Computational Statistics

  1. Advanced Computational Topics
    1. Density Estimation
      1. Histograms
        1. Bin Width Selection
          1. Sturges' Rule
            1. Scott's Rule
              1. Freedman-Diaconis Rule
                1. Limitations of Histograms
                2. Kernel Density Estimation (KDE)
                  1. Choice of Kernel Function
                    1. Bandwidth Selection
                      1. Rule of Thumb
                        1. Cross-Validation
                          1. Plug-in Methods
                          2. Multivariate KDE
                            1. Adaptive Kernels
                            2. Mixture Models for Density Estimation
                              1. Gaussian Mixture Models
                                1. EM Algorithm for Mixtures
                                  1. Model Selection
                                2. Non-parametric Regression
                                  1. Smoothing Splines
                                    1. Spline Basis Functions
                                      1. Smoothing Parameter Selection
                                        1. Cross-Validation
                                          1. Generalized Cross-Validation
                                          2. Kernel Regression
                                            1. Nadaraya-Watson Estimator
                                              1. Local Linear Regression
                                                1. Bandwidth Selection
                                                2. Local Polynomial Regression (LOESS)
                                                  1. Degree of Local Polynomial
                                                    1. Span Selection
                                                      1. Robust Fitting
                                                      2. Gaussian Process Regression
                                                        1. Covariance Functions
                                                          1. Hyperparameter Estimation
                                                            1. Predictive Distributions
                                                          2. Statistical Learning and Machine Learning Models
                                                            1. Classification and Regression Trees (CART)
                                                              1. Tree Construction
                                                                1. Splitting Criteria
                                                                  1. Pruning Methods
                                                                    1. Cross-Validation Pruning
                                                                    2. Ensemble Methods
                                                                      1. Bagging
                                                                        1. Bootstrap Aggregation
                                                                          1. Out-of-Bag Error
                                                                          2. Random Forests
                                                                            1. Random Feature Selection
                                                                              1. Variable Importance
                                                                                1. Out-of-Bag Error Estimation
                                                                                2. Boosting
                                                                                  1. AdaBoost
                                                                                    1. Gradient Boosting Machines
                                                                                      1. XGBoost
                                                                                    2. Support Vector Machines
                                                                                      1. Maximum Margin Principle
                                                                                        1. Kernel Trick
                                                                                          1. Soft Margin Classification
                                                                                          2. Neural Networks
                                                                                            1. Feedforward Networks
                                                                                              1. Backpropagation Algorithm
                                                                                                1. Deep Learning Basics
                                                                                              2. Models for Dependent Data
                                                                                                1. Time Series Analysis
                                                                                                  1. Autoregressive Models (AR)
                                                                                                    1. Parameter Estimation
                                                                                                      1. Order Selection
                                                                                                      2. Moving Average Models (MA)
                                                                                                        1. Invertibility Conditions
                                                                                                        2. ARMA and ARIMA Models
                                                                                                          1. Box-Jenkins Methodology
                                                                                                            1. Forecasting
                                                                                                            2. Seasonal Decomposition
                                                                                                              1. Classical Decomposition
                                                                                                                1. STL Decomposition
                                                                                                                2. Vector Autoregression (VAR)
                                                                                                                  1. Multivariate Time Series
                                                                                                                    1. Granger Causality
                                                                                                                  2. Hidden Markov Models (HMMs)
                                                                                                                    1. State Transition Probabilities
                                                                                                                      1. Emission Probabilities
                                                                                                                        1. Forward-Backward Algorithm
                                                                                                                          1. Viterbi Algorithm
                                                                                                                            1. Baum-Welch Algorithm
                                                                                                                            2. State-Space Models and Kalman Filters
                                                                                                                              1. State-Space Representation
                                                                                                                                1. Kalman Filter Algorithm
                                                                                                                                  1. Extended Kalman Filter
                                                                                                                                    1. Unscented Kalman Filter
                                                                                                                                      1. Smoothing and Prediction
                                                                                                                                      2. Particle Filters (Sequential Monte Carlo)
                                                                                                                                        1. Importance Sampling in Particle Filters
                                                                                                                                          1. Resampling Methods
                                                                                                                                            1. Degeneracy Problem
                                                                                                                                              1. Particle MCMC
                                                                                                                                            2. Computational Analysis of Statistical Graphics
                                                                                                                                              1. Graphical Models
                                                                                                                                                1. Bayesian Networks
                                                                                                                                                  1. Directed Acyclic Graphs
                                                                                                                                                    1. Conditional Independence
                                                                                                                                                    2. Markov Random Fields
                                                                                                                                                      1. Undirected Graphs
                                                                                                                                                        1. Clique Potentials
                                                                                                                                                        2. Inference in Graphical Models
                                                                                                                                                          1. Variable Elimination
                                                                                                                                                            1. Belief Propagation
                                                                                                                                                              1. Junction Tree Algorithm
                                                                                                                                                            2. Network Analysis
                                                                                                                                                              1. Network Representation
                                                                                                                                                                1. Adjacency Matrices
                                                                                                                                                                  1. Edge Lists
                                                                                                                                                                  2. Community Detection
                                                                                                                                                                    1. Modularity Optimization
                                                                                                                                                                      1. Spectral Clustering
                                                                                                                                                                      2. Centrality Measures
                                                                                                                                                                        1. Degree Centrality
                                                                                                                                                                          1. Betweenness Centrality
                                                                                                                                                                            1. Eigenvector Centrality
                                                                                                                                                                              1. PageRank
                                                                                                                                                                            2. Spatial Statistics
                                                                                                                                                                              1. Spatial Point Processes
                                                                                                                                                                                1. Kriging and Spatial Interpolation
                                                                                                                                                                                  1. Spatial Autocorrelation
                                                                                                                                                                                    1. Markov Random Fields for Spatial Data

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                                                                                                                                                                                6. High-Dimensional Data Analysis

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                                                                                                                                                                                1. Foundations of Computational Statistics