The Trace Restriction: An Alternative Identification Strategy for the Bayesian Multinomial Probit Model

Previous authors have made Bayesian multinomial probit models identifiable by fixing a parameter on the main diagonal of the covariance matrix. The choice of which element one fixes can influence posterior predictions. Thus, we propose restricting the trace of the covariance matrix, which we achieve without computational penalty. This permits a prior that is symmetric to permutations of the nonbase outcome categories. We find in real and simulated consumer choice datasets that the trace-restricted model is less prone to making extreme predictions. Further, the trace restriction can provide stronger identification, yielding marginal posterior distributions that are more easily interpreted.     

Bayesian adaptive Lasso for quantile regression models with nonignorably missing response data

Abstract

Handling data with the nonignorably missing mechanism is still a challenging problem in statistics. In this paper, we develop a fully Bayesian adaptive Lasso approach for quantile regression models with nonignorably missing response data, where the nonignorable missingness mechanism is specified by a logistic regression model. The proposed method extends the Bayesian Lasso by allowing different penalization parameters for different regression coefficients. Furthermore, a hybrid algorithm that combined the Gibbs sampler and Metropolis-Hastings algorithm is implemented to simulate the parameters from posterior distributions, mainly including regression coefficients, shrinkage coefficients, parameters in the non-ignorable missing models. Finally, some simulation studies and a real example are used to illustrate the proposed methodology.     

Robust Model-Based Inference for Incomplete Data via Penalized Spline Propensity Prediction

Parametric model-based regression imputation is commonly applied to missing-data problems, but is sensitive to misspecification of the imputation model. Little and An (2004 Little , R. J. A. , An , H. ( 2004 ). Robust likelihood-based analysis of multivariate data with missing values . Statistica Sinica 14 : 949 – 968 .[Web of Science ®] , [Google Scholar]) proposed a semiparametric approach called penalized spline propensity prediction (PSPP), where the variable with missing values is modeled by a penalized spline (P-Spline) of the response propensity score, which is logit of the estimated probability of being missing given the observed variables. Variables other than the response propensity are included parametrically in the imputation model. However they only considered point estimation based on single imputation with PSPP. We consider here three approaches to standard errors estimation incorporating the uncertainty due to non response: (a) standard errors based on the asymptotic variance of the PSPP estimator, ignoring sampling error in estimating the response propensity; (b) standard errors based on the bootstrap method; and (c) multiple imputation-based standard errors using draws from the joint posterior predictive distribution of missing values under the PSPP model. Simulation studies suggest that the bootstrap and multiple imputation approaches yield good inferences under a range of simulation conditions, with multiple imputation showing some evidence of closer to nominal confidence interval coverage when the sample size is small.     

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.     

市场风险的高效率加速算法研究

在计算投资组合市场风险时,采用高效率重要性抽样技术来处理大规模、高维度和稀有事件问题可以提高计算的速度和效率。在对投资组合损失进行Delta-Gamma近似的基础上,通过利用辅助分布变换函数,将求解抽样参数的最小抽样方差问题转化为一个非线性的广义最小二乘问题;在指数族抽样核的假设下,进一步将问题转化为迭代线性回归问题,从而简化了计算;通过德尔塔对冲和指数对冲投资组合的模拟算例验证了所提出方法的有效性。     

A note on Markov chain Monte Carlo sweep strategies

Markov chain Monte Carlo (MCMC) routines have become a fundamental means for generating random variates from distributions otherwise difficult to sample. The Hastings sampler, which includes the Gibbs and Metropolis samplers as special cases, is the most popular MCMC method. A number of implementations are available for running these MCMC routines varying in the order through which the components or blocks of the random vector of interest X are cycled or visited. The two most common implementations are the deterministic sweep strategy, whereby the components or blocks of X are updated successively and in a fixed order, and the random sweep strategy, whereby the coordinates or blocks of X are updated in a randomly determined order. In this article, we present a general representation for MCMC updating schemes showing that the deterministic scan is a special case of the random scan. We also discuss decision criteria for choosing a sweep strategy.     

The Monte Carlo EM method for estimating multivariate tobit latent variable models

We propose a multivariate tobit (MT) latent variable model that is defined by a confirmatory factor analysis with covariates for analysing the mixed type data, which is inherently non-negative and sometimes has a large proportion of zeros. Some useful MT models are special cases of our proposed model. To obtain maximum likelihood estimates, we use the expectation maximum algorithm with its E-step via the Gibbs sampler made feasible by Monte Carlo simulation and its M-step greatly simplified by a sequence of conditional maximization. Standard errors are evaluated by inverting a Monte Carlo approximation of the information matrix using Louis's method. The methodology is illustrated with a simulation study and a real example.     

Behaviour of the Gibbs sampler when conditional distributions are potentially incompatible

The Gibbs sampler has been used extensively in the statistics literature. It relies on iteratively sampling from a set of compatible conditional distributions and the sampler is known to converge to a unique invariant joint distribution. However, the Gibbs sampler behaves rather differently when the conditional distributions are not compatible. Such applications have seen increasing use in areas such as multiple imputation. In this paper, we demonstrate that what a Gibbs sampler converges to is a function of the order of the sampling scheme. Besides providing the mathematical background of this behaviour, we also explain how that happens through a thorough analysis of the examples.     

Variable selection in quantile regression via Gibbs sampling

Due to computational challenges and non-availability of conjugate prior distributions, Bayesian variable selection in quantile regression models is often a difficult task. In this paper, we address these two issues for quantile regression models. In particular, we develop an informative stochastic search variable selection (ISSVS) for quantile regression models that introduces an informative prior distribution. We adopt prior structures which incorporate historical data into the current data by quantifying them with a suitable prior distribution on the model parameters. This allows ISSVS to search more efficiently in the model space and choose the more likely models. In addition, a Gibbs sampler is derived to facilitate the computation of the posterior probabilities. A major advantage of ISSVS is that it avoids instability in the posterior estimates for the Gibbs sampler as well as convergence problems that may arise from choosing vague priors. Finally, the proposed methods are illustrated with both simulation and real data.     

Cascade model with Dirichlet process for analyzing multiple dyadic matrices

Dyadic matrices are natural data representations in a wide range of domains. A dyadic matrix often involves two types of abstract objects and is based on observations of pairs of elements with one element from each object. Owing to the increasing needs from practical applications, dyadic data analysis has recently attracted increasing attention and many techniques have been developed. However, most existing approaches, such as co-clustering and relational reasoning, only handle a single dyadic table and lack flexibility to perform prediction using multiple dyadic matrices. In this article, we propose a general nonparametric Bayesian framework with a cascaded structure to model multiple dyadic matrices and then describe an efficient hybrid Gibbs sampling algorithm for posterior inference and analysis. Empirical evaluations using both synthetic data and real data show that the proposed model captures the hidden structure of data and generalizes the predictive inference in a unique way.