Bound and convergence of the non-constant dynamic linear model

This paper extends the limiting results of West and Harrison (1997, section 5.5) about the convergence of the variances of time series dynamic linear models (TSDLMs) when both, the variances of the observation and evolution errors of the model, are time-varying with steady limits. Analytical results are derived and an illustrative example is provided.     

A discrete/continuous choice model on a nonconvex budget set

Decreasing block rate pricing is a nonlinear price system often used for public utility services. Residential gas services in Japan and the United Kingdom are provided under this price schedule. The discrete/continuous choice approach is used to analyze the demand under decreasing block rate pricing. However, the nonlinearity problem, which has not been examined in previous studies, arises because a consumer’s budget set (a set of affordable consumption amounts) is nonconvex, and hence, the resulting model includes highly nonlinear functions. To address this problem, we propose a feasible, efficient method of demand estimation on the nonconvex budget. The advantages of our method are as follows: (i) the construction of an Markov chain Monte Carlo algorithm with an efficient blanket based on the Hermite–Hadamard integral inequality and the power-mean inequality, (ii) the explicit consideration of the (highly nonlinear) separability condition, which often makes numerical likelihood maximization difficult, and (iii) the introduction of normal disturbance into the discrete/continuous choice model on the nonconvex budget set. The proposed method is applied to estimate the Japanese residential gas demand function and evaluate the effect of price schedule changes as a policy experiment.     

Multivariate stochastic volatility with Bayesian dynamic linear models

This paper develops a Bayesian procedure for estimation and forecasting of the volatility of multivariate time series. The foundation of this work is the matrix-variate dynamic linear model, for the volatility of which we adopt a multiplicative stochastic evolution, using Wishart and singular multivariate beta distributions. A diagonal matrix of discount factors is employed in order to discount the variances element by element and therefore allowing a flexible and pragmatic variance modelling approach. Diagnostic tests and sequential model monitoring are discussed in some detail. The proposed estimation theory is applied to a four-dimensional time series, comprising spot prices of aluminium, copper, lead and zinc of the London metal exchange. The empirical findings suggest that the proposed Bayesian procedure can be effectively applied to financial data, overcoming many of the disadvantages of existing volatility models.     

Constrained retropolation of high-frequency data using related series: A simple dynamic model approach

The static approach by Chow and Lin (1971) to temporal disaggregation of an economic series by related indicators is extended to back-calculate high-frequency data constrained to their low-frequency counterpart according to a simple dynamic model. I wish to thank Fabio Sartori and an anonymous referee for useful comments on a previous version of this paper. The usual disclaimer applies.     

A bayesian approach to dynamic tobit models

This paper develops a posterior simulation method for a dynamic Tobit model. The major obstacle rooted in such a problem lies in high dimensional integrals, induced by dependence among censored observations, in the likelihood function. The primary contribution of this study is to develop a practical and efficient sampling scheme for the conditional posterior distributions of the censored (i.e., unobserved) data, so that the Gibbs sampler with the data augmentation algorithm is successfully applied. The substantial differences between this approach and some existing methods are highlighted. The proposed simulation method is investigated by means of a Monte Carlo study and applied to a regression model of Japanese exports of passenger cars to the U.S. subject to a non-tariff trade barrier.     

A bayesian approach to dynamic tobit models

This paper develops a posterior simulation method for a dynamic Tobit model. The major obstacle rooted in such a problem lies in high dimensional integrals, induced by dependence among censored observations, in the likelihood function. The primary contribution of this study is to develop a practical and efficient sampling scheme for the conditional posterior distributions of the censored (i.e., unobserved) data, so that the Gibbs sampler with the data augmentation algorithm is successfully applied. The substantial differences between this approach and some existing methods are highlighted. The proposed simulation method is investigated by means of a Monte Carlo study and applied to a regression model of Japanese exports of passenger cars to the U.S. subject to a non-tariff trade barrier.     

