SOME POSTERIOR DISTRIBUTIONS FOR THE LAPLACE MEAN

Two posterior distributions for the mean of the Laplace distribution are obtained by deriving the distributions of the product XY and the ratio X/Y when X and Y are Student＇s t and Laplace random variables distributed independently of each other. Tabulations of the associated percentage points are given along with computer programs for generating them.

A Bayesian Mixture Model Approach to Disparity Testing

The topic of this article is one-sided hypothesis testing for disparity, i.e., the mean of one group is larger than that of another when there is uncertainty as to which group a datum is drawn. For each datum, the uncertainty is captured with a given discrete probability distribution over the groups. Such situations arise, for example, in the use of Bayesian imputation methods to assess race and ethnicity disparities with certain insurance, health, and financial data. A widely used method to implement this assessment is the Bayesian Improved Surname Geocoding (BISG) method which assigns a discrete probability over six race/ethnicity groups to an individual given the individual’s surname and address location. Using a Bayesian framework and Markov Chain Monte Carlo sampling from the joint posterior distribution of the group means, the probability of a disparity hypothesis is estimated. Four methods are developed and compared with an illustrative data set. Three of these methods are implemented in an R-code and one method in WinBUGS. These methods are programed for any number of groups between two and six inclusive. All the codes are provided in the appendices.

Reliability Estimation of Aviation Pyrotechnics System Based on Mixed Beta Distribution

For evaluating reliability of an aviation pyrotechnics system,a Bayesian reliability estimation method utilizing reliability information of a system and its units was put forward. Firstly,an inheritance factor was determined by chi-square goodness of fit test.Then the mixed prior distribution was obtained based on the inheritance factor. Finally, the density function of posterior distribution was obtained and used to assess the reliability of system.According to the new method, the reliability of an aviation pyrotechnics system was evaluated to reach 0. 989 6 at the confidence level of 0. 90. To reach the reliability index,the required numbers of trials of system and its units were given. It is instructional to apply the new method on the reliability estimation of aviation pyrotechnics systems.

Bayesian Posterior Predictive Probability Happiness

We propose to determine the underlying causal structure of the elements of happiness from a set of empirically obtained data based on Bayesian. We consider the proposal to study happiness as a multidimensional construct which converges four dimensions with two different Bayesian techniques, in the first we use the Bonferroni correction to estimate the mean multiple comparisons, on this basis it is that we use the function t and a z-test, in both cases the results do not vary, so it is decided to present only those shown by the t test. In the Bayesian Multiple Linear Regression, we prove that happiness can be explained through three dimensions. The technical numerical used is MCMC, of four samples. The results show that the sample has not atypical behavior too and that suitable modifications can be described through a test. Another interesting result obtained is that the predictive probability for the case of sense positive of life and personal fulfillment dimensions exhibit a non-uniform variation.

PARAMETER IDENTIFICATION OF DYNAMIC MODELS USING A BAYES APPROACH

The Bayesian method of statistical analysis has been applied to the parameter identification problem. A method is presented to identify parameters of dynamic models with the Bayes estimators of measurement frequencies. This is based on the solution of an inverse generalized evaluate problem. The stochastic nature of test data is considered and a normal distribution is used for the measurement frequencies. An additional feature is that the engineer's confidence in the measurement frequencies is quantified and incorporated into the identification procedure. A numerical example demonstrates the efficiency of the method.

BAYESIAN LOCAL INFLUENCE ASSESSMENTS IN A GROWTH CURVE MODEL WITH GENERAL COVARIANCE STRUCTURE

The objective of this paper is to present a Bayesian approach based on Kullback- Leibler divergence for assessing local influence in a growth curve model with general co- variance structure. Under certain prior distribution assumption, the Kullback-Leibler di- vergence is used to measure the influence of some minor perturbation on the posterior distribution of unknown parameter. This leads to the diagnostic statistic for detecting which response is locally influential. As an application, the common covariance-weighted perturbation scheme is thoroughly considered.

