Statistics

14.

Advanced Topics in Statistics

14.1.

Bayesian Statistics

14.1.1.

Philosophy of Bayesian Inference

14.1.1.1.

Subjective Probability

14.1.1.2.

Prior Information Use

14.1.2.

Bayes' Theorem Revisited

14.1.2.1.

Continuous Version

14.1.2.2.

Likelihood Function

14.1.3.

Prior and Posterior Distributions

14.1.3.1.

Types of Priors

14.1.3.1.1.

Informative Priors

14.1.3.1.2.

Non-informative Priors

14.1.3.1.3.

Conjugate Priors

14.1.3.2.

Updating Beliefs

14.1.3.3.

Prior Sensitivity Analysis

14.1.4.

Bayesian Inference

14.1.4.1.

Parameter Estimation

14.1.4.2.

Credible Intervals

14.1.4.3.

Hypothesis Testing

14.1.4.4.

Comparison with Frequentist Inference

14.1.5.

Computational Methods

14.1.5.1.

Markov Chain Monte Carlo (MCMC)

14.1.5.2.

14.2.

Time Series Analysis

14.2.1.

Introduction to Time Series

14.2.1.1.

Time Series Data Characteristics

14.2.2.

Components of a Time Series

14.2.2.1.

14.2.2.1.1.

14.2.2.1.2.

Non-linear Trends

14.2.2.2.

14.2.2.2.1.

Seasonal Patterns

14.2.2.2.2.

Seasonal Indices

14.2.2.3.

Cyclical Variation

14.2.2.3.1.

Business Cycles

14.2.2.3.2.

Long-term Cycles

14.2.2.4.

Irregular Variation

14.2.2.4.1.

Random Fluctuations

14.2.2.4.2.

14.2.3.

Time Series Decomposition

14.2.3.1.

Additive Models

14.2.3.2.

Multiplicative Models

14.2.4.

Smoothing Methods

14.2.4.1.

Moving Averages

14.2.4.1.1.

Simple Moving Averages

14.2.4.1.2.

Weighted Moving Averages

14.2.4.2.

Exponential Smoothing

14.2.4.2.1.

Simple Exponential Smoothing

14.2.4.2.2.

14.2.4.2.3.

Winters' Method

14.2.5.

14.2.5.1.

Time Series Models

14.2.5.1.1.

14.2.5.1.2.

Seasonal Models

14.2.5.2.

Model Selection

14.2.5.3.

Model Evaluation

14.2.5.3.1.

Forecast Accuracy Measures

14.2.5.3.2.

Cross-validation

14.3.

Survival Analysis

14.3.1.

14.3.1.1.

Time-to-Event Data

14.3.2.

14.3.2.1.

Right Censoring

14.3.2.2.

14.3.2.3.

Interval Censoring

14.3.3.

Survival and Hazard Functions

14.3.3.1.

Survival Function

14.3.3.2.

Hazard Function

14.3.3.3.

Cumulative Hazard

14.3.4.

Kaplan-Meier Estimator

14.3.4.1.

Non-parametric Estimation

14.3.4.2.

Confidence Intervals

14.3.4.3.

Comparison of Survival Curves

14.3.5.

Cox Proportional Hazards Model

14.3.5.1.

Semi-parametric Model

14.3.5.2.

14.4.

Multivariate Statistics

14.4.1.

Introduction to Multivariate Analysis

14.4.1.1.

Multiple Variables Simultaneously

14.4.1.2.

Interdependence

14.4.2.

Principal Component Analysis (PCA)

14.4.2.1.

Dimension Reduction

14.4.2.2.

Eigenvalues and Eigenvectors

14.4.2.3.

Component Interpretation

14.4.2.4.

14.4.3.

Factor Analysis

14.4.3.1.

Latent Variables

14.4.3.2.

Factor Loadings

14.4.3.3.

Rotation Methods

14.4.3.4.

Model Fit Assessment

14.4.4.

Cluster Analysis

14.4.4.1.

Hierarchical Clustering

14.4.4.2.

K-means Clustering

14.4.4.3.

Distance Measures

14.4.4.4.

Cluster Validation

14.4.5.

Discriminant Analysis

14.4.5.1.

14.4.5.2.

Linear Discriminant Analysis

14.4.5.3.

Quadratic Discriminant Analysis

14.4.5.4.

Cross-validation

14.4.6.

Multivariate Analysis of Variance (MANOVA)

14.4.6.1.

Multiple Dependent Variables

14.4.6.2.

Test Statistics

14.4.6.3.

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1. Introduction to Statistics