Nonparametric Predictive Inference in Statistical Process Control

Journal of Statistical Theory and Practice

Himd

2014

Reproducibility of tests is an important characteristic of the practical relevance of test outcomes. Recently, there has been substantial interest in the reproducibility probability (RP), where not only its estimation but also its actual definition and interpretation are not uniquely determined in the classical frequentist statistics framework. Nonparametric predictive inference (NPI) is a frequentist statistics approach that makes few assumptions, enabled by the use of lower and upper probabilities to quantify uncertainty, and that explicitly focuses on future observations. The explicitly predictive nature of NPI provides a natural formulation for inferences on RP. In this article, we introduce the NPI approach to RP for some basic nonparametric tests.

Section: Nonparametric Predictive Inference For the Reproducibility Pmentioning

confidence: 97%

Nonparametric Predictive Inference for Reproducibility of Basic Nonparametric Tests

Journal of Statistical Theory and Practice

Himd

2014

“…NPI for real-valued observations is also available for multiple future observations (Arts et al, 2004;Coolen, 2011), where the inter-dependence of these future observations is explicitly taken into account. Development of NPI-based methods for diagnostic accuracy with explicit focus on m ≥ 2 future observations is an interesting topic for future research, where particularly the strength of the inferences as function of m should be studied carefully, see Coolen and Coolen-Schrijner (2007) for a similar study with focus on the role of m for comparison of groups of Bernoulli data.…”

Section: Discussionmentioning

confidence: 99%

Three-group ROC analysis: A nonparametric predictive approach

Coolen‐Maturi

Elkhafifi

Computational Statistics & Data Analysis

2014

. (2014) Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractMeasuring the accuracy of diagnostic tests is crucial in many application areas, in particular medicine and health care. The receiver operating characteristic (ROC) surface is a useful tool to assess the ability of a diagnostic test to discriminate among three ordered classes or groups. In this paper, nonparametric predictive inference (NPI) for three-group ROC analysis is presented. NPI is a frequentist statistical method that is explicitly aimed at using few modelling assumptions in addition to data, enabled through the use of lower and upper probabilities to quantify uncertainty. It focuses exclusively on a future observation, which may be particularly relevant if one considers decisions about a diagnostic test to be applied to a future patient. This paper presents the NPI approach to three-group ROC analysis, including results on the volumes under the ROC surfaces and choice of decision thresholds for the diagnosis.

“…For examples of the use of these lower and upper probabilities (4) and (5) for nonparametric predictive inference (NPI) in statistics and operational research, see (Arts et al, 2004;Coolen, 1996a;Coolen and Coolen-Schrijner, 2000;Coolen and Coolen-Schrijner, 2003;Coolen and van der Laan, 2001). In these papers, NPI is also compared with more established methods, both via examples using data from the literature, and simulation studies, leading to the conclusion that NPI performs well.…”

Section: Nonparametric Predictive Inferencementioning

confidence: 99%

On Nonparametric Predictive Inference and Objective Bayesianism

2006

JoLLI

Self Cite

111

Abstract. This paper consists of three main parts. First, we give an introduction to Hill's assumption A (n) and to theory of interval probability, and an overview of recently developed theory and methods for nonparametric predictive inference (NPI), which is based on A (n) and uses interval probability to quantify uncertainty. Thereafter, we illustrate NPI by introducing a variation to the assumption A (n) , suitable for inference based on circular data, with applications to several data sets from the literature. This includes attention to comparison of two groups of circular data, and to grouped data. We briefly discuss such inference for multiple future observations. We end the paper with a discussion of NPI and objective Bayesianism.