Likelihood and Bayesian inference with applications in biology and medicine /: with applications in biology and medicine. (©2020)
- Record Type:
- Book
- Title:
- Likelihood and Bayesian inference with applications in biology and medicine /: with applications in biology and medicine. (©2020)
- Main Title:
- Likelihood and Bayesian inference with applications in biology and medicine
- Further Information:
- Note: Leonard Held, Daniel Sabanés Bové.
- Other Names:
- Held, Leonhard
Sabanés Bové, Daniel - Contents:
- Intro -- Likelihood and Bayesian Inference -- Preface -- Contents -- Chapter 1: Introduction -- 1.1 Examples -- 1.1.1 Inference for a Proportion -- 1.1.2 Comparison of Proportions -- 1.1.3 The Capture-Recapture Method -- 1.1.4 Hardy-Weinberg Equilibrium -- 1.1.5 Estimation of Diagnostic Tests Characteristics -- 1.1.6 Quantifying Disease Risk from Cancer Registry Data -- 1.1.7 Predicting Blood Alcohol Concentration -- 1.1.8 Analysis of Survival Times -- 1.2 Statistical Models -- 1.3 Contents and Notation of the Book -- 1.4 References -- Chapter 2: Likelihood 2.1 Likelihood and Log-Likelihood Function -- 2.1.1 Maximum Likelihood Estimate -- 2.1.2 Relative Likelihood -- 2.1.3 Invariance of the Likelihood -- 2.1.4 Generalised Likelihood -- 2.2 Score Function and Fisher Information -- 2.3 Numerical Computation of the Maximum Likelihood Estimate -- 2.3.1 Numerical Optimisation -- 2.3.2 The EM Algorithm -- 2.4 Quadratic Approximation of the Log-Likelihood Function -- 2.5 Suf ciency -- 2.5.1 Minimal Suf ciency -- 2.5.2 The Likelihood Principle -- 2.6 Exercises -- 2.7 References -- Chapter 3: Elements of Frequentist Inference 3.1 Unbiasedness and Consistency -- 3.2 Standard Error and Con dence Interval -- 3.2.1 Standard Error -- 3.2.2 Con dence Interval -- 3.2.3 Pivots -- 3.2.4 The Delta Method -- 3.2.5 The Bootstrap -- 3.3 Signi cance Tests and P-Values -- 3.4 Exercises -- 3.5 References -- Chapter 4: Frequentist Properties of the Likelihood -- 4.1 The Expected Fisher InformationIntro -- Likelihood and Bayesian Inference -- Preface -- Contents -- Chapter 1: Introduction -- 1.1 Examples -- 1.1.1 Inference for a Proportion -- 1.1.2 Comparison of Proportions -- 1.1.3 The Capture-Recapture Method -- 1.1.4 Hardy-Weinberg Equilibrium -- 1.1.5 Estimation of Diagnostic Tests Characteristics -- 1.1.6 Quantifying Disease Risk from Cancer Registry Data -- 1.1.7 Predicting Blood Alcohol Concentration -- 1.1.8 Analysis of Survival Times -- 1.2 Statistical Models -- 1.3 Contents and Notation of the Book -- 1.4 References -- Chapter 2: Likelihood 2.1 Likelihood and Log-Likelihood Function -- 2.1.1 Maximum Likelihood Estimate -- 2.1.2 Relative Likelihood -- 2.1.3 Invariance of the Likelihood -- 2.1.4 Generalised Likelihood -- 2.2 Score Function and Fisher Information -- 2.3 Numerical Computation of the Maximum Likelihood Estimate -- 2.3.1 Numerical Optimisation -- 2.3.2 The EM Algorithm -- 2.4 Quadratic Approximation of the Log-Likelihood Function -- 2.5 Suf ciency -- 2.5.1 Minimal Suf ciency -- 2.5.2 The Likelihood Principle -- 2.6 Exercises -- 2.7 References -- Chapter 3: Elements of Frequentist Inference 3.1 Unbiasedness and Consistency -- 3.2 Standard Error and Con dence Interval -- 3.2.1 Standard Error -- 3.2.2 Con dence Interval -- 3.2.3 Pivots -- 3.2.4 The Delta Method -- 3.2.5 The Bootstrap -- 3.3 Signi cance Tests and P-Values -- 3.4 Exercises -- 3.5 References -- Chapter 4: Frequentist Properties of the Likelihood -- 4.1 The Expected Fisher Information and the Score Statistic -- 4.1.1 The Expected Fisher Information -- 4.1.2 Properties of the Expected Fisher Information -- 4.1.3 The Score Statistic -- 4.1.4 The Score Test -- 4.1.5 Score Con dence Intervals 4.2 The Distribution of the ML Estimator and the Wald Statistic -- 4.2.1 Cramér-Rao Lower Bound -- 4.2.2 Consistency of the ML Estimator -- 4.2.3 The Distribution of the ML Estimator -- 4.2.4 The Wald Statistic -- 4.3 Variance-Stabilising Transformations -- 4.4 The Likelihood Ratio Statistic -- 4.4.1 The Likelihood Ratio Test -- 4.4.2 Likelihood Ratio Con dence Intervals -- 4.5 The p* Formula -- 4.6 A Comparison of Likelihood-Based Con dence Intervals -- 4.7 Exercises -- 4.8 References -- Chapter 5: Likelihood Inference in Multiparameter Models -- 5.1 Score Vector and Fisher Information Matrix 5.2 Standard Error and Wald Con dence Interval -- 5.3 Pro le Likelihood -- 5.4 Frequentist Properties of the Multiparameter Likelihood -- 5.4.1 The Score Statistic -- 5.4.2 The Wald Statistic -- 5.4.3 The Multivariate Delta Method -- 5.4.4 The Likelihood Ratio Statistic -- 5.5 The Generalised Likelihood Ratio Statistic -- 5.6 Conditional Likelihood -- 5.7 Exercises -- 5.8 References -- Chapter 6: Bayesian Inference -- 6.1 Bayes' Theorem -- 6.2 Posterior Distribution -- 6.3 Choice of the Prior Distribution -- 6.3.1 Conjugate Prior Distributions -- 6.3.2 Improper Prior Distributions … (more)
- Edition:
- Second edition
- Publisher Details:
- Berlin : Springer
- Publication Date:
- 2020
- Copyright Date:
- 2020
- Extent:
- 1 online resource (409 p.)
- Subjects:
- 519.542
Bayesian statistical decision theory
Decision making -- Statistical methods
Bayesian statistical decision theory
Decision making -- Statistical methods
Electronic books - Languages:
- English
- ISBNs:
- 9783662607923
3662607921
9783662607916
3662607913
9783662607930
9783662607947
3662607948 - Related ISBNs:
- 366260793X
- Notes:
- Note: Includes bibliographical references and index.
- Access Rights:
- Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
- Access Usage:
- Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.
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- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library HMNTS - ELD.DS.510054
- Ingest File:
- 03_088.xml