Bayesian Inference of Empirical Coefficient for Foundation Settlement

A new approach based on Bayesian theory is proposed to determine the empirical coefficient in soil settlement calculation. Prior distribution is assumed to he uniform in [ 0.2,1.4 ]. Posterior density function is developed in the condition of prior distribution combined with the information of observed samples at four locations on a passenger dedicated fine. The results show that the posterior distribution of the empirical coefficient obeys Gaussian distribution. The mean value of the empirical coefficient decreases gradually with the increasing of the load on ground, and variance variation shows no regularity.

Key parameter optimization and analysis of stochastic seismic inversion

Stochastic seismic inversion is the combination of geostatistics and seismic inversion technology which integrates information from seismic records, well logs, and geostatistics into a posterior probability density function （PDF） of subsurface models. The Markov chain Monte Carlo （MCMC） method is used to sample the posterior PDF and the subsurface model characteristics can be inferred by analyzing a set of the posterior PDF samples. In this paper, we first introduce the stochastic seismic inversion theory, discuss and analyze the four key parameters： seismic data signal-to-noise ratio （S/N）, variogram, the posterior PDF sample number, and well density, and propose the optimum selection of these parameters. The analysis results show that seismic data S/N adjusts the compromise between the influence of the seismic data and geostatistics on the inversion results, the variogram controls the smoothness of the inversion results, the posterior PDF sample number determines the reliability of the statistical characteristics derived from the samples, and well density influences the inversion uncertainty. Finally, the comparison between the stochastic seismic inversion and the deterministic model based seismic inversion indicates that the stochastic seismic inversion can provide more reliable information of the subsurface character.

Acoustic field distribution posterior to a tumor in B-Mode diagnostic ultrasonography

The image features, such as enhancements, shadows and lateral shadows, posterior to a tumor in a B-Mode diagnostic ultrasonography, are studied. The tumor is simplified as a homogeneous cylinder in an inhomogeneous medium. Using the ray theory we derive the intensity in the region behind the cylinder. Taking the influences of sound attenuation and the time gain compensation of the B-Mode displyer into acount , we simulate with a computer five images corresponding to our experiments conducted with a tissue equivalent phantom. The theoratical images seem to be in good qualitative agreement with the experimental results.

Application of Bayesian approach to hydrological frequency analysis

An existing Bayesian flood frequency analysis method is applied to quantile estimation for Pearson type three (P-III) probability distribution. The method couples prior and sample information under the framework of Bayesian formula, and the Markov Chain Monte Carlo (MCMC) sampling approach is used to estimate posterior distributions of parameters. Different from the original sampling algorithm (i.e. the important sampling) used in the existing approach, we use the adaptive metropolis (AM) sampling technique to generate a large number of parameter sets from Bayesian parameter posterior distributions in this paper. Consequently, the sampling distributions for quantiles or the hydrological design values are constructed. The sampling distributions of quantiles are estimated as the Bayesian method can provide not only various kinds of point estimators for quantiles, e.g. the expectation estimator, but also quantitative evaluation on uncertainties of these point estimators. Therefore, the Bayesian method brings more useful information to hydrological frequency analysis. As an example, the flood extreme sample series at a gauge are used to demonstrate the procedure of application.

A Shrinkage Estimator for Combination of Bioassays

A shrinkage estimator and a maximum likelihood estimator are proposed in this paper for combination of bioassays. The shrinkage estimator is obtained in closed form which incorporates prior information just on the common log relative potency after the homogeneity test for combination of bioassays is accepted. It is a practical improvement over other estimators which require iterative procedure to obtain the estimator for the relative potency. A real data is also used to show the superiorities for the newly-proposed procedures.

Three-Component Mixture of RayleighModel Under Doubly Censored Samples:A Bayesian Look

Feroze and Aslam(J Natl Sci Found Sri Lanka 42:325-334,2014)and Sindhu et al.(J Mod Appl Stat Methods 13:259-286,2014)have considered the Bayesian analysis of the two-component mixture of lifetime distributions under doubly censored samples.In this paper,the concept has been extended for the three-component mixture of lifetime(Rayleigh)distribution under doubly censored samples.The likelihood function for the mixture of lifetime models under doubly type-II censored samples has been introduced.Different priors and loss functions have been assumed for the derivation of Bayes estimators and posterior risks.The comparisons among various estimators have been made by analyzing the simulated and real data sets.