We consider problems involving groups of data where each observation within a group is a draw from a mixture model and where it is desirable to share mixture components between groups. We assume that the number of mixture components is unknown a priori and is to be inferred from the data. In this setting it is natural to consider sets of Dirichlet processes, one for each group, where the well-known clustering property of the Dirichlet process provides a nonparametric prior for the number of mixture components within each group. Given our desire to tie the mixture models in the various groups, we consider a hierarchical model, specifically one in which the base measure for the child Dirichlet processes is itself distributed according to a Dirichlet process. Such a base measure being discrete, the child Dirichlet processes necessarily share atoms. Thus, as desired, the mixture models in the different groups necessarily share mixture components. We discuss representations of hierarchical Dirichlet processes ...

/pdf/hierarchical-dirichlet-processes-5fvop2j00w.pdf

Hierarchical Dirichlet Processes

An overview is given of current research on control charting methods for process monitoring and improvement. A historical perspective and ideas for future research also are given. Research topics include: variable sample size and sampling interval met..

Research Issues and Ideas in Statistical Process Control

In this paper we discuss the basic procedures for the implementation of multivariate statistical process control via control charting. Furthermore, we review multivariate extensions for all kinds of univariate control charts, such as multivariate Shewhart-type control charts, multivariate CUSUM control charts and multivariate EWMA control charts. In addition, we review unique procedures for the construction of multivariate control charts, based on multivariate statistical techniques such as principal components analysis (PCA) and partial lest squares (PLS). Finally, we describe the most significant methods for the interpretation of an out-of-control signal.

/pdf/multivariate-statistical-process-control-charts-an-overview-1vbmsl9ae7.pdf

Multivariate statistical process control charts: an overview

Multivariate Statistical Process Control Charts: An Overview

In a randomized experiment comparing two treatments, there is interference between units if applying the treatment to one unit may affect other units. Interference implies that treatment effects are not comparisons of two potential responses that a unit may exhibit, one under treatment and the other under control, but instead are inherently more complex. Interference is common in social settings where people communicate, compete, or spread disease; in studies that treat one part of an organism using a symmetrical part as control; in studies that apply different treatments to the same organism at different times; and in many other situations. Available statistical tools are limited. For instance, Fisher's sharp null hypothesis of no treatment effect implicitly entails no interference, and so his randomization test may be used to test no effect, but conventional ways of inverting the test to obtain confidence intervals, say for an additive effect, are not applicable with interference. Another commonly used ...

Interference Between Units in Randomized Experiments

The literature on nonparametric or distribution-free control charts for univariate variables data is examined. The advantages of these charts have over more traditional distribution-based control charts are demonstrated. Constructive criticism of the li..

Nonparametric Control Charts: An Overview and Some Results

Distribution-free Shewhart-type control charts are proposed for future sample percentiles based on a reference sample. These charts have a key advantage that their in-control run length distribution do not depend on the underlying continuous process distribution. Tables are given to help implement the charts for given sample sizes and false alarm rates. Expressions for the exact run length distribution and the average run length (ARL) are obtained using expectation by conditioning. Properties of the charts are studied, via evaluations of the run length distribution and the ARL. These computations show that in certain cases the proposed charts have attractive ARL properties over standard parametric charts such as the CUSUM and the EWMA. Calculations are illustrated with several short examples. Also included is a numerical example, using data from Montgomery (1997), where an application of the precedence chart produced slightly different results.

/pdf/a-class-of-distribution-free-control-charts-1oc8fts0si.pdf

A class of distribution-free control charts

A class of Shewhart-type distribution-free control charts is considered. A key advantage of these charts is that the in-control run length distribution is the same for all continuous process distributions. Exact expressions for the run length distribution and the average run length (ARL) are derived and properties of the charts are studied via evaluations of the run length distribution probabilities and the ARL. Tables are provided for implementation for some typical ARL values and false alarm rates. The charts proposed are preferable from a robustness point of view, have attractive ARL properties and would be particularly useful in situations where one uses a classical Shewhart X-chart. A numerical illustration is given.

/pdf/a-class-of-distribution-free-control-charts-36d58fmkmg.pdf

An overview of some nonparametric procedures based on precedence (or exceedance) statistics is given. The procedures include both tests and confidence intervals. In particular, the construction of some simple distribution-free confidence bounds for location difference of two distributions with the same shape is considered and some properties are derived. The asymptotic relative efficiency of an asymptotic form of the corresponding test relative to Wilcoxon's two-sample rank sum test and the two-sample Student t-test is given for various cases. Some K-sample problems are discussed where precedence-type tests are useful, along with a review of the literature.

/pdf/precedence-tests-and-confidence-bounds-for-complete-data-an-4g04qi46tk.pdf

Precedence tests and confidence bounds for complete data : an overview and some results

https://pure.tue.nl/ws/files/1406505/513887.pdf

van der P Paul Laan

Papers

Nonparametric Control Charts: An Overview and Some Results

A class of distribution-free control charts

A class of distribution-free control charts

Precedence tests and confidence bounds for complete data : an overview and some results

Imprecise predictive selection based on low structure assumptions