Discussion of ‘Modern Statistics for Spatial Point Processes’

Abstract. The paper ‘Modern statistics for spatial point processes’ by Jesper Møller and Rasmus P. Waagepetersen is based on a special invited lecture given by the authors at the 21st Nordic Conference on Mathematical Statistics, held at Rebild, Denmark, in June 2006. At the conference, Antti Penttinen and Eva B. Vedel Jensen were invited to discuss the paper. We here present the comments from the two invited discussants and from a number of other scholars, as well as the authors’ responses to these comments. Below Figure 1, Figure 2, etc., refer to figures in the paper under discussion, while Figure A , Figure B , etc., refer to figures in the current discussion. All numbered sections and formulas refer to the paper.

Figure A Open in figure viewer PowerPoint The estimate of A(k) (solid curve) and pointwise maximum and minimum envelopes (dotted curves) from 99 simulations under independent marking, conditional on the point locations. Zero boundary has been applied.     

Idle thoughts of a ‘well‐calibrated’ Bayesian in clinical drug development

The use of Bayesian approaches in the regulated world of pharmaceutical drug development has not been without its difficulties or its critics. The recent Food and Drug Administration regulatory guidance on the use of Bayesian approaches in device submissions has mandated an investigation into the operating characteristics of Bayesian approaches and has suggested how to make adjustments in order that the proposed approaches are in a sense calibrated. In this paper, I present examples of frequentist calibration of Bayesian procedures and argue that we need not necessarily aim for perfect calibration but should be allowed to use procedures, which are well‐calibrated, a position supported by the guidance. Copyright © 2016 John Wiley & Sons, Ltd.     

Statistical Analysis of ‘Probabilities of Causation’ Using Co‐variate Information

Abstract. This article deals with two problems concering the probabilities of causation defined by Pearl (Causality: models, reasoning, and inference, 2nd edn, 2009, Cambridge University Press, New York) namely, the probability that one observed event was a necessary (or sufficient, or both) cause of another; one is to derive new bounds, and the other is to provide the covariate selection criteria. Tian & Pearl (Ann. Math. Artif. Intell., 28, 2000, 287–313) showed how to bound the probabilities of causation using information from experimental and observational studies, with minimal assumptions about the data‐generating process, and identifiable conditions for these probabilities. In this article, we derive narrower bounds using covariate information that is available from those studies. In addition, we propose the conditional monotonicity assumption so as to further narrow the bounds. Moreover, we discuss the covariate selection problem from the viewpoint of the estimation accuracy, and show that selecting a covariate that has a direct effect on an outcome variable cannot always improve the estimation accuracy, which is contrary to the situation in linear regression models. These results provide more accurate information for public policy, legal determination of responsibility and personal decision making.     

A class of tests for testing ‘new is better than used’

A class of tests is proposed for testing H₀ F?(x) = e^?λx, λ > 0, x≥0 vs. H₁ F?(x + y) ≤ F?(x)F?(y), x, y≥0, with strict inequality for some x, y ≥ 0 (F = new is better than used). Efficiency comparisons of some tests within the class are made and a new test is proposed on the basis of these comparisons. Consistency and the asymptotic normality of the class of tests is proved under fairly broad conditions on the underlying entities.     

Discussion on ‘Detection of intrusions in information systems by sequential change-point methods’ by Tartakovsky, Rozovskii, Blažek, and Kim

The discussion points on the inadequacy of the ARL as an index of efficiency of a detection procedure for change points. It is shown that the FAR=1/ARL might be small, while the probability of false alarm (PFA) is at the same time considerable. This is illustrated with simulation runs, using the Shiryayev–Roberts detection procedure. The need to develop procedures based on continuous monitoring is also mentioned.     

Issues in applying recent CPMP ‘Points to Consider’ and FDA guidance documents with biostatistical implications

The International Conference on Harmonisation guideline ‘Statistical Principles for Clinical Trials’ was adopted by the Committee for Proprietary Medicinal Products (CPMP) in March 1998, and consequently is operational in Europe. Since then more detailed guidance on selected topics has been issued by the CPMP in the form of ‘Points to Consider’ documents. The intent of these was to give guidance particularly to non‐statistical reviewers within regulatory authorities, although of course they also provide a good source of information for pharmaceutical industry statisticians. In addition, the Food and Drug Administration has recently issued a draft guideline on data monitoring committees. In November 2002 a one‐day discussion forum was held in London by Statisticians in the Pharmaceutical Industry (PSI). The aim of the meeting was to discuss how statisticians were responding to some of the issues covered in these new guidelines, and to document consensus views where they existed. The forum was attended by industry, academic and regulatory statisticians. This paper outlines the questions raised, resulting discussions and consensus views reached. It is clear from the guidelines and discussions at the workshop that the statistical analysis strategy must be planned during the design phase of a clinical trial and carefully documented. Once the study is complete the analysis strategy should be thoughtfully executed and the findings reported. Copyright © 2003 John Wiley & Sons, Ltd.     

A discussion on ‘Detection of intrusions in information systems by sequential change-point methods’ by Tartakovsky, Rozovskii, Blažek, and Kim

Tartakovsky et al. provide us with, and should be thanked for, an illuminating introduction to the problems of detecting intrusions and other denial of services attacks, and a thorough discussion and analysis of the relevance of CUSUM-based change detection algorithms for this purpose.This discussion mainly addresses three issues: introducing a minimum change magnitude, adaptation and tuning of CUSUM algorithms, and processing binary quantized data. The influence of the adaptation in the NP-CUSUM algorithm on its performances is questioned.     

A flexible class of models for data arising from a ‘thorough QT/QTc study’

The standard methods for analyzing data arising from a ‘thorough QT/QTc study’ are based on multivariate normal models with common variance structure for both drug and placebo. Such modeling assumptions may be violated and when the sample sizes are small, the statistical inference can be sensitive to such stringent assumptions. This article proposes a flexible class of parametric models to address the above‐mentioned limitations of the currently used models. A Bayesian methodology is used for data analysis and models are compared using the deviance information criteria. Superior performance of the proposed models over the current models is illustrated through a real dataset obtained from a GlaxoSmithKline (GSK) conducted ‘thorough QT/QTc study’. Copyright © 2010 John Wiley & Sons, Ltd.     

GETTING THE ‘CORRECT’ ANSWER FROM SURVEY RESPONSES: A SIMPLE APPLICATION OF THE EM ALGORITHM

This note addresses a problem that can arise in surveys, namely when some respondents misinterpret the rating method and so assign high ratings when they intended to assign low ratings, and vice versa. We present a method that allows these misinterpretations to be corrected with high probability, and more meaningful conclusions to be drawn. The method is illustrated with data from a Community Value survey.     

Estimation of Pr{yp > max(y1, …, yp-1)}: Predictive approach in exponential case

The structural-inference approach to predictive distributions is used to derive the estimator of P = Pr{Y_p > max(Y₁, …, Y_p-₁)} when the independent random variables Y₁, …, Y_p follow exponential distributions with unequal location parameters and equal scale parameters. The result is Equation (4.6).