Marschner Inference Principles for Biostatisticians

1. Auflage 2014
ISBN: 978-1-4822-2224-1
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: 0 - No protection

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.