Effect of Injection Parameters and Addition of Nanoscale Materials on the Shrinkage of Polypropylene Copolymer

The effect of variation of injection conditions and addition of nano-calcium carbonate (CaCO₃), nano-silicon dioxide (SiO₂) and full-vulcanized nano-powdered styrene butadiene rubber (PSBR) on the shrinkage of injection-molded polypropylene-ethylene copolymer (90/10, co-PP) were investigated. The results showed that the shrinkage was different for different locations along the flow path. The shrinkage in the length direction of the injection-molded sample varied with the adjustment of the processing parameters, while the shrinkage in the width and thickness direction was almost unchanged. The addition of nano-CaCO₃ and PSBR decreased the shrinkage of co-PP, while the shrinkage of co-PP/ SiO₂ composite was almost unchanged.     

A Bayesian approach to seafloor classification using multi-beam echo-sounder backscatter data

Seafloor classification using acoustic remote sensing techniques is an attractive approach due to its high-coverage capabilities and limited costs. The multi-beam echo-sounder (MBES) system provides high-resolution bathymetry and backscatter information with 100% coverage. In this paper, we present a seafloor classification method that employs the MBES backscatter data. The method uses the averaged backscatter data per beam. It, therefore, is independent on the quality of the MBES calibration. Also, its performance is insensitive to seafloor type variation along the MBES swathe and corrections for the angular dependence of the backscatter are not needed. The method accounts for the ping-to-ping variability of the backscatter intensity. It estimates both the number of seafloor types present in the survey area and the probability density function for the backscatter strength at a certain angle for each of the seafloor types. Application of the method to MBES backscatter data acquired in a well-known test area in the North Sea shows very good agreement with available ground truth. The method’s discriminatory performance for this area is demonstrated to be comparable to that of taking samples of the sediment. All seafloor types known to be present in the area are resolved for. Application of the method to the Stanton bank data set shows clearly separable areas that differ in seafloor composition.     

Smoothness in Bayesian Non-parametric Regression with Wavelets

Consider the classical nonparametric regression problem y_i = f(t_i) + _ii = 1,...,n where t_i = i/n, and _i are i.i.d. zero mean normal with variance ². The aim is to estimate the true function f which is assumed to belong to the smoothness class described by the Besov space B _pq ^q . These are functions belonging to L_p with derivatives up to order s, in L_p sense. The parameter q controls a further finer degree of smoothness. In a Bayesian setting, a prior on B _pq ^q is chosen following Abramovich, Sapatinas and Silverman (1998). We show that the optimal Bayesian estimator of f is then also a.s. in B _pq ^q if the loss function is chosen to be the Besov norm of B _pq ^q . Because it is impossible to compute this optimal Bayesian estimator analytically, we propose a stochastic algorithm based on an approximation of the Bayesian risk and simulated annealing. Some simulations are presented to show that the algorithm performs well and that the new estimator is competitive when compared to the more standard posterior mean.     

A class of loss functions of catenary form

The catenary form of loss function is considered in the framework of Bayesian decision theory. The mathematical tractability of this form seems to be unrecognized; it contains quadratic loss as a limiting case. For various probability distributions expressions are given for posterior analysis, and limiting properties are investigated.     

On low order moments of the homodyned-K distribution

Fractional low order moments have been reported as beneficial for sampling computations using the K distribution. However, it has been recently pointed out that this it not the case for the homodyned-K distribution for a tissue discrimination problem. In this paper we show that such an statement is not fully justified. To that end, we follow a standard pattern recognition procedure both to determine class separability measures and to classify data with several classifiers. We conclude that the optimum order of the moments is intimately linked to the specific statistical properties of the tissues to be discriminated. Some ideas on how to choose the optimum order are discussed.     

