Calculation of marginal densities for parameters of multinomial distributions

The full Bayesian analysis of multinomial data using informative and flexible prior distributions has, in the past, been restricted by the technical problems involved in performing the numerical integrations required to obtain marginal densities for parameters and other functions thereof. In this paper it is shown that Gibbs sampling is suitable for obtaining accurate approximations to marginal densities for a large and flexible family of posterior distributions—the family. The method is illustrated with a three-way contingency table. Two alternative Monte Carlo strategies are also discussed.     

A fast splitting procedure for classification trees

This paper provides a faster method to find the best split at each node when using the CART methodology. The predictability index is proposed as a splitting rule for growing the same classification tree as CART does when using the Gini index of heterogeneity as an impurity measure. A theorem is introduced to show a new property of the index : the for a given predictor has a value not lower than the for any split generated by the predictor. This property is used to make a substantial saving in the time required to generate a classification tree. Three simulation studies are presented in order to show the computational gain in terms of both the number of splits analysed at each node and the CPU time. The proposed splitting algorithm can prove computational efficiency in real data sets as shown in an example.     

Winding Stairs: A sampling tool to compute sensitivity indices

Sensitivity analysis aims to ascertain how each model input factor influences the variation in the model output. In performing global sensitivity analysis, we often encounter the problem of selecting the required number of runs in order to estimate the first order and/or the total indices accurately at a reasonable computational cost. The Winding Stairs sampling scheme (Jansen M.J.W., Rossing W.A.H., and Daamen R.A. 1994. In: Gasman J. and van Straten G. (Eds.), Predictability and Nonlinear Modelling in Natural Sciences and Economics. pp. 334–343.) is designed to provide an economic way to compute these indices. The main advantage of it is the multiple use of model evaluations, hence reducing the total number of model evaluations by more than half. The scheme is used in three simulation studies to compare its performance with the classic Sobol' LP. Results suggest that the Jansen Winding Stairs method provides better estimates of the Total Sensitivity Indices at small sample sizes.     

Sample Size Calculation for Rank Tests Comparing K Survival Distributions

Rank tests, such as logrank or Wilcoxon rank sum tests, have been popularly used to compare survival distributions of two or more groups in the presence of right censoring. However, there has been little research on sample size calculation methods for rank tests to compare more than two groups. An existing method is based on a crude approximation, which tends to underestimate sample size, i.e., the calculated sample size has lower power than projected. In this paper we propose an asymptotically correct method and an approximate method for sample size calculation. The proposed methods are compared to other methods through simulation studies.     

Simultaneous inference on diversity of biological communities

In environmental statistics, surveys on the structure of biological communities are generally carried out by focusing on diversity indexes. A more complete analysis may be performed by means of an appropriate function giving a spectrum of different measures of diversity: diversity profiles. They can be expressed as a function of the unknown abundance vector of the ecological population. In this paper we develop a non parametric approach based on bootstrap in order to make inference on diversity profiles. The proposed procedure is applied on biological data of four parks in Milan, Italy.     

Sensitivity analysis approaches to high-dimensional screening problems at low sample size

Sensitivity analysis is an essential tool in the development of robust models for engineering, physical sciences, economics and policy-making, but typically requires running the model a large number of times in order to estimate sensitivity measures. While statistical emulators allow sensitivity analysis even on complex models, they only perform well with a moderately low number of model inputs: in higher dimensional problems they tend to require a restrictively high number of model runs unless the model is relatively linear. Therefore, an open question is how to tackle sensitivity problems in higher dimensionalities, at very low sample sizes. This article examines the relative performance of four sampling-based measures which can be used in such high-dimensional nonlinear problems. The measures tested are the Sobol' total sensitivity indices, the absolute mean of elementary effects, a derivative-based global sensitivity measure, and a modified derivative-based measure. Performance is assessed in a ‘screening’ context, by assessing the ability of each measure to identify influential and non-influential inputs on a wide variety of test functions at different dimensionalities. The results show that the best-performing measure in the screening context is dependent on the model or function, but derivative-based measures have a significant potential at low sample sizes that is currently not widely recognised.     

Convexity-based clustering criteria: theory,algorithms, and applications in statistics

This paper deals with the construction of optimum partitions of for a clustering criterion which is based on a convex function of the class centroids as a generalization of the classical SSQ clustering criterion for n data points. We formulate a dual optimality problem involving two sets of variables and derive a maximum-support-plane (MSP) algorithm for constructing a (sub-)optimum partition as a generalized k-means algorithm. We present various modifications of the basic criterion and describe the corresponding MSP algorithm. It is shown that the method can also be used for solving optimality problems in classical statistics (maximizing Csiszárs -divergence) and for simultaneous classification of the rows and columns of a contingency table.     

Robust logistic regression modelling via the elastic net-type regularization and tuning parameter selection

The penalized logistic regression is a useful tool for classifying samples and feature selection. Although the methodology has been widely used in various fields of research, their performance takes a sudden turn for the worst in the presence of outlier, since the logistic regression is based on the maximum log-likelihood method which is sensitive to outliers. It implies that we cannot accurately classify samples and find important factors having crucial information for classification. To overcome the problem, we propose a robust penalized logistic regression based on a weighted likelihood methodology. We also derive an information criterion for choosing the tuning parameters, which is a vital matter in robust penalized logistic regression modelling in line with generalized information criteria. We demonstrate through Monte Carlo simulations and real-world example that the proposed robust modelling strategies perform well for sparse logistic regression modelling even in the presence of outliers.     

A tool to facilitate the production of control charts within a spreadsheet

Abstract

The adoption of control charts can be traced to the classic text by Shewhart (1931 Shewhart, W. A. 1931. Economic control of quality of manufactured product. London: Macmillan. ISBN: 1614278115. [Google Scholar]) and championed by many writers since then, including Deming (1982 Deming, W. E. 1982. Out of the crisis: Quality, productivity and competitive position. Cambridge: Cambridge University Press. ISBN: 0521305535. [Google Scholar]). Numerous other texts and publications stress the continuing importance of this area. While tables of key Shewhart control chart parameters are extremely useful they are easily lost or mislaid and can sometimes be difficult to interpret. To address this issue spreadsheet code is implemented to produce all the key control chart factors.     

A two-sample test for mean functions with increasing number of projections

We propose a test for equality of two means when data are functions and obtain the asymptotic properties of the test statistic as data dimension increases with the sample size. We also derive the asymptotic power of the test under some local alternatives and show that the test statistic is root-n consistent. A simulation study is conducted to evaluate the performance of the test numerically and to compare the proposed test with other existing four popular tests.