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Engineering Biostatistics

Book Description

Provides a one-stop resource for engineers learning biostatistics using MATLAB® and WinBUGS

Through its scope and depth of coverage, this book addresses the needs of the vibrant and rapidly growing bio-oriented engineering fields while implementing software packages that are familiar to engineers. The book is heavily oriented to computation and hands-on approaches so readers understand each step of the programming. Another dimension of this book is in parallel coverage of both Bayesian and frequentist approaches to statistical inference. It avoids taking sides on the classical vs. Bayesian paradigms, and many examples in this book are solved using both methods. The results are then compared and commented upon. Readers have the choice of MATLAB® for classical data analysis and WinBUGS/OpenBUGS for Bayesian data analysis. Every chapter starts with a box highlighting what is covered in that chapter and ends with exercises, a list of software scripts, datasets, and references.

Engineering Biostatistics: An Introduction using MATLAB® and WinBUGS also includes:

  • parallel coverage of classical and Bayesian approaches, where appropriate
  • substantial coverage of Bayesian approaches to statistical inference
  • material that has been classroom-tested in an introductory statistics course in bioengineering over several years
  • exercises at the end of each chapter and an accompanying website with full solutions and hints to some exercises, as well as additional materials and examples

Engineering Biostatistics: An Introduction using MATLAB® and WinBUGS can serve as a textbook for introductory-to-intermediate applied statistics courses, as well as a useful reference for engineers interested in biostatistical approaches.

