated with recalcitrant nodes, with a specific focus on whether coalescent variance is generally responsible for the lack of resolution. By determining the proportion of coalescent genealogies that support a particular node, we demonstrate that (1) species-tree methods account for coalescent variance at deep nodes and (2) mutational variance – not gene-tree discord arising from the coalescent – posed the primary challenge for accurate reconstruction across the tree. For example, many nodes were accurately resolved despite predicted discord from the random coalescence of gene lineages and nodes with poor support were distributed across a range of depths (i.e., they were not restricted to a particular recent divergences). Given their broad taxonomic scope and large sampling of taxa, deep level phylogenies pose several potential methodological complications including difficulties with MCMC convergence and estimation of requisite population genetic parameters for coalescent-based approaches. Despite these difficulties, the findings generally support the utility of species-tree analyses for the estimation of species relationships throughout the ToL. We discuss strategies for successful application of species-tree approaches to deep phylogenies.