Nonparametric regression is a set of techniques for estimating a regression curve without making strong assumptions about the shape of the true regression function. These techniques are therefore useful for building and checking parametric models, as well as for data description. Kernel and nearest-neighbor regression estimators are local versions of univariate location estimators, and so they can readily be introduced to beginning students and consulting clients who are familiar with such summaries as the sample mean and median.

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An Introduction to Kernel and Nearest-Neighbor Nonparametric Regression

: The classification maximum likelihood approach is sufficiently general to encompass many current clustering algorithms, including those based on the sum of squares criterion and on the criterion of Friedman and Rubin (1967). However, as currently implemented, it does not allow the specification of which features (orientation, size and shape) are to be common to all clusters and which may differ between clusters. Also, it is restricted to Gaussian distributions and it does not allow for noise. We propose ways of overcoming these limitations. A reparameterization of the covariance matrix allows us to specify that some features, but not all, be the same for all clusters. A practical framework for non-Gaussian clustering is outlined, and a means of incorporating noise in the form of a Poisson process is described. An approximate Bayesian method for choosing the number of clusters is given. The performance of the proposed methods is studied by simulation, with encouraging results. The methods are applied to the analysis of a data set arising in the study of diabetes, and the results seem better than those of previous analyses. (RH)

Model-based Gaussian and non-Gaussian clustering

This paper reviews the literature on Bayesian experimental design. A unified view of this topic is presented, based on a decision-theoretic approach. This framework casts criteria from the Bayesian literature of design as part of a single coherent approach. The decision-theoretic structure incorporates both linear and nonlinear design problems and it suggests possible new directions to the experimental design problem, motivated by the use of new utility functions. We show that, in some special cases of linear design problems, Bayesian solutions change in a sensible way when the prior distribution and the utility function are modified to allow for the specific structure of the experiment. The decision-theoretic approach also gives a mathematical justification for selecting the appropriate optimality criterion.

/pdf/bayesian-experimental-design-a-review-1z4pqf25ac.pdf

Bayesian Experimental Design: A Review

Many survival studies record the times to two or more distinct failures on each subject. The failures may be events of different natures or may be repetitions of the same kind of event. In this article, we consider the regression analysis of such multivariate failure time observations. Each marginal distribution of the failure times is formulated by a Cox proportional hazards model. No specific structure of dependence among the distinct failure times on each subject is imposed. The regression parameters in the Cox models are estimated by maximizing the failure-specific partial likelihoods. The resulting estimators are shown to be asymptotically jointly normal with a covariance matrix that can be consistently estimated. Simultaneous inferential procedures are then proposed. Extensive Monte Carlo studies indicate that the normal approximation is adequate for practical use. The new methods allow time-dependent covariates, missing observations, and arbitrary patterns of censorship. They are illustrat...

Regression analysis of multivariate incomplete failure time data by modeling marginal distributions

The purpose of this article is to provide a survey of the various stages in the development of response surface methodology RSM. The coverage of these stages is organized in three parts that describe the evolution of RSM since its introduction in the early 1950s. Part I covers the period, 1951-1975, during which the so-called classical RSM was developed. This includes a review of basic experimental designs for fitting linear response surface models, in addition to a description of methods for the determination of optimum operating conditions. Part II, which covers the period, 1976-1999, discusses more recent modeling techniques in RSM, in addition to a coverage of Taguchi's robust parameter design and its response surface alternative approach. Part III provides a coverage of further extensions and research directions in modern RSM. This includes discussions concerning response surface models with random effects, generalized linear models, and graphical techniques for comparing response surface designs. Copyright © 2010 John Wiley & Sons, Inc.

Response Surface Methodology.

Data: A Collection of Problems from Many Fields for the Student and Research Worker

SUMMARY Three properties of interest in bioavailability studies using compartmental models are the area under the concentration curve, the maximum concentration, and the time to maximum concentration Methods are described for finding designs that minimize the variance of the estimates of these quantities in such a model These methods use prior information Both prior estimates and prior distributions are used The designs for an open one-compartment model are compared with the corresponding D,-optimum design for all parameters and also with designs that minimize the sum of the scaled variances of the individual properties

Agnes M. Herzberg

Papers

Data: A Collection of Problems from Many Fields for the Student and Research Worker

Optimum Experimental Designs for Properties of a Compartmental Model

Some Considerations in the Optimal Design of Experiments in Non-Optimal Situations

Elemental information matrices and optimal experimental design for generalized regression models

The robustness and optimality of response surface designs