Bayesian model averaging for dynamic panels with an application to a trade gravity model

We extend the Bayesian Model Averaging (BMA) framework to dynamic panel data models with endogenous regressors using a Limited Information Bayesian Model Averaging (LIBMA) methodology. Monte Carlo simulations confirm the asymptotic performance of our methodology both in BMA and selection, with high posterior inclusion probabilities for all relevant regressors, and parameter estimates very close to their true values. In addition, we illustrate the use of LIBMA by estimating a dynamic gravity model for bilateral trade. Once model uncertainty, dynamics, and endogeneity are accounted for, we find several factors that are robustly correlated with bilateral trade. We also find that applying methodologies that do not account for either dynamics or endogeneity (or both) results in different sets of robust determinants.     

A dependent fatigue lifetime model

An ARMA(p,q) Box-Jenkins fatigue model which allows to take into account the dependence between the strengths of neighbouring pieces of material for constant stress range is presented and the asymptotic convergence, for large lengths of materials, to a Gumbel distribution is shown. When the stress range varies, a regression model, compatible with Gumbel result, is derived. This model is based on a functional equation which is solved and a three parameter family is obtained as the only solution. Finally, an example of application with real fatigue data is included. Monte Carlo simulations give the distribution functions of the fatigue strength of wires of different lengths and allow their design. In this way, the influence of dependence is analyzed.     

A comparison of Bayesian model selection based on MCMC with an application to GARCH-type models

This paper presents a comprehensive review and comparison of five computational methods for Bayesian model selection, based on MCMC simulations from posterior model parameter distributions. We apply these methods to a well-known and important class of models in financial time series analysis, namely GARCH and GARCH-t models for conditional return distributions (assuming normal and t-distributions). We compare their performance with the more common maximum likelihood-based model selection for simulated and real market data. All five MCMC methods proved reliable in the simulation study, although differing in their computational demands. Results on simulated data also show that for large degrees of freedom (where the t-distribution becomes more similar to a normal one), Bayesian model selection results in better decisions in favor of the true model than maximum likelihood. Results on market data show the instability of the harmonic mean estimator and reliability of the advanced model selection methods.     

Estimation of Dynamic Discrete Choice Models Using Artificial Neural Network Approximations

I propose a method for inference in dynamic discrete choice models (DDCM) that utilizes Markov chain Monte Carlo (MCMC) and artificial neural networks (ANNs). MCMC is intended to handle high-dimensional integration in the likelihood function of richly specified DDCMs. ANNs approximate the dynamic-program (DP) solution as a function of the parameters and state variables prior to estimation to avoid having to solve the DP on each iteration. Potential applications of the proposed methodology include inference in DDCMs with random coefficients, serially correlated unobservables, and dependence across individual observations. The article discusses MCMC estimation of DDCMs, provides relevant background on ANNs, and derives a theoretical justification for the method. Experiments suggest this to be a promising approach.     

Modeling the density of US yield curve using Bayesian semiparametric dynamic Nelson-Siegel model

Abstract

This paper proposes the Bayesian semiparametric dynamic Nelson-Siegel model for estimating the density of bond yields. Specifically, we model the distribution of the yield curve factors according to an infinite Markov mixture (iMM). The model allows for time variation in the mean and covariance matrix of factors in a discrete manner, as opposed to continuous changes in these parameters such as the Time Varying Parameter (TVP) models. Estimating the number of regimes using the iMM structure endogenously leads to an adaptive process that can generate newly emerging regimes over time in response to changing economic conditions in addition to existing regimes. The potential of the proposed framework is examined using US bond yields data. The semiparametric structure of the factors can handle various forms of non-normalities including fat tails and nonlinear dependence between factors using a unified approach by generating new clusters capturing these specific characteristics. We document that modeling parameter changes in a discrete manner increases the model fit as well as forecasting performance at both short and long horizons relative to models with fixed parameters as well as the TVP model with continuous parameter changes. This is mainly due to fact that the discrete changes in parameters suit the typical low frequency monthly bond yields data characteristics better.     

