BAYESIAN ANALYSIS OF THE ADDITIVE MIXED MODEL FOR RANDOMIZED BLOCK DESIGNS

This paper deals with the Bayesian analysis of the additive mixed model experiments. Consider b randomly chosen subjects who respond once to each of t treatments. The subjects are treated as random effects and the treatment effects are fixed. Suppose that some prior information is available, thus motivating a Bayesian analysis. The Bayesian computation, however, can be difficult in this situation, especially when a large number of treatments is involved. Three computational methods are suggested to perform the analysis. The exact posterior density of any parameter of interest can be simulated based on random realizations taken from a restricted multivariate t distribution. The density can also be simulated using Markov chain Monte Carlo methods. The simulated density is accurate when a large number of random realizations is taken. However, it may take substantial amount of computer time when many treatments are involved. An alternative Laplacian approximation is discussed. The Laplacian method produces smooth and very accurate approximates to posterior densities, and takes only seconds of computer time. An example of a pipeline cracks experiment is used to illustrate the Bayesian approaches and the computational methods.     

The efficient estimation of tail probabilities for extremes of moving average processes using conditional simulation

This paper describes a conditional simulation technique which can be used to estimate probabilities associated with the distribution of the maximum of a real-valued process which can be written in the form of a moving average. The class of processes to which the technique applies includes non-stationary and spatial processes, and autoregressive processes. The technique is shown to achieve a considerable variance reduction compared with the obvious simulation-based estimator, particularly for estimating small upper-tail probabilities.     

Using Markov Chains for Non-perennial Daily Streamflow Data Generation

The use of Markov chains to simulate non-perennial streamflow data is considered. A non-perennial stream may be thought as having three states, namely zero flow, increasing flow and decreasing flow, for which a three-state Markov chain can be constructed. Alternatively, two two-state Markov chains can be used, the first of which represents the existence and non-existence of flow, whereas the second deals with the increment and decrement in the flow for periods with flow. Probabilistic relationships between the two alternatives are derived. Their performances in simulating the state of the stream are compared on the basis of data from two different geographical regions in Turkey. It is concluded that both alternatives are capable of simulating the state of the stream.     

对提高物理实验课程教学质量的设想

针对我院的具体情况提出了对提高我院物理实验课程教学质量的几点设想。     

Correlations Between Parameters in Risk Models: Estimation and Propagation of Uncertainty by Markov Chain Monte Carlo

Monte Carlo simulation has become the accepted method for propagating parameter uncertainty through risk models. It is widely appreciated, however, that correlations between input variables must be taken into account if models are to deliver correct assessments of uncertainty in risk. Various two-stage methods have been proposed that first estimate a correlation structure and then generate Monte Carlo simulations, which incorporate this structure while leaving marginal distributions of parameters unchanged. Here we propose a one-stage alternative, in which the correlation structure is estimated from the data directly by Bayesian Markov Chain Monte Carlo methods. Samples from the posterior distribution of the outputs then correctly reflect the correlation between parameters, given the data and the model. Besides its computational simplicity, this approach utilizes the available evidence from a wide variety of structures, including incomplete data and correlated and uncorrelated repeat observations. The major advantage of a Bayesian approach is that, rather than assuming the correlation structure is fixed and known, it captures the joint uncertainty induced by the data in all parameters, including variances and covariances, and correctly propagates this through the decision or risk model. These features are illustrated with examples on emissions of dioxin congeners from solid waste incinerators.     

Incorporating Previous Results Into the Analysis of General Balanced Designed Experiments

When previous results are available about quantities of interest in a designed experiment they should be incorporated into the analysis. We suppose that estimates of treatment effects and variance components and their precisions are available from previous data but not necessarily the full data. A prior-posterior method is described which incorporates these previous estimates directly into the analysis of a current set of data. General but concise formula are derived for the class of generally balanced designs. Previous results are represented by a multivariate normal prior for the treatment means and independent inverse chi-squared distributions for the variance components. Joint and marginal posterior modes and a measure of dispersion are proposed as combined or updated estimates. These posterior summary statistics have highly interpretable forms and are readily computed.     

Human Interindividual Variability–A Major Source of Uncertainty in Assessing Risks for Noncancer Health Effects

For noncancer effects, the degree of human interindividual variability plays a central role in determining the risk that can be expected at low exposures. This discussion reviews available data on observations of interindividual variability in (a) breathing rates, based on observations in British coal miners; (b) systemic pharmacokinetic parameters, based on studies of a number of drugs; (c) susceptibility to neurological effects from fetal exposure to methyl mercury, based on observations of the incidence of effects in relation to hair mercury levels; and (d) chronic lung function changes in relation to long-term exposure to cigarette smoke. The quantitative ranges of predictions that follow from uncertainties in estimates of interindividual variability in susceptibility are illustrated.     

Bayesian analysis of contingency tables: a simulation and graphics-based approach

In this paper we present a simulation and graphics-based model checking and model comparison methodology for the Bayesian analysis of contingency tables. We illustrate the approach by testing the hypotheses of independence and symmetry on complete and incomplete simulated tables.     

运动人体科学开放式实验研究

运动人体科学实验有着不同于其他学科的特征。若面向学生、面向全校师生、面向社会开放,突出以人为本、质量第一的原则,便能有效地配置实验资源,发挥实验的最优效应,为学生服务,为社会服务,为健康第一服务,达到培养高质量人才的目的。     

Exact and efficient Bayesian inference for multiple changepoint problems

We demonstrate how to perform direct simulation from the posterior distribution of a class of multiple changepoint models where the number of changepoints is unknown. The class of models assumes independence between the posterior distribution of the parameters associated with segments of data between successive changepoints. This approach is based on the use of recursions, and is related to work on product partition models. The computational complexity of the approach is quadratic in the number of observations, but an approximate version, which introduces negligible error, and whose computational cost is roughly linear in the number of observations, is also possible. Our approach can be useful, for example within an MCMC algorithm, even when the independence assumptions do not hold. We demonstrate our approach on coal-mining disaster data and on well-log data. Our method can cope with a range of models, and exact simulation from the posterior distribution is possible in a matter of minutes.