Statistical Computing

  1. Advanced Computational Methods
    1. Markov Chain Monte Carlo
      1. Bayesian Inference Foundations
        1. Bayes' Theorem
          1. Prior Distributions
            1. Likelihood Functions
              1. Posterior Distributions
                1. Conjugate Priors
                2. Markov Chain Theory
                  1. Markov Property
                    1. Transition Matrices
                      1. Stationary Distributions
                        1. Ergodicity and Mixing
                          1. Detailed Balance
                          2. MCMC Algorithms
                            1. Metropolis Algorithm
                              1. Metropolis-Hastings Algorithm
                                1. Proposal Distributions
                                  1. Acceptance Probability
                                    1. Tuning Parameters
                                    2. Gibbs Sampler
                                      1. Full Conditional Distributions
                                        1. Blocked Gibbs Sampling
                                          1. Data Augmentation
                                          2. Hamiltonian Monte Carlo
                                            1. Leapfrog Integration
                                              1. No-U-Turn Sampler
                                            2. MCMC Implementation
                                              1. Chain Initialization
                                                1. Burn-in Period
                                                  1. Thinning
                                                    1. Multiple Chains
                                                    2. MCMC Diagnostics
                                                      1. Convergence Assessment
                                                        1. Trace Plots
                                                          1. Running Means
                                                            1. Gelman-Rubin Statistic
                                                              1. Geweke Diagnostic
                                                              2. Autocorrelation Analysis
                                                                1. Effective Sample Size
                                                                  1. Monte Carlo Standard Error
                                                                  2. Advanced MCMC Topics
                                                                    1. Adaptive MCMC
                                                                      1. Parallel Tempering
                                                                        1. Reversible Jump MCMC
                                                                      2. High-Performance Computing
                                                                        1. Performance Analysis
                                                                          1. Profiling Code
                                                                            1. Time Profiling
                                                                              1. Memory Profiling
                                                                                1. Line-by-Line Analysis
                                                                                2. Identifying Bottlenecks
                                                                                  1. Benchmarking
                                                                                  2. Code Optimization
                                                                                    1. Algorithmic Improvements
                                                                                      1. Data Structure Optimization
                                                                                        1. Memory Access Patterns
                                                                                          1. Compiler Optimizations
                                                                                          2. Parallel Computing Concepts
                                                                                            1. Shared Memory vs. Distributed Memory
                                                                                              1. Task Parallelism vs. Data Parallelism
                                                                                                1. Synchronization and Communication
                                                                                                  1. Load Balancing
                                                                                                  2. Parallel Programming
                                                                                                    1. Thread-Based Parallelism
                                                                                                      1. OpenMP
                                                                                                        1. Pthreads
                                                                                                        2. Process-Based Parallelism
                                                                                                          1. MPI
                                                                                                            1. MapReduce
                                                                                                            2. Language-Specific Parallel Computing
                                                                                                              1. Parallel Processing in R
                                                                                                                1. Multiprocessing in Python
                                                                                                                  1. Distributed Computing in Julia
                                                                                                                2. GPU Computing
                                                                                                                  1. GPU Architecture
                                                                                                                    1. CUDA Programming
                                                                                                                      1. OpenCL
                                                                                                                        1. GPU Libraries for Statistics
                                                                                                                          1. cuBLAS
                                                                                                                            1. cuSolver
                                                                                                                              1. GPU-accelerated R packages
                                                                                                                          2. Big Data and Scalable Computing
                                                                                                                            1. Big Data Characteristics
                                                                                                                              1. Volume, Velocity, Variety
                                                                                                                                1. Data Storage Challenges
                                                                                                                                  1. Processing Challenges
                                                                                                                                  2. Memory-Efficient Computing
                                                                                                                                    1. Out-of-Core Algorithms
                                                                                                                                      1. Memory Mapping
                                                                                                                                        1. Chunked Processing
                                                                                                                                          1. Sparse Data Structures
                                                                                                                                          2. Distributed Computing Frameworks
                                                                                                                                            1. Hadoop Ecosystem
                                                                                                                                              1. Apache Spark
                                                                                                                                                1. Dask for Python
                                                                                                                                                  1. Distributed R
                                                                                                                                                  2. Streaming Data Processing
                                                                                                                                                    1. Online Algorithms
                                                                                                                                                      1. Incremental Statistics
                                                                                                                                                        1. Real-Time Analytics
                                                                                                                                                        2. Cloud Computing
                                                                                                                                                          1. Cloud Platforms
                                                                                                                                                            1. Containerization
                                                                                                                                                              1. Serverless Computing
                                                                                                                                                                1. Auto-scaling

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                                                                                                                                                            5. Simulation and Resampling Methods

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                                                                                                                                                            7. Statistical Model Implementation