Prediction-based classification for longitudinal biomarkers

Assessment of circulating CD4 count change over time in HIV-infected subjects on antiretroviral therapy (ART) is a central component of disease monitoring. The increasing number of HIV-infected subjects starting therapy and the limited capacity to support CD4 count testing within resource-limited settings have fueled interest in identifying correlates of CD4 count change such as total lymphocyte count, among others. The application of modeling techniques will be essential to this endeavor due to the typically nonlinear CD4 trajectory over time and the multiple input variables necessary for capturing CD4 variability. We propose a prediction-based classification approach that involves first stage modeling and subsequent classification based on clinically meaningful thresholds. This approach draws on existing analytical methods described in the receiver operating characteristic curve literature while presenting an extension for handling a continuous outcome. Application of this method to an independent test sample results in greater than 98% positive predictive value for CD4 count change. The prediction algorithm is derived based on a cohort of $n=270$ HIV-1 infected individuals from the Royal Free Hospital, London who were followed for up to three years from initiation of ART. A test sample comprised of $n=72$ individuals from Philadelphia and followed for a similar length of time is used for validation. Results suggest that this approach may be a useful tool for prioritizing limited laboratory resources for CD4 testing after subjects start antiretroviral therapy.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS326 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Bayesian Learning for a Class of Priors with Prescribed Marginals

We present Bayesian updating of an imprecise probability measure, represented by a class of precise multidimensional probability measures. Choice and analysis of our class are motivated by expert interviews that we conducted with modelers in the context of climatic change. From the interviews we deduce that generically, experts hold a much more informed opinion on the marginals of uncertain parameters rather than on their correlations. Accordingly, we specify the class by prescribing precise measures for the marginals while letting the correlation structure subject to complete ignorance. For sake of transparency, our discussion focuses on the tutorial example of a linear two-dimensional Gaussian model. We operationalize Bayesian learning for that class by various updating rules, starting with (a modified version of) the generalized Bayes' rule and the maximum likelihood update rule (after Gilboa and Schmeidler). Over a large range of potential observations, the generalized Bayes' rule would provide non-informative results. We restrict this counter-intuitive and unnecessary growth of uncertainty by two means, the discussion of which refers to any kind of imprecise model, not only to our class. First, we find our class of priors too inclusive and, hence, require certain additional properties of prior measures in terms of smoothness of probability density functions. Second, we argue that both updating rules are dissatisfying, the generalized Bayes' rule being too conservative, i.e., too inclusive, the maximum likelihood rule being too exclusive. Instead, we introduce two new ways of Bayesian updating of imprecise probabilities: a ``weighted maximum likelihood method'' and a ``semi-classical method.'' The former bases Bayesian updating on the whole set of priors, however, with weighted influence of its members. By referring to the whole set, the weighted maximum likelihood method allows for more robust inferences than the standard maximum likelihood method and, hence, is better to justify than the latter.Furthermore, the semi-classical method is more objective than the weighted maximum likelihood method as it does not require the subjective definition of a weighting function. Both new methods reveal much more informative results than the generalized Bayes' rule, what we demonstrate for the example of a stylized insurance model

CHIRPS: Explaining random forest classification

Modern machine learning methods typically produce “black box” models that are opaque to interpretation. Yet, their demand has been increasing in the Human-in-the-Loop pro-cesses, that is, those processes that require a human agent to verify, approve or reason about the automated decisions before they can be applied. To facilitate this interpretation, we propose Collection of High Importance Random Path Snippets (CHIRPS); a novel algorithm for explaining random forest classification per data instance. CHIRPS extracts a decision path from each tree in the forest that contributes to the majority classification, and then uses frequent pattern mining to identify the most commonly occurring split conditions. Then a simple, conjunctive form rule is constructed where the antecedent terms are derived from the attributes that had the most influence on the classification. This rule is returned alongside estimates of the rule’s precision and coverage on the training data along with counter-factual details. An experimental study involving nine data sets shows that classification rules returned by CHIRPS have a precision at least as high as the state of the art when evaluated on unseen data (0.91–0.99) and offer a much greater coverage (0.04–0.54). Furthermore, CHIRPS uniquely controls against under- and over-fitting solutions by maximising novel objective functions that are better suited to the local (per instance) explanation setting

VSS : a VHDL synthesis system

This report describes a register transfer synthesis system that allows a designer to interact with the design process. The designer can modify the compiled design by changing the input description, selecting optimization and mapping strategies, or graphically changing the generated design schematic. The VHDL language is used for input and output descriptions. An intermediate representation which incorporates signal typing and component attributes simplifies compilation and facilitates design optimization. The compilation process consists of two phases. First, a design composed of generic components is synthesized from the input description. Second, this design is translated into components from a particular library by a mapper and optimized by a logic optimizer. Redesign to new technologies can be accomplished by changing only the component library

Cumulative sum quality control charts design and applications

Includes bibliographical references (pages 165-169).Classical Statistical Process Control Charts are essential in Statistical Control exercises and thus constantly obtained attention for quality improvements. However, the establishment of control charts requires large-sample data (say, no less than I 000 data points). On the other hand, we notice that the small-sample based Grey System Theory Approach is well-established and applied in many areas: social, economic, industrial, military and scientific research fields. In this research, the short time trend curve in terms of GM( I, I) model will be merged into Shewhart and CU SUM two-sided version control charts and establish Grey Predictive Shewhart Control chart and Grey Predictive CUSUM control chart. On the other hand the GM(2, I) model is briefly checked its of how accurate it could be as compared to GM( I, 1) model in control charts. Industrial process data collected from TBF Packaging Machine Company in Taiwan was analyzed in terms of these new developments as an illustrative example for grey quality control charts

Modeling of systems

The handbook contains the fundamentals of modeling of complex systems. The classification of mathematical models is represented and the methods of their construction are given. The analytical modeling of the basic types of processes in the complex systems is considered. The principles of simulation, statistical and business processes modeling are described. The handbook is oriented on students of higher education establishments that obtain a degree in directions of “Software engineering” and “Computer science” as well as on lecturers and specialists in the domain of computer modeling

Tools for Composite Indicators Building

Our society is changing so fast we need to know as soon as possible when things go wrong (Euroabstracts, 2003). This is where composite indicators enter into the discussion. A composite indicator is an aggregated index comprising individual indicators and weights that commonly represent the relative importance of each indicator. However, the construction of a composite indicator is not straightforward and the methodological challenges raise a series of technical issues that, if not addressed adequately, can lead to composite indicators being misinterpreted or manipulated. Therefore, careful attention needs to be given to their construction and subsequent use. This document reviews the steps involved in a composite indicator’s construction process and discusses the common pitfalls to be avoided. We stress the need for multivariate analysis prior to the aggregation of the individual indicators. We deal with the problem of missing data and with the techniques used to bring into a common unit the indicators that are of very different nature. We explore different methodologies for weighting and aggregating indicators into a composite and test the robustness of the composite using uncertainty and sensitivity analysis. Finally we show how the same information that is communicated by the composite indicator can be presented in very different ways and how this can influence the policy message.JRC.G.9-Econometrics and statistical support to antifrau