Bayesian Bandwidth Estimation in Nonparametric Time-Varying Coefficient Models

Bandwidth plays an important role in determining the performance of nonparametric estimators, such as the local constant estimator. In this article, we propose a Bayesian approach to bandwidth estimation for local constant estimators of time-varying coefficients in time series models. We establish a large sample theory for the proposed bandwidth estimator and Bayesian estimators of the unknown parameters involved in the error density. A Monte Carlo simulation study shows that (i) the proposed Bayesian estimators for bandwidth and parameters in the error density have satisfactory finite sample performance; and (ii) our proposed Bayesian approach achieves better performance in estimating the bandwidths than the normal reference rule and cross-validation. Moreover, we apply our proposed Bayesian bandwidth estimation method for the time-varying coefficient models that explain Okun’s law and the relationship between consumption growth and income growth in the U.S. For each model, we also provide calibrated parametric forms of the time-varying coefficients. Supplementary materials for this article are available online.     

Sampling from a Max‐Stable Process Conditional on a Homogeneous Functional with an Application for Downscaling Climate Data

Conditional simulation of max‐stable processes allows for the analysis of spatial extremes taking into account additional information provided by the conditions. Instead of observations at given sites as usually done, we consider a single condition given by a more general functional of the process as may occur in the context of climate models. As the problem turns out to be intractable analytically, we make use of Markov chain Monte Carlo methods to sample from the conditional distribution. Simulation studies indicate fast convergence of the Markov chains involved. In an application to precipitation data, the utility of the procedure as a tool to downscale climate data is demonstrated.     

A new non-parametric multivariate EWMA sign control chart for monitoring process dispersion

In this paper, a new non-parametric multivariate exponentially weighted moving average (NMEWMA) sign chart is proposed for monitoring the process dispersion. The run length characteristics of the NMEWMA sign chart are computed with the help of Markov chain and Monte Carlo simulations. Moreover, the NMEWMA sign chart is also used to detect changes in the process mean and dispersion simultaneously. An illustrative example is also used to explain the implementation of proposed control chart.     

Bayesian comparison of private and common values in structural second-price auctions

Private and common values (CVs) are the two main competing valuation models in auction theory and empirical work. In the framework of second-price auctions, we compare the empirical performance of the independent private value (IPV) model to the CV model on a number of different dimensions, both on real data from eBay coin auctions and on simulated data. Both models fit the eBay data well with a slight edge for the CV model. However, the differences between the fit of the models seem to depend to some extent on the complexity of the models. According to log predictive score the IPV model predicts auction prices slightly better in most auctions, while the more robust CV model is much better at predicting auction prices in more unusual auctions. In terms of posterior odds, the CV model is clearly more supported by the eBay data.     

Reliability Research of k-out-of-n: G Supply Chain System Based on Copula

Supply chain management has received considerable attention in the literature and it is meaningful and important to be able to measure the reliability of supply chains. In the article, the suppliers in the supply chain systems are not independent of each other and the dependency relation may be either linear or nonlinear correlation. From the view of the distribution service process, a copula-based method is proposed for analyzing the reliability of supply chains. In this article, by introducing the model of k-out-of-n: G system into the studies of supply chains, an evaluation method is suggested and the reliability indexes are obtained. Finally, a numerical example is presented to illustrate the results obtained in this article.     

Explicit Distributional Results In Pattern Formation II

The paper derives the joint generating function of a collection of pattern statistics associated with binary sequences. The models discussed cover independent and some dependent Bernoulli trials, including Markov dependent ones. The results cover, in particular, the moment generating function of the random search time for certain general binary patterns in the popular Knuth-Morris-Pratt algorithm and hence shed more light into its performance.     

Non-linear state space modelling of fisheries biomass dynamics by using Metropolis-Hastings within-Gibbs sampling

State space modelling and Bayesian analysis are both active areas of applied research in fisheries stock assessment. Combining these two methodologies facilitates the fitting of state space models that may be non-linear and have non-normal errors, and hence it is particularly useful for modelling fisheries dynamics. Here, this approach is demonstrated by fitting a non-linear surplus production model to data on South Atlantic albacore tuna ( Thunnus alalunga ). The state space approach allows for random variability in both the data (the measurement of relative biomass) and in annual biomass dynamics of the tuna stock. Sampling from the joint posterior distribution of the unobservables was achieved by using Metropolis-Hastings within-Gibbs sampling.     

Hierarchical priors for Bayesian CART shrinkage

The Bayesian CART (classification and regression tree) approach proposed by Chipman, George and McCulloch (1998) entails putting a prior distribution on the set of all CART models and then using stochastic search to select a model. The main thrust of this paper is to propose a new class of hierarchical priors which enhance the potential of this Bayesian approach. These priors indicate a preference for smooth local mean structure, resulting in tree models which shrink predictions from adjacent terminal node towards each other. Past methods for tree shrinkage have searched for trees without shrinking, and applied shrinkage to the identified tree only after the search. By using hierarchical priors in the stochastic search, the proposed method searches for shrunk trees that fit well and improves the tree through shrinkage of predictions.     

Stochastic approximation Monte Carlo EM for change-point analysis

In the expectation–maximization (EM) algorithm for maximum likelihood estimation from incomplete data, Markov chain Monte Carlo (MCMC) methods have been used in change-point inference for a long time when the expectation step is intractable. However, the conventional MCMC algorithms tend to get trapped in local mode in simulating from the posterior distribution of change points. To overcome this problem, in this paper we propose a stochastic approximation Monte Carlo version of EM (SAMCEM), which is a combination of adaptive Markov chain Monte Carlo and EM utilizing a maximum likelihood method. SAMCEM is compared with the stochastic approximation version of EM and reversible jump Markov chain Monte Carlo version of EM on simulated and real datasets. The numerical results indicate that SAMCEM can outperform among the three methods by producing much more accurate parameter estimates and the ability to achieve change-point positions and estimates simultaneously.     

Designing of a mixed-chain sampling plan based on the process capability index with chain sampling as the attributes plan

In this article, we propose a new mixed chain sampling plan based on the process capability index C_pk, where the quality characteristic of interest having double specification limits and follows the normal distribution with unknown mean and variance. In the proposed mixed plan, the chain sampling inspection plan is used for the inspection of attribute quality characteristics. The advantages of this proposed mixed sampling plan are also discussed. Tables are constructed to determine the optimal parameters for practical applications by formulating the problem as a non linear programming in which the objective function to be minimized is the average sample number and the constraints are related to lot acceptance probabilities at acceptable quality level and limiting quality level under the operating characteristic curve. The practical application of the proposed mixed sampling plan is explained with an illustrative example. Comparison of the proposed sampling plan is also made with other existing sampling plans.