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Course Outline
Statistics & Probabilistic Programming in Julia
Basic statistics
- Statistics
- Summary Statistics with the statistics package
- Distributions & StatsBase package
- Univariate & multivariate
- Moments
- Probability functions
- Sampling and RNG
- Histograms
- Maximum likelihood estimation
- Product, trucation, and censored distribution
- Robust statistics
- Correlation & covariance
DataFrames
(DataFrames package)
- Data I/O
- Creating Data Frames
- Data types, including categorical and missing data
- Sorting & joining
- Reshaping & pivoting data
Hypothesis testing
(HypothesisTests package)
- Principle outline of hypothesis testing
- Chi-Squared test
- z-test and t-test
- F-test
- Fisher exact test
- ANOVA
- Tests for normality
- Kolmogorov-Smirnov test
- Hotelling's T-test
Regression & survival analysis
(GLM & Survival packages)
- Principle outline of linear regression and exponential family
- Linear regression
- Generalized linear models
- Logistic regression
- Poisson regression
- Gamma regression
- Other GLM models
- Survival analysis
- Events
- Kaplan-Meier
- Nelson-Aalen
- Cox Proportional Hazard
Distances
(Distances package)
- What is a distance?
- Euclidean
- Cityblock
- Cosine
- Correlation
- Mahalanobis
- Hamming
- MAD
- RMS
- Mean squared deviation
Multivariate statistics
(MultivariateStats, Lasso, & Loess packages)
- Ridge regression
- Lasso regression
- Loess
- Linear discriminant analysis
- Principal Component Analysis (PCA)
- Linear PCA
- Kernel PCA
- Probabilistic PCA
- Independent CA
- Principal Component Regression (PCR)
- Factor Analysis
- Canonical Correlation Analysis
- Multidimensional scaling
Clustering
(Clustering package)
- K-means
- K-medoids
- DBSCAN
- Hierarchical clustering
- Markov Cluster Algorithm
- Fuzzy C-means clustering
Bayesian Statistics & Probabilistic Programming
(Turing package)
- Markov Chain Model Carlo
- Hamiltonian Montel Carlo
- Gaussian Mixture Models
- Bayesian Linear Regression
- Bayesian Exponential Family Regression
- Bayesian Neural Networks
- Hidden Markov Models
- Particle Filtering
- Variational Inference
Requirements
This course is intended for people that already have a background in data science and statistics.
21 Hours
