Statistics

  1. Advanced Topics in Statistics
    1. Bayesian Statistics
      1. Philosophy of Bayesian Inference
        1. Subjective Probability
          1. Prior Information Use
          2. Bayes' Theorem Revisited
            1. Continuous Version
              1. Likelihood Function
              2. Prior and Posterior Distributions
                1. Types of Priors
                  1. Informative Priors
                    1. Non-informative Priors
                      1. Conjugate Priors
                      2. Updating Beliefs
                        1. Prior Sensitivity Analysis
                        2. Bayesian Inference
                          1. Parameter Estimation
                            1. Credible Intervals
                              1. Hypothesis Testing
                                1. Comparison with Frequentist Inference
                                2. Computational Methods
                                  1. Markov Chain Monte Carlo (MCMC)
                                    1. Gibbs Sampling
                                  2. Time Series Analysis
                                    1. Introduction to Time Series
                                      1. Time Series Data Characteristics
                                      2. Components of a Time Series
                                        1. Trend
                                        2. Seasonality
                                          1. Seasonal Patterns
                                            1. Seasonal Indices
                                            2. Cyclical Variation
                                              1. Business Cycles
                                                1. Long-term Cycles
                                                2. Irregular Variation
                                                  1. Random Fluctuations
                                                    1. Noise
                                                  2. Time Series Decomposition
                                                    1. Additive Models
                                                      1. Multiplicative Models
                                                      2. Smoothing Methods
                                                        1. Moving Averages
                                                          1. Simple Moving Averages
                                                            1. Weighted Moving Averages
                                                            2. Exponential Smoothing
                                                              1. Simple Exponential Smoothing
                                                                1. Holt's Method
                                                                  1. Winters' Method
                                                                2. Forecasting
                                                                  1. Time Series Models
                                                                    1. ARIMA Models
                                                                      1. Seasonal Models
                                                                      2. Model Selection
                                                                        1. Model Evaluation
                                                                          1. Forecast Accuracy Measures
                                                                            1. Cross-validation
                                                                        2. Survival Analysis
                                                                          1. Introduction
                                                                            1. Time-to-Event Data
                                                                            2. Censoring
                                                                              1. Right Censoring
                                                                                1. Left Censoring
                                                                                  1. Interval Censoring
                                                                                  2. Survival and Hazard Functions
                                                                                    1. Survival Function
                                                                                      1. Hazard Function
                                                                                        1. Cumulative Hazard
                                                                                        2. Kaplan-Meier Estimator
                                                                                          1. Non-parametric Estimation
                                                                                            1. Confidence Intervals
                                                                                              1. Comparison of Survival Curves
                                                                                              2. Cox Proportional Hazards Model
                                                                                                1. Semi-parametric Model
                                                                                                  1. Hazard Ratios
                                                                                                2. Multivariate Statistics
                                                                                                  1. Introduction to Multivariate Analysis
                                                                                                    1. Multiple Variables Simultaneously
                                                                                                      1. Interdependence
                                                                                                      2. Principal Component Analysis (PCA)
                                                                                                        1. Dimension Reduction
                                                                                                          1. Eigenvalues and Eigenvectors
                                                                                                            1. Component Interpretation
                                                                                                              1. Scree Plots
                                                                                                              2. Factor Analysis
                                                                                                                1. Latent Variables
                                                                                                                  1. Factor Loadings
                                                                                                                    1. Rotation Methods
                                                                                                                      1. Model Fit Assessment
                                                                                                                      2. Cluster Analysis
                                                                                                                        1. Hierarchical Clustering
                                                                                                                          1. K-means Clustering
                                                                                                                            1. Distance Measures
                                                                                                                              1. Cluster Validation
                                                                                                                              2. Discriminant Analysis
                                                                                                                                1. Classification
                                                                                                                                  1. Linear Discriminant Analysis
                                                                                                                                    1. Quadratic Discriminant Analysis
                                                                                                                                      1. Cross-validation
                                                                                                                                      2. Multivariate Analysis of Variance (MANOVA)
                                                                                                                                        1. Multiple Dependent Variables
                                                                                                                                          1. Test Statistics
                                                                                                                                            1. Assumptions

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                                                                                                                                        13. Experimental Design

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                                                                                                                                        1. Introduction to Statistics