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

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