# Statistics for life and health sciences EBook

Welcome to the UCLA Statistics for the Biomedical and Health Sciences (Stats 13) electronic book (EBook).

## Contents

- 1 Preface
- 2 Chapter I: Introduction to Statistics
- 3 Chapter II: Data and variability
- 4 Chapter III: Randomization-based statistical inference
- 5 Chapter IV: Probability Models
- 6 Chapter V: Statistical Parametric Models and Inference
- 7 Chapter VI: Limiting Theorems
- 8 Chapter VII: Multivariate Statistics
- 9 Chapter VIII: Multinomial Experiments and Inference
- 10 Chapter IX: Parameter Estimation
- 11 Chapter X: Bayesian Inference
- 12 Chapter XI: Dimensionality Reduction
- 13 Chapter XII: Classification Methods
- 14 Chapter XIII: Survival Analysis
- 15 Chapter XIV: Mixture modeling
- 16 Chapter XV: Causality
- 17 Appendix

## Preface

This is an Internet-based *probability and statistics for biomedical and health sciences EBook*. The materials, tools and demonstrations presented in this EBook would are used for the UCLA Statistics 13 course. The EBook is developed, updated and manages by the UCLA Statistics faculty teaching this course over the years. Many other instructors, researchers, students and educators have contributed to this EBook.

There are four novel features of this *Statistics EBook*. It is community-built and allows easy modifications and customizations, completely open-access (in terms of use and contributions), blends information technology, scientific techniques, heterogeneous data and modern pedagogical concepts, and is multilingual.

### Format

Each section in this EBook includes

- Motivation
- Concepts, definitions, formulations
- Examples
- Small (mock-up) and real (research-derived) data
- Webapp demonstration with real data (HTML5)
- R programming
- Problems

### Pedagogical Use

...

### Copyright

The Probability and Statistics EBook is a freely and openly accessible electronic book for the entire community under CC-BY license ...

## Chapter I: Introduction to Statistics

- Natural Biomedical and Health Research Studies
- Data-driven Statistics
- Uses and Abuses of Statistics
- Statistical Software Tools

## Chapter II: Data and variability

- Data
- Measures of center, dispersion/variation, skewness, flatness
- Design of experiments
- R data management (Import and Export)
- Histograms, densities and summary statistics

## Chapter III: Randomization-based statistical inference

- Samples, Populations, Repeated Samples, Resampling
- Bootstrapping
- Testing one, two or more samples
- Confidence intervals

## Chapter IV: Probability Models

- Fundamentals
- Rules for Computing Probabilities
- Probabilities Simulations
- Counting Principles

## Chapter V: Statistical Parametric Models and Inference

- Hypothesis testing foundations
- Type I and II errors, Power, sensitivity, specificity
- Parametric Assumptions

### One sample inference

- T-Test
- Normal Z-test
- Confidence intervals

### Two sample inference

- Independent samples
- Paired samples

## Chapter VI: Limiting Theorems

- Law of Large Numbers (First Fundamental Law of Probability Theory)
- Central Limit Theorem (Second Fundamental Law of Probability Theory)
- Relations between Distributions (Distributome)

## Chapter VII: Multivariate Statistics

- Parametric (simple and multivatiate) regression
- Parametric ANOVA/ANCOVA/MANCOVA
- Logistic Regression
- Parametric assumptions and model validation
- Non-parametric linear modeling
- Randomization and Resampling based multivariate inference
- Genome-wide association studies (GWAS)

## Chapter VIII: Multinomial Experiments and Inference

- Chi-square

## Chapter IX: Parameter Estimation

- MOM
- MLE

## Chapter X: Bayesian Inference

## Chapter XI: Dimensionality Reduction

- PCA
- ICA

## Chapter XII: Classification Methods

- Supervised classification methods (Support Vector Machines, SVM, ADABOOST)
- Unsupervised (K-means clustering, hierarchical clustering)

## Chapter XIII: Survival Analysis

## Chapter XIV: Mixture modeling

## Chapter XV: Causality

## Appendix

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