Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Nomenclature
- 1 Overview of biomedical image analysis
- Part I Signals and systems, image formation, and image modality
- Part II Stochastic models
- 4 Random variables
- 5 Random processes
- 6 Basics of random fields
- 7 Probability density estimation by linear models
- Part III Computational geometry
- Part IV Variational approaches and level sets
- Part V Image analysis tools
- Index
- References
4 - Random variables
from Part II - Stochastic models
Published online by Cambridge University Press: 05 November 2014
- Frontmatter
- Dedication
- Contents
- Preface
- Nomenclature
- 1 Overview of biomedical image analysis
- Part I Signals and systems, image formation, and image modality
- Part II Stochastic models
- 4 Random variables
- 5 Random processes
- 6 Basics of random fields
- 7 Probability density estimation by linear models
- Part III Computational geometry
- Part IV Variational approaches and level sets
- Part V Image analysis tools
- Index
- References
Summary
Introduction
Statistical experiments are conducted in order to infer information about various processes and thus to guide decision making. The effectiveness of a certain drug on a particular disease, surgical procedures, therapy techniques, or demographic effects on disease are a few examples of statistical inference based on a statistical experiment.
A statistical experiment may be described in terms of a population, a phenomenon to be investigated, and a scaling procedure to quantify the spread of the phenomena in a population. Traditionally, a statistical experiment E is described in terms of a trilogy:
the sample space Ω, which is the set of all possible elementary outcomes (the ‘alphabet’ of the experiment);
the field σF, which is the set of all measurable events;
probability measure P, which is a positive scalar function measuring the occurrence of the events; i.e. it assigns probabilities to events on σF.
- Type
- Chapter
- Information
- Biomedical Image AnalysisStatistical and Variational Methods, pp. 79 - 106Publisher: Cambridge University PressPrint publication year: 2014