Verfasst von:	Aitkin, Murray A. [VerfasserIn]
Titel:	Introduction to statistical modelling and inference
Verf.angabe:	Murray Aitkin (University of Melbourne, Australia)
Ausgabe:	First edition
Verlagsort:	Boca Raton ; London ; New York
Verlag:	CRC Press, Taylor & Francis Group
Jahr:	2023
Umfang:	xvi, 374 Seiten
Illustrationen:	Illustrationen, Diagramme
Fussnoten:	Literaturverzeichnis Seite 359-364
ISBN:	978-1-032-10571-0
	978-1-032-10573-4
Abstract:	"The complexity of large-scale data sets ("Big Data") has stimulated the development of advanced computational methods for analyzing them. There are two different kinds of methods to aid this. The model-based method uses probability models and likelihood and Bayesian theory, while the model-free method does not require a probability model, likelihood or Bayesian theory. These two approaches are based on different philosophical principles of probability theory, espoused by the famous statisticians Ronald Fisher and Jerzy Neyman Introduction to Statistical Modelling and Inference covers simple experimental and survey designs, and probability models up to and including generalised linear (regression) models and some extensions of these, including finite mixtures. A wide range of examples from different application fields are also discussed and analyzed. No special software is used, beyond that needed for maximum likelihood analysis of generalised linear models. Students are expected to have a basic mathematical background of algebra, coordinate geometry and calculus. Features Probability models are developed from the shape of the sample empirical cumulative distribution function, (cdf) or a transformation of it. Bounds for the value of the population cumulative distribution function are obtained from the Beta distribution at each point of the empirical cdf. Bayes's theorem is developed from the properties of the screening test for a rare condition. The multinomial distribution provides an always-true model for any randomly sampled data. The model-free bootstrap method for finding the precision of a sample estimate has a model-based parallel - the Bayesian bootstrap - based on the always-true multinomial distribution. The Bayesian posterior distributions of model parameters can be obtained from the maximum likelihood analysis of the model. This book is aimed at students in a wide range of disciplines including Data Science. The book is based on the model-based theory, used widely by scientists in many fields, and compares it, in less detail, with the model-free theory, popular in computer science, machine learning and official survey analysis. The development of the model-based theory is accelerated by recent developments in Bayesian analysis"--
DOI:	doi:10.1201/9781003216025
URL:	Inhaltsverzeichnis: https://www.gbv.de/dms/tib-ub-hannover/1815037083.pdf
	zbMATH: https://zbmath.org/1499.62001
	DOI: https://doi.org/10.1201/9781003216025
Schlagwörter:	(s)Inferenzstatistik    / (s)Stochastisches Modell    / (s)Frequentistisches Verfahren    / (s)Bayes-Verfahren    / (s)Statistischer Test    / (s)Regressionsanalyse    / (s)Verallgemeinertes lineares Modell
Sprache:	eng
Bibliogr. Hinweis:	Erscheint auch als : Online-Ausgabe: Aitkin, Murray: Introduction to Statistical Modelling and Inference. - Milton : CRC Press LLC, 2022. - 1 online resource (391 pages)
RVK-Notation:	SK 850
K10plus-PPN:	1815037083