Asymptotic Behaviour of the Number of Labelled Essential Acyclic Digraphs and Labelled Chain Graphs

We provide an asymptotic formula for the number of labelled essential DAGs a_n and show that lim_na_n/a_n=c, where a_n is the number of labelled DAGs and c13.65, which is interesting in the field of Bayesian networks. Furthermore, we present an asymptotic formula for the number of labelled chain graphs.Acknowledgment. I would like to thank Prof. Peter Grabner for his support and very helpful discussions, which where constitutive for this article. I am also thankful to the referees for their comments.This Research was supported by the Austrian Science Fund (FWF), START-Project Y96-MATFinal version received: January 28, 2004     

Bayesian networks applied to credit scoring

Email: kchang{at}gmu.eduEmail: RobertFung{at}Fairlsaac.comEmail: alan.lucas{at}hotmail.com^¶Email: BobOliver{at}Fairlsaac.com^||Email: NShikaloff{at}Fairlsaac.com The objectives of this paper are to apply the theory and numericalalgorithms of Bayesian networks to risk scoring, and comparethe results with traditional methods for computing scores andposterior predictions of performance variables. Model identification,inference, and prediction of random variables using Bayesiannetworks have been successfully applied in a number of areas,including medical diagnosis, equipment failure, informationretrieval, rare-event prediction, and pattern recognition. Theability to graphically represent conditional dependencies andindependencies among random variables may also be useful incredit scoring. Although several papers have already appearedin the literature which use graphical models for model identification,as far as we know there have been no explicit experimental resultsthat compare a traditionally computed risk score with predictionsbased on Bayesian learning algorithms. In this paper, we examine a database of credit-card applicantsand attempt to ‘learn’ the graphical structure ofthe characteristics or variables that make up the database.We identify representative Bayesian networks in a developmentsample as well as the associated Markov blankets and cliquestructures within the Markov blanket. Once we obtain the structureof the underlying conditional independencies, we are able toestimate the probabilities of each node conditional on its directpredecessor node(s). We then calculate the posterior probabilitiesand scores of a performance variable for the development sample.Finally, we calculate the receiver operating characteristic(ROC) curves and relative profitability of scorecards basedon these identifications. The results of the different modelsand methods are compared with both development and validationsamples. Finally, we report on a statistical entropy calculationthat measures the degree to which cliques identified in theBayesian network are independent of one another.     

Approximate importance sampling Monte Carlo for data assimilation

Importance sampling Monte Carlo offers powerful approaches to approximating Bayesian updating in sequential problems. Specific classes of such approaches are known as particle filters. These procedures rely on the simulation of samples or ensembles of the unknown quantities and the calculation of associated weights for the ensemble members. As time evolves and/or when applied in high-dimensional settings, such as those of interest in many data assimilation problems, these weights typically display undesirable features. The key difficulty involves a collapse toward approximate distributions concentrating virtually all of their probability on an implausibly few ensemble members.

After reviewing ensembling, Monte Carlo, importance sampling and particle filters, we present some approximations intended to moderate the problem of collapsing weights. The motivations for these suggestions are combinations of (i) the idea that key dynamical behavior in many systems actually takes place on a low dimensional manifold, and (ii) notions of statistical dimension reduction. We illustrate our suggestions in a problem of inference for ocean surface winds and atmospheric pressure. Real observational data are used.     

Joint Monitoring of Several Types of Shocks in Normal Dynamic Linear Models: A Bayesian Decision Theoretic Approach

In this article we consider the sequential monitoring process in normal dynamic linear models as a Bayesian sequential decision problem. We use this approach to build a general procedure that jointly analyzes the existence of outliers, level changes, variance changes, and the development of local correlations. In addition, we study the frequentist performance of this procedure and compare it with the monitoring algorithm proposed in an earlier article.     

Bayesian Multiscale Smoothing for Making Inferences About Features in Scatterplots

A rather common problem of data analysis is to find interesting features, such as local minima, maxima, and trends in a scatterplot. Variance in the data can then be a problem and inferences about features must be made at some selected level of significance. The recently introduced SiZer technique uses a family of nonparametric smooths of the data to uncover features in a whole range of scales. To aid the analysis, a color map is generated that visualizes the inferences made about the significance of the features. The purpose of this article is to present Bayesian versions of SiZer methodology. Both an analytically solvable regression model and a fully Bayesian approach that uses Gibbs sampling are presented. The prior distributions of the smooths are based on a roughness penalty. Simulation based algorithms are proposed for making simultaneous inferences about the features in the data.