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 $p \geqslant 4$ and one observation $X$ on a $p$-dimensional spherically symmetric distribution, minimax estimators of $\theta$ whose risks are smaller than the risk of $X$ (the best invariant estimator) are found when the loss is a nondecreasing concave function of quadratic loss. For $n$ observations $X_1, X_2, \cdots, X_n$, we have classes of minimax estimators which are better than the usual procedures, such as the best invariant estimator, $\bar{X}$, or a maximum likelihood estimator.

/pdf/minimax-estimation-of-location-parameters-for-spherically-2dbz4syglc.pdf

Minimax estimation of location parameters for spherically symmetric distributions with concave loss

The Bayesian synthesis method (BSYN) was used to bound the uncertainty in projections calculated with PIPESTEM, a mechanistic model of forest growth. The application furnished posterior distributions of (a) the values of the model's parameters, and (b) the values of three of the model's output variables--basal area per unit land area, average tree height, and tree density--at different points in time. Confidence or credible intervals for the output variables were obtained directly from the posterior distributions. The application also provides estimates of correlation among the parameters and output variables. BSYN, which originally was applied to a population dynamics model for bowhead whales, is generally applicable to deterministic models. Extension to two or more linked models is discussed. A simple worked example is included in an appendix.

Assessing uncertainty in a stand growth model by Bayesian synthesis

Families of minimax estimators are found for the location parameter of a p-variate (p> or = 3) spherically symmetric unimodal(s.s.u.)distribution with respect to general quadratic loss. The estimators of James and Stein, Baranchik, Bock and Strawderman are all considered for this general problem. Specifically, when the loss is general quadratic loss given by L(delta,theta) = (delta - theta)'D(delta - theta) where D is a known pxp positive definite matrix, one main result, for one observation, X, on a multivariate s.s.u. distribution about theta, presents a class of minimax estimators whose risks dominate the risk of X, provided p> or = 3 and trace D > or equal 2dL where dL is the maximum eigenvalue of D. This class is given by Delta a,r(X)=(1-a(r(||X||2)/||X||2))X where 0 or = 4 and co = .96 when p=3.

Minimax Estimation of Location Parameters for Spherically Symmetric Unimodal Distributions under Quadratic Loss

Families of minimax estimators are found for the location parameter of a $p$-variate $(p \geqq 3)$ spherically symmetric unimodal distribution with respect to general quadratic loss. The estimators of James and Stein, Baranchik, Bock and Strawderman are all considered for this general problem. Specifically, when the loss is general quadratic loss given by $L(\delta, \theta) = (\delta - \theta)'D(\delta - \theta)$ where $D$ is a known $p \times p$ positive definite matrix, one main result, for one observation, $X$, on a multivariate s.s.u. distribution about $\theta$, presents a class of minimax estimators whose risk dominate the risk of $X$, provided $p \geqq 3$ and trace $D \geqq 2d_L$ where $d_L$ is the maximum eigenvalue of $D$. This class is given by $\delta_{a,r}(X) = (1 - a(r(\|X\|^2)/\|X\|^2)) X$ where $0 \leqq r(\bullet) \leqq 1, r(\|X\|^2)$ is nondecreasing, $r(\|X\|^2)/\|X\|^2$ is nonincreasing, and $0 \leqq a \leqq (c_0/E_0(\|X\|^{-2}))((\operatorname{trace} D/d_L) - 2)$, where $c_0 = 2p/((p + 2)(p - 2))$ when $p \geqq 4$ and $c_0 \approx .96$ when $p = 3$.

/pdf/minimax-estimation-of-location-parameters-for-spherically-18y6angoiw.pdf

Minimax Estimation of Location Parameters for Spherically Symmetric Unimodal Distributions Under Quadratic Loss

Suppose a random variable has a density belonging to a one parameter family which has strict monotone likelihood ratio. For inference regarding the parameter (or a monotone function of the parameter) consider the loss function to be bowl shaped for each fixed parameter and also to have each action be a "point of increase" or a "point of decrease" for some value of the parameter. Under these conditions, given any nonmonotone decision procedure, a unique monotone procedure is constructed which is strictly better than the given procedure for all the above loss functions. This result has application to the following areas: combining data problems, sufficiency, a multivariate one-sided testing problem.

/pdf/a-complete-class-theorem-for-strict-monotone-likelihood-3yg86rln9p.pdf

William E. Strawderman

Papers

Minimax estimation of location parameters for spherically symmetric distributions with concave loss

Assessing uncertainty in a stand growth model by Bayesian synthesis

Minimax Estimation of Location Parameters for Spherically Symmetric Unimodal Distributions under Quadratic Loss

Minimax Estimation of Location Parameters for Spherically Symmetric Unimodal Distributions Under Quadratic Loss

A Complete Class Theorem for Strict Monotone Likelihood Ratio With Applications