We generalize the method proposed by Gelman and Rubin (1992a) for monitoring the convergence of iterative simulations by comparing between and within variances of multiple chains, in order to obtain a family of tests for convergence. We review methods of inference from simulations in order to develop convergence-monitoring summaries that are relevant for the purposes for which the simulations are used. We recommend applying a battery of tests for mixing based on the comparison of inferences from individual sequences and from the mixture of sequences. Finally, we discuss multivariate analogues, for assessing convergence of several parameters simultaneously.

/pdf/general-methods-for-monitoring-convergence-of-iterative-45g63vyekv.pdf

General methods for monitoring convergence of iterative simulations

http://www.geog.ucl.ac.uk/~mdisney/teaching/PPRS/papers/foody.pdf

Status of land cover classification accuracy assessment

Publishing data about individuals without revealing sensitive information about them is an important problem. In recent years, a new definition of privacy called k-anonymity has gained popularity. In a k-anonymized dataset, each record is indistinguishable from at least k − 1 other records with respect to certain identifying attributes.In this article, we show using two simple attacks that a k-anonymized dataset has some subtle but severe privacy problems. First, an attacker can discover the values of sensitive attributes when there is little diversity in those sensitive attributes. This is a known problem. Second, attackers often have background knowledge, and we show that k-anonymity does not guarantee privacy against attackers using background knowledge. We give a detailed analysis of these two attacks, and we propose a novel and powerful privacy criterion called e-diversity that can defend against such attacks. In addition to building a formal foundation for e-diversity, we show in an experimental evaluation that e-diversity is practical and can be implemented efficiently.

/pdf/l-diversity-privacy-beyond-k-anonymity-54qdj1526d.pdf

L-diversity: Privacy beyond k-anonymity

On robust estimation of the location parameter

The objective of this paper is to provide a basic framework for researchers interested in reporting the results of their PLS analyses. Since the dominant paradigm in reporting Structural Equation Modeling results is covariance based, this paper begins by providing a discussion of key differences and rationale that researchers can use to support their use of PLS. This is followed by two examples from the discipline of Information Systems. The first consists of constructs with reflective indicators (mode A). This is followed up with a model that includes a construct with formative indicators (mode B).

Chapter 28 How to Write Up and Report PLS Analyses

This paper reviews minimax best equivariant estimation in these invariant estimation problems: a location parameter, a scale parameter and a (Wishart) covariance matrix. We briefly review development of the best equivariant estimator as a generalized Bayes estimator relative to right invariant Haar measure in each case. Then we prove minimaxity of the best equivariant procedure by giving a least favorable prior sequence based on non-truncated Gaussian distributions. The results in this paper are all known, but we bring a fresh and somewhat unified approach by using, in contrast to most proofs in the literature, a smooth sequence of non truncated priors. This approach leads to some simplifications in the minimaxity proofs.

A Gaussian sequence approach for proving minimaxity: A Review

During the course of a scientific investigation, it is common to consider more than one model to explain or predict the phenomenon of interest. In some cases, it might be wise to cull the candidate models to a manageable number, and then use model averaging methods. However, often a scientist needs/wants to select a single model. In this chapter we consider the situation in which a scientist would like to select one of the candidate models to use for inference. Model selection shares many concepts with hypothesis testing, and so we begin this chapter with a discussion of hypothesis testing.

Hypothesis Testing and Model Choice

In this chapter, we will consider the problem of estimating a location vector which is constrained to lie in a convex subset of \(\mathbb {R}^P\). Estimators that are constrained to a set should be constrasted to the shrinkage estimators discussed in Sect. 2.4.4 where one has “vague knowledge” that a location vector is in or near the specified set and consequently wishes to shrink toward the set but does not wish to restrict the estimator to lie in the set. Much of the chapter is devoted to one of two types of constraint sets, balls, and polyhedral cones. However, Sect.7.2 is devoted to general convex constraint sets and more particularly to a striking result of Hartigan (2004) which shows that in the normal case, the Bayes estimator of the mean with respect to the uniform prior over any convex set, \(\mathcal {C}\), dominates X for all \(\theta \in \mathcal {C}\) under the usual quadratic loss ∥δ − θ∥2.

Restricted Parameter Spaces

In estimating the variance of a normal distribution when the loss function is essentially squared error, a sequential version of Stein's estimator is used to show the existence of sequential estimators which are better both in risk (expected loss) and sample size than the usual estimator of a given fixed sample size

William E. Strawderman

Papers

A Gaussian sequence approach for proving minimaxity: A Review

Hypothesis Testing and Model Choice

Restricted Parameter Spaces

Sequential estimation of the variance of a normal distribution

A unified approach to non-minimaxity of sets of linear combinations of restricted location estimators