Marschner Inference Principles for Biostatisticians

1. Auflage 2014
ISBN: 978-1-4822-2224-1
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 274 Seiten

Reihe: Chapman & Hall/CRC Biostatistics Series

Statistical inference is the science of drawing conclusions on the basis of information that is subject to randomness. Biostatistics underpins the use of statistical inference in the health and medical sciences. This classroom-tested book presents the principles of statistical inference from a biostatistical perspective. It prepares students for more rigorous work on core methodologies, such as linear models, generalized linear models, survival analysis, longitudinal methods, and randomized trials. Each chapter includes one main example that provides context to the theoretical and conceptual foundations of biostatistics.

Zielgruppe

Graduate students training to be biostatisticians; researchers and professionals in biostatistics and related areas.

Autoren/Hrsg.

Marschner, Ian C.

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik

Inhaltsverzeichnis

Probability and Random Samples

Statistical inference

Probability

Random variables

Probability distributions

Independence

Random samples

Sampling bias

Sampling variation

Large samples

Extended example

Estimation Concepts

Statistical models

Parametric models

Statistics and data reduction

Estimators and estimates

Properties of estimators

Large sample properties

Interval estimation

Coverage probability

Towards hypothesis testing

Extended example

Likelihood

Statistical likelihood

Likelihood function

Log-likelihood function

Sufficient statistics and data reduction

Multiple parameters

Nuisance parameters

Extended example

Estimation Methods

Maximum likelihood estimation

Computation of the MLE

Information and standard errors

Properties of the MLE

Multiple parameters

Further estimation methods

Extended example

Hypothesis Testing Concepts

Hypotheses

Statistical tests

Acceptance versus non-rejection

Statistical errors

Power and sample size

P-values

Extended example

Hypothesis Testing Methods

Approaches to hypothesis testing

Likelihood ratio test

Score test

Wald test

Comparison of the three approaches

Multiple parameters

Hypotheses about all parameters

Hypotheses about one parameter

Hypotheses about some parameters

Test-based confidence intervals

Extended example

Bayesian Inference

Probability and uncertainty

Bayes’ rule

Prior and posterior distributions

Conjugate prior distributions

Estimation of a normal mean

Credible intervals

Non-informative prior distributions

Multiple parameters

Connection to likelihood inference

Extended example

Further Inference Topics

Exact methods

Non-parametric methods

Semi-parametric methods

Bootstrapping

Permutation methods

Extended example

Appendix A: Common probability distributions

Appendix B: Simulation tools

Über Autor(innen)

Ian Marschner has over 25 years of experience as a biostatistician working on health and medical research. He is currently a Professor of Statistics and Head of the Department of Statistics at Macquarie University. He is also a Professor of Biostatistics in the National Health and Medical Research Council (NHMRC) Clinical Trials Centre at the University of Sydney. Formerly, he was Director of the Asia Biometrics Centre with Pfizer and Associate Professor of Biostatistics at Harvard University.