Statistics for life and health sciences EBook

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

Contents

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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