Self
Intro
(PART) 20-02
1
Categorical
1.1
Overview
1.1.1
Data Type and Statistical Analysis
2
Bayesian
2.1
Abstract
2.1.1
변수의 독립성
2.1.2
교환가능성
2.2
Continual Aeassessment Method
2.3
Horseshoe Prior
(PART) 21-01
3
Mathematical Stats
3.1
Inference
3.1.1
Rao-Blackwell thm.
3.1.2
Completeness
3.1.3
레만-쉐페 thm.
3.1.4
Rao-Blackwell thm.
3.2
Hypothesis Test
3.3
Power Fucntion
3.3.1
Significance Probability (p-value)
3.4
Optimal Testing Method
3.5
Data Reduction
3.5.1
Sufficiency Principle
3.6
Borel Paradox
3.7
Neyman–Pearson lemma
3.7.1
Overview
3.7.2
Generalized LRT
3.8
개념
4
MCMC
4.1
Importance Sampling
4.1.1
Independent Monte Carlo
4.2
Markov Chain Monte Carlo
4.2.1
MH Algorithm
4.2.2
Random Walk Chains (Most Widely Used)
4.2.3
Basic Gibbs Sampler
4.2.4
Implementation
4.3
Advanced MCMC (wk08)
4.3.1
Data Augmentation
4.3.2
Hit-and-Run Algorithm
4.3.3
Metropolis-Adjusted Langevin Algorithm
4.3.4
Multiple-Try Metropolis Algorithm
4.3.5
Reversible Jump MCMC Algorithm
4.4
Auxiliary Variable MCMC
4.4.1
Introduction
4.4.2
Multimodal Target Distribution
4.4.3
Doubly-intractable Normalizing Constants
4.5
Approximate Bayesian Computation
4.5.1
Simulator-Based Models
4.5.2
ABCifying Monte Carlo Methods
4.5.3
ABC-MCMC Algorithm
4.6
Hamiltonian Monte Carlo
4.6.1
Introduction to Hamiltonian Monte Carlo
4.7
Population Monte Carlo
4.7.1
Adaptive Direction Sampling
4.7.2
Conjugate Gradient MC
4.7.3
Parallel Tempering
4.7.4
Evolutionary MC
4.7.5
Sequential Parallel Tempering
4.8
Stochastic Approximation Monte Carlo
4.9
Review
4.9.1
Wk01
4.9.2
wk03
4.9.3
wk04, 05
4.10
Else
4.10.1
Hw4. Rasch Model
4.10.2
DA) Example: MVN
4.10.3
Bayesian adaptive clinical trial with delayed outcomes
4.10.4
NMAR의 종류
4.10.5
wk10) Bayesian Model Selection
4.10.6
Autologistic model
4.10.7
wk10) Bayesian Model Averaging
5
MVA
5.1
Overview of mva (not ended)
5.1.1
Notation
5.1.2
Summary Statistics
5.1.3
Statistical Inference on Correlation
5.1.4
Standardization
5.1.5
Missing Value Treatment
5.2
Multivariate Nomral (wk2)
5.2.1
Overview
5.2.2
Spectral Decomposition
5.2.3
Properties of MVN
5.2.4
\(\Chi^2\)
distribution
5.2.5
Linear Combination of Random Vectors
5.2.6
Multivariate Normal Likelihood
5.2.7
Sampling Distribtion of
\(\bar {\pmb y}, S\)
5.2.8
Assessing Normality
5.2.9
Power Transformation
5.3
Inference about Mean Vector (wk3)
5.3.1
Overview
5.3.2
1. Confidence Region
5.3.3
2. Simultaneous CI
5.3.4
3. Note: Bonferroni Multiple Comparison
5.3.5
4. Large Sample Inferences about a Mean Vector
5.3.6
1. Profile Analysis (wk4, 5)
5.3.7
2. Test for Linear Trend
5.3.8
3. Inferences about a Covariance Matrix
5.4
Comparison of Several MV Means (wk5)
5.4.1
Paired Comparison
5.4.2
Comparing Mean Vectors from Two Populations
5.4.3
Profile Analysis (for
\(g=2\)
)
5.4.4
Comparing Several Multivariate Population Means
5.5
Multivariate Multiple Regression (wk6)
