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

For estimating a lower bounded parametric function in the framework of Marchand and Strawderman [6], we provide through a unified approach a class of Bayesian confidence intervals with credibility $1-\alpha$ and frequentist coverage probability bounded below by $\frac{1-\alpha}{1+\alpha}$. In cases where the underlying pivotal distribution is symmetric, the findings represent extensions with respect to the specification of the credible set achieved through the choice of a spending function, and include Marchand and Strawderman’s HPD procedure result. For non-symmetric cases, the determination of a such a class of Bayesian credible sets fills a gap in the literature and includes an “equal-tails” modification of the HPD procedure. Several examples are presented demonstrating wide applicability.

/pdf/on-bayesian-credible-sets-restricted-parameter-spaces-and-306r83ijlw.pdf

On Bayesian credible sets, restricted parameter spaces and frequentist coverage

Empirical Bayes development of Honduran pine yield models

Bayes minimax estimation of the multivariate normal mean vector for the case of common unknown variance

Theory of Preliminary Test and Stein-Type Estimation With Applications. A. K. Md. Ehsanes Saleh

In this article, we develop a modern perspective on Akaike's information criterion and Mallows's Cp for model selection, and propose generalisations to spherically and elliptically symmetric distributions. Despite the differences in their respective motivation, Cp and Akaike's information criterion are equivalent in the special case of Gaussian linear regression. In this case, they are also equivalent to a third criterion, an unbiased estimator of the quadratic prediction loss, derived from loss estimation theory. We then show that the form of the unbiased estimator of the quadratic prediction loss under a Gaussian assumption still holds under a more general distributional assumption, the family of spherically symmetric distributions. One of the features of our results is that our criterion does not rely on the specificity of the distribution, but only on its spherical symmetry. The same kind of criterion can be derived for a family of elliptically contoured distribution, which allows correlations, when considering the invariant loss. More specifically, the unbiasedness property is relative to a distribution associated to the original density.

https://hal.archives-ouvertes.fr/hal-00851206/document

William E. Strawderman

Papers

On Bayesian credible sets, restricted parameter spaces and frequentist coverage

Empirical Bayes development of Honduran pine yield models

Bayes minimax estimation of the multivariate normal mean vector for the case of common unknown variance

Theory of Preliminary Test and Stein-Type Estimation With Applications. A. K. Md. Ehsanes Saleh

AIC, Cp and estimators of loss for elliptically symmetric distributions