Short run spc based upon the second order dynamic linear model for trend detection

Recently, several new applications of control chart procedures for short production runs have been introduced. Bothe (1989) and Burr (1989) proposed the use of control chart statistics which are obtained by scaling the quality characteristic by target values or process estimates of a location and scale parameter. The performance of these control charts can be significantly affected by the use of incorrect scaling parameters, resulting in either an excessive "false alarm rate," or insensitivity to the detection of moderate shifts in the process. To correct for these deficiencies, Quesenberry (1990, 1991) has developed the Q-Chart which is formed from running process estimates of the sample mean and variance. For the case where both the process mean and variance are unknown, the Q-chaxt statistic is formed from the standard inverse Z-transformation of a t-statistic. Q-charts do not perform correctly, however, in the presence of special cause disturbances at process startup. This has recently been supported by results published by Del Castillo and Montgomery (1992), who recommend the use of an alternative control chart procedure which is based upon a first-order adaptive Kalman filter model Consistent with the recommendations by Castillo and Montgomery, we propose an alternative short run control chart procedure which is based upon the second order dynamic linear model (DLM). The control chart is shown to be useful for the early detection of unwanted process trends. Model and control chart parameters are updated sequentially in a Bayesian estimation framework, providing the greatest degree of flexibility in the level of prior information which is incorporated into the model. The result is a weighted moving average control chart statistic which can be used to provide running estimates of process capability. The average run length performance of the control chart is compared to the optimal performance of the exponentially weighted moving average (EWMA) chart, as reported by Gan (1991). Using a simulation approach, the second order DLM control chart is shown to provide better overall performance than the EWMA for short production run applications     

A hierarchical Bayesian model for predicting the functional consequences of amino-acid polymorphisms

Summary.  Genetic polymorphisms in deoxyribonucleic acid coding regions may have a phenotypic effect on the carrier, e.g. by influencing susceptibility to disease. Detection of deleterious mutations via association studies is hampered by the large number of candidate sites; therefore methods are needed to narrow down the search to the most promising sites. For this, a possible approach is to use structural and sequence-based information of the encoded protein to predict whether a mutation at a particular site is likely to disrupt the functionality of the protein itself. We propose a hierarchical Bayesian multivariate adaptive regression spline (BMARS) model for supervised learning in this context and assess its predictive performance by using data from mutagenesis experiments on lac repressor and lysozyme proteins. In these experiments, about 12 amino-acid substitutions were performed at each native amino-acid position and the effect on protein functionality was assessed. The training data thus consist of repeated observations at each position, which the hierarchical framework is needed to account for. The model is trained on the lac repressor data and tested on the lysozyme mutations and vice versa. In particular, we show that the hierarchical BMARS model, by allowing for the clustered nature of the data, yields lower out-of-sample misclassification rates compared with both a BMARS and a frequen-tist MARS model, a support vector machine classifier and an optimally pruned classification tree.     

A Bayesian Approach to Selecting Covariates for Prediction

We consider the problem of selecting a regression model from a large class of possible models in the case where no true model is believed to exist. In practice few statisticians, or scientists who employ statistical methods, believe that a "true" model exists, but nonetheless they seek to select a model as a proxy from which they want to predict. Unlike much of the recent work in this area we address this problem explicitly. We develop Bayesian predictive model selection techniques when proper conjugate priors are used and obtain an easily computed expression for the model selection criterion. We also derive expressions for updating the value of the statistic when a predictor is dropped from the model and apply this approach to a large well-known data set.     

A comparison of scientific and engineering criteria for Bayesian model selection

Given a set of possible models for variables X and a set of possible parameters for each model, the Bayesian estimate of the probability distribution for X given observed data is obtained by averaging over the possible models and their parameters. An often-used approximation for this estimate is obtained by selecting a single model and averaging over its parameters. The approximation is useful because it is computationally efficient, and because it provides a model that facilitates understanding of the domain. A common criterion for model selection is the posterior probability of the model. Another criterion for model selection, proposed by San Martini and Spezzafari (1984), is the predictive performance of a model for the next observation to be seen. From the standpoint of domain understanding, both criteria are useful, because one identifies the model that is most likely, whereas the other identifies the model that is the best predictor of the next observation. To highlight the difference, we refer to the posterior-probability and alternative criteria as the scientific criterion (SC) and engineering criterion (EC), respectively. When we are interested in predicting the next observation, the model-averaged estimate is at least as good as that produced by EC, which itself is at least as good as the estimate produced by SC. We show experimentally that, for Bayesian-network models containing discrete variables only, the predictive performance of the model average can be significantly better than those of single models selected by either criterion, and that differences between models selected by the two criterion can be substantial.     