Table of Contents

  1. Preface
    1. Acknowledgments
  2. Chapter 1: Introduction
    1. Chapter References
  3. Chapter 2: The Sample and Its Properties
    1. 2.1 Introduction
    2. 2.2 A MATLAB Session on Univariate Descriptive Statistics
    3. 2.3 Location Measures
    4. 2.4 Variability Measures
    5. 2.5 Ranks
    6. 2.6 Displaying Data
    7. 2.7 Multidimensional Samples: Fisher's Iris Data and Body Fat Data
    8. 2.8 Multivariate Samples and Their Summaries*
    9. 2.9 Principal Components of Data
    10. 2.10 Visualizing Multivariate Data
    11. 2.11 Observations as Time Series
    12. 2.12 About Data Types
    13. 2.13 Big Data Paradigm
    14. 2.14 Exercises
    15. Chapter References
  4. Chapter 3: Probability, Conditional Probability, and Bayes’ Rule
    1. 3.1 Introduction
    2. 3.2 Events and Probability
    3. 3.3 Odds
    4. 3.4 Venn Diagrams*
    5. 3.5 Counting Principles*
    6. 3.6 Conditional Probability and Independence of Events
    7. 3.7 Total Probability
    8. 3.8 Reassessing Probabilities: Bayes’ Rule
    9. 3.9 Bayesian Networks*
    10. 3.10 Exercises
    11. Chapter References
  5. Chapter 4: Sensitivity, Specificity, and Relatives
    1. 4.1 Introduction
    2. 4.2 Notation
    3. 4.3 Combining Two or More Tests
    4. 4.4 ROC Curves
    5. 4.5 Exercises
    6. Chapter References
  6. Chapter 5: Random Variables
    1. 5.1 Introduction
    2. 5.2 Discrete Random Variables
    3. 5.3 Some Standard Discrete Distributions
    4. 5.4 Continuous Random Variables
    5. 5.5 Some Standard Continuous Distributions
    6. 5.6 Random Numbers and Probability Tables
    7. 5.7 Transformations of Random Variables*
    8. 5.8 Mixtures*
    9. 5.9 Markov Chains*
    10. 5.10 Exercises
    11. Chapter References
  7. Chapter 6: Normal Distribution
    1. 6.1 Introduction
    2. 6.2 Normal Distribution
    3. 6.3 Examples with a Normal Distribution
    4. 6.4 Combining Normal Random Variables
    5. 6.5 Central Limit Theorem
    6. 6.6 Distributions Related to Normal
    7. 6.7 Delta Method and Variance-Stabilizing Transformations*
    8. 6.8 Exercises
    9. Chapter References
  8. Chapter 7: Point and Interval Estimators
    1. 7.1 Introduction
    2. 7.2 Moment-Matching and Maximum Likelihood Estimators
    3. 7.3 Unbiasedness and Consistency of Estimators
    4. 7.4 Estimation of a Mean, Variance, and Proportion
    5. 7.5 Confidence Intervals
    6. 7.6 Prediction and Tolerance Intervals*
    7. 7.7 Confidence Intervals for Quantiles*
    8. 7.8 Confidence Intervals for the Poisson Rate*
    9. 7.9 Exercises
    10. Chapter References
  9. Chapter 8: Bayesian Approach to Inference
    1. 8.1 Introduction
    2. 8.2 Ingredients for Bayesian Inference
    3. 8.3 Conjugate Priors
    4. 8.4 Point Estimation
    5. 8.5 Prior Elicitation
    6. 8.6 Bayesian Computation and Use of WinBUGS
    7. 8.7 Bayesian Interval Estimation: Credible Sets
    8. 8.8 Learning by Bayes' Theorem
    9. 8.9 Bayesian Prediction
    10. 8.10 Consensus Means*
    11. 8.11 Exercises
    12. Chapter References
  10. Chapter 9: Testing Statistical Hypotheses
    1. 9.1 Introduction
    2. 9.2 Classical Testing Problem
    3. 9.3 Bayesian Approach to Testing
    4. 9.4 Criticism and Calibration of p-Values*
    5. 9.5 Testing the Normal Mean
    6. 9.6 Testing the Multivariate Normal Mean*
    7. 9.7 Testing the Normal Variances
    8. 9.8 Testing the Proportion
    9. 9.9 Multiplicity in Testing, Bonferroni Correction, and False Discovery Rate
    10. 9.10 Exercises
    11. Chapter References
  11. Chapter 10: Two Samples
    1. 10.1 Introduction
    2. 10.2 Means and Variances in Two Independent Normal Populations
    3. 10.3 Testing the Equality of Normal Means When Samples Are Paired
    4. 10.4 Two Multivariate Normal Means*
    5. 10.5 Two Normal Variances
    6. 10.6 Comparing Two Proportions
    7. 10.7 Risk Differences, Risk Ratios, and Odds Ratios
    8. 10.8 Two Poisson Rates*
    9. 10.9 Equivalence Tests*
    10. 10.10 Exercises
    11. Chapter References
  12. Chapter 11: ANOVA and Elements of Experimental Design
    1. 11.1 Introduction
    2. 11.2 One-Way ANOVA
    3. 11.3 Welch's ANOVA*
    4. 11.4 Two-Way ANOVA and Factorial Designs
    5. 11.5 Blocking
    6. 11.6 Repeated Measures Design
    7. 11.7 Nested Designs*
    8. 11.8 Power Analysis in ANOVA
    9. 11.9 Functional ANOVA*
    10. 11.10 Analysis of Means (ANOM)*
    11. 11.11 The Capability of a Measurement System (Gauge R&R ANOVA)*
    12. 11.12 Testing Equality of Several Proportions
    13. 11.13 Testing the Equality of Several Poisson Means*
    14. 11.14 Exercises
    15. Chapter References
  13. Chapter 12: Models for Tables
    1. 12.1 Introduction
    2. 12.2 Contingency Tables: Testing for Independence
    3. 12.3 Three-Way Tables
    4. 12.4 Contingency Tables with Fixed Marginals: Fisher's Exact Test
    5. 12.5 Stratified Tables: Mantel–Haenszel Test
    6. 12.6 Paired Tables: McNemar's Test
    7. 12.7 Risk Differences, Risk Ratios, and Odds Ratios for Paired Tables
    8. 12.8 Exercises
    9. Chapter References
  14. Chapter 13: Correlation
    1. 13.1 Introduction
    2. 13.2 The Pearson Coefficient of Correlation
    3. 13.3 Spearman's Coefficient of Correlation
    4. 13.4 Kendall's Tau
    5. 13.5 Cum hoc ergo propter hoc
    6. 13.6 Exercises
    7. Chapter References
  15. Chapter 14: Regression
    1. 14.1 Introduction
    2. 14.2 Simple Linear Regression
    3. 14.3 Inference in Simple Linear Regression
    4. 14.4 Calibration
    5. 14.5 Testing the Equality of Two Slopes*
    6. 14.6 Multiple Regression
    7. 14.7 Diagnostics in Multiple Regression
    8. 14.8 Sample Size in Regression
    9. 14.9 Linear Regression That Is Nonlinear in Predictors
    10. 14.10 Errors-in-Variables Linear Regression*
    11. 14.11 Analysis of Covariance
    12. 14.12 Exercises
    13. Chapter References
  16. Chapter 15: Regression for Binary and Count Data
    1. 15.1 Introduction
    2. 15.2 Logistic Regression
    3. 15.3 Poisson Regression
    4. 15.4 Log-linear Models
    5. 15.5 Exercises
    6. Chapter References
  17. Chapter 16: Inference for Censored Data and Survival Analysis
    1. 16.1 Introduction
    2. 16.2 Definitions
    3. 16.3 Inference with Censored Observations
    4. 16.4 The Cox Proportional Hazards Model
    5. 16.5 Bayesian Approach
    6. 16.6 Survival Analysis in WinBUGS
    7. 16.7 Exercises
    8. Chapter References
  18. Chapter 17: Goodness-of-Fit Tests
    1. 17.1 Introduction
    2. 17.2 Probability Plots
    3. 17.3 Pearson's Chi-Square Test
    4. 17.4 Kolmogorov–Smirnov Tests
    5. 17.5 Cramér-von Mises and Watson's Tests*
    6. 17.6 Rosenblatt's Test*
    7. 17.7 Moran's Test*
    8. 17.8 Departures from Normality
    9. 17.9 Ellimination of Unknown Parameters by Transformations
    10. 17.10 Exercises
    11. Chapter References
  19. Chapter 18: Distribution-Free Methods
    1. 18.1 Introduction
    2. 18.2 Sign Test
    3. 18.3 Wilcoxon Signed-Rank Test
    4. 18.4 Wilcoxon Sum-Rank and Mann–Whitney Tests
    5. 18.5 Kruskal–Wallis Test
    6. 18.6 Friedman's Test
    7. 18.7 Resampling Methods
    8. 18.8 Exercises
    9. Chapter References
  20. Chapter 19: Bayesian Inference Using Gibbs Sampling - BUGS Project
    1. 19.1 Introduction
    2. 19.2 Step-by-Step Session
    3. 19.3 Built-in Functions and Common Distributions in WinBUGS
    4. 19.4 MATBUGS: A MATLAB Interface to WinBUGS
    5. 19.5 Exercises
    6. Chapter References
  21. Index
  22. EULA