5.5.1
Overview
5.5.2
Multivariate Multiple Regression
5.5.3
Example)
5.6
PCA
5.7
Factor
5.7.1
Method of Estimation
5.7.2
Factor Rotation
5.7.3
Varimax Criterion
5.7.4
Factor Scores
5.8
Discrimination and Classification
5.8.1
Bayes Rule
5.8.2
Classification with Two mv
\(N\)
Populations
5.8.3
Evaluating Classification Functions
5.8.4
Classification with several Populations (wk13)
5.8.5
Other Discriminant Analysis Methods
5.9
Clustering, Distance Methods, and Ordination
5.9.1
Overview
5.9.2
Hierarchical Clustering
5.9.3
K-means Clustering
5.9.4
군집의 평가방법
5.9.5
Clustering using Density Estimation (wk14)
5.9.6
Multidimensional Scaling (MDS)
6
Linear
6.1
Overview & SVD
6.1.1
Spectral Decomposition
6.1.2
Singular value Decomposition: General-version
6.1.3
Singular value Decomposition: Another-version
6.1.4
Quadratic Forms
6.1.5
Partitioned Matrices
6.1.6
Geometrical Aspects
6.1.7
Column, Row and Null Space
6.2
Introduction
6.2.1
What
6.2.2
Random Vectors and Matrices
6.2.3
Multivariate Normal Distributions
6.2.4
Distributions of Quadratic Forms
6.3
Estimation
6.3.1
Identifiability and Estimability
6.3.2
Estimation: Least Squares
6.3.3
Estimation: Best Linear Unbiased
6.3.4
Estimation: Maximum Likelihood
6.3.5
Estimation: Minimum Variance Unbiased
6.3.6
Sampling Distributions of Estimates
6.3.7
Generalized Least Squares(GLS)
6.4
One-Way ANOVA
6.4.1
One-Way ANOVA
6.4.2
More About Models
6.4.3
Estimating and Testing Contrasts
6.4.4
Cochran’s Theorem
6.5
Testing
6.5.1
More About Models: Two approaches for linear model
6.5.2
Testing Models
6.5.3
A Generalized Test Procedure
6.5.4
Testing Linear Parametric Functions
6.5.5
Theoretical Complements
6.5.6
A Generalized Test Procedure
6.5.7
Testing Single Degrees of Freedom in a Given Subspace
6.5.8
Breaking SS into Independent Components
6.5.9
General Theory
6.5.10
Two-Way ANOVA
6.5.11
Confidence Regions
6.5.12
Tests for Generalized Least Squares Models
6.6
Generalized Least Squares
6.6.1
A direct solution via inner products
6.7
Flat
6.7.1
1.Flat
6.7.2
2. Solutions to systems of linear equations
6.8
Unified Approach to Balanced ANOVA Models
(PART) 21-02
7
Network Stats
7.1
Introduction
7.1.1
Types of Network Analysis
7.1.2
Network Modeling and Inference
7.1.3
Network Processes
7.2
Descriptive Statistics of Networks
7.2.1
Vertex and Edge Characteristics
7.2.2
Characterizing Network Cohesion
7.2.3
Graph Partitioning
7.2.4
Assortativity and Mixing
7.3
Data Collection and Sampling
7.3.1
Sampling Designs
7.3.2
Coping Strategies
7.3.3
Big Data Solves Nothing
7.4
Mathematical Models for Network Graphs
7.4.1
Classical Random Graph Models
7.4.2
Generalized Random Graph Models
7.4.3
Network Graph Models Based on Mechanisms
7.4.4
Assessing Significance of Network Graph Characteristics
7.5
Introduction to ERGM
7.5.1
Exponential Random Graph Models
7.5.2