Using the Reversible Jump MCMC Procedure for Identifying and Estimating Univariate TAR Models

One way that has been used for identifying and estimating threshold autoregressive (TAR) models for nonlinear time series follows the Markov chain Monte Carlo (MCMC) approach via the Gibbs sampler. This route has major computational difficulties, specifically, in getting convergence to the parameter distributions. In this article, a new procedure for identifying a TAR model and for estimating its parameters is developed by following the reversible jump MCMC procedure. It is found that the proposed procedure conveys a Markov chain with convergence properties.     

A refined parameter estimating approach for HIV dynamic model

HIV dynamic models, a set of ordinary differential equations (ODEs), have provided new understanding of the pathogenesis of HIV infection and the treatment effects of antiviral therapies. However, to estimate parameters for ODEs is very challenging due to the complexity of this nonlinear system. In this article, we propose a comprehensive procedure to deal with this issue. In the proposed procedure, a series of cutting-edge statistical methods and techniques are employed, including nonparametric mixed-effects smoothing-based methods for ODE models and stochastic approximation expectation–maximization (EM) approach for mixed-effects ODE models. A simulation study is performed to validate the proposed approach. An application example from a real HIV clinical trial study is used to illustrate the usefulness of the proposed method.     

A generalized bivariate Bernoulli model with covariate dependence

Dependence in outcome variables may pose formidable difficulty in analyzing data in longitudinal studies. In the past, most of the studies made attempts to address this problem using the marginal models. However, using the marginal models alone, it is difficult to specify the measures of dependence in outcomes due to association between outcomes as well as between outcomes and explanatory variables. In this paper, a generalized approach is demonstrated using both the conditional and marginal models. This model uses link functions to test for dependence in outcome variables. The estimation and test procedures are illustrated with an application to the mobility index data from the Health and Retirement Survey and also simulations are performed for correlated binary data generated from the bivariate Bernoulli distributions. The results indicate the usefulness of the proposed method.     

A parametric dynamic survival model applied to breast cancer survival times

Summary. Much current analysis of cancer registry data uses the semiparametric proportional hazards Cox model. In this paper, the time-dependent effect of various prognostic indicators on breast cancer survival times from the West Midlands Cancer Intelligence Unit are investigated. Using Bayesian methodology and Markov chain Monte Carlo estimation methods, we develop a parametric dynamic survival model which avoids the proportional hazards assumption. The model has close links to that developed by both Gamerman and Sinha and co-workers: the log-base-line hazard and covariate effects are piecewise constant functions, related between intervals by a simple stochastic evolution process. Here this evolution is assigned a parametric distribution, with a variance that is further included as a hyperparameter. To avoid problems of convergence within the Gibbs sampler, we consider using a reparameterization. It is found that, for some of the prognostic indicators considered, the estimated effects change with increasing follow-up time. In general those prognostic indicators which are thought to be representative of the most hazardous groups (late-staged tumour and oldest age group) have a declining effect.     

A Bayesian compartmental model for the evaluation of 1,3-butadiene metabolism

Summary. We propose a Bayesian model for physiologically based pharmacokinetics of 1,3-butadiene (BD). BD is classified as a suspected human carcinogen and exposure to it is common, especially through cigarette smoke as well as in urban settings. The main aim of the methodology and analysis that are presented here is to quantify variability in the rates of BD metabolism by human subjects. A three-compartmental model is described, together with informative prior distributions for the population parameters, all of which represent real physiological variables. The model is described in detail along with the meanings and interpretations of the associated parameters. A four-compartment model is also given for comparison. Markov chain Monte Carlo methods are described for fitting the model proposed. The model is fitted to toxicokinetic data obtained from 133 healthy subjects (males and females) from the four major racial groups in the USA, with ages ranging from 19 to 62 years. Subjects were exposed to 2 parts per million of BD for 20 min through a face mask by using a computer-controlled exposure and respiratory monitoring system. Stratification by ethnic group results in major changes in the physiological parameters. Sex and age were also tested but not found to have a significant effect.