Difficulty in Parameter Estimation
7.6
Parameter Estimation of ERGM
7.6.1
Current Methods for ERGM
7.6.2
Approximation-based Algorithm
7.6.3
Auxiliary Variable MCMC-based Approaches
7.6.4
Varying Trunction Stochastic Approximation MCMC
7.6.5
Conclusion
7.7
ERGM for Dynamic Networks
7.7.1
Temporal ERGM (TERGM, T ERGM)
7.7.2
Separable Temporal ERGM (STERGM, ST ERGM)
7.8
Latent Network Models
7.8.1
Latent Position Model
7.8.2
Latent Position Cluster Model
7.9
Additive and Multiplicative Effects Network Models
7.9.1
Introduction
7.9.2
Social Relations Regression
7.9.3
Multiplicative Effects Models
7.9.4
Inference via Posterior Approximation
7.9.5
Discussion and Example with R
7.10
Stochastic Block Models
7.10.1
Stochastic Block Model
7.10.2
Mixed Membership Block Model (MMBM)
8
High Dimension
8.1
Introduction
8.2
Concentration inequalities
8.2.1
Motivation
8.2.2
From Markov to Chernoff
8.2.3
sub-Gaussian random variables
8.2.4
Properties of sub-Gaussian random variables
8.2.5
Equivalent definitions
8.2.6
Sub-Gaussian random vectors
8.2.7
Hoeffding’s inequality
8.2.8
Maximal inequalities
8.2.9
8.3
Concentration inequalities
8.3.1
Sub-exponential random variables
8.3.2
Bernstein’s condition
8.3.3
McDiarmid’s inequality
8.3.4
Levy’s inequality
8.3.5
Quadratic form
8.3.6
The Johnson–Lindenstrauss Lemma
8.4
Metric entropy and its uses
8.4.1
Metric space
8.4.2
Covering numbers and metric entropy
8.4.3
Packing numbers
8.4.4
8.4.5
8.4.6
8.5
Covariance estimation
8.5.1
Matrix algebra review
8.5.2
Covariance matrix estimation in the operator norm
8.5.3
Bounds for structured covariance matrices
8.6
Matrix concentration inequalities
8.6.1
Matrix calculus
8.6.2
Matrix Chernoff
8.6.3
Sub-Gaussian and sub-exponential matrices
8.6.4
랜덤 매트릭스에 대한 Hoeffding and Bernstein bounds
8.7
Principal Component Analysis
8.7.1
PCA
8.7.2
Matrix Perturbation
8.7.3
Spiked Cov Model
8.7.4
sparse PCA
8.8
Linear Regression
8.8.1
Problem formulation
8.8.2
Least Squares Estimator in high dimensions
8.8.3
Sparse linear regression
8.9
Uniform laws of large numbers
8.9.1
Motivation
8.9.2
A uniform law via Rademacher complexity
8.9.3
Upper bounds on the Rademacher complexity
9
Survival Analysis
9.1
Introduction
9.2
9.3
Counting Processes and Martingales
9.3.1
Conditional Expectation
9.3.2
Martingale
9.3.3
Key Martingales Properties
9.3.4
9.3.5
9.4
9.5
Cox Regression
9.6
Filtration의 개념을 정복하자!
9.6.1
Random Process를 이야기 하기까지의 긴 여정의 요약
9.6.2
Ft-measurable
9.6.3
EPILOGUE
9.7
Concepts
(PART) 22-01
10
scikit
10.1
Linear Models
10.1.1
Ordinary Least Squares
(APPENDIX) 00-00
11
Concepts
11.1
Autologistics
11.2
Ordered Logit
11.3
Concepts Questions
11.3.1
통계 및 수학
12
About Cluster-GCN
12.0.1
ANN
12.0.2
CNN
12.0.3
Graph Convolution Network
12.0.4
Cluster-GCN
13
CNN
14
CNN
15
CNN
16
01
Published with bookdown
Self-Study
Chapter 8
High Dimension