Statistics and Probabilistic Programming in Julia Training Course

Statistics & Probabilistic Programming in Julia

Basic Statistics

• Statistics
  • Summary statistics using the Statistics package
• Distributions & StatsBase Package
  • Univariate and multivariate distributions
  • Moments
  • Probability functions
  • Sampling and random number generation (RNG)
  • Histograms
  • Maximum likelihood estimation
  • Product, truncation, and censored distributions
  • Robust statistics
  • Correlation and covariance

DataFrames

(DataFrames package)

• Data input/output (I/O)
• Creating data frames
• Data types, including categorical and missing data
• Sorting and joining data
• Reshaping and pivoting data

Hypothesis Testing

(HypothesisTests package)

• Principles of hypothesis testing
• Chi-Squared test
• Z-test and t-test
• F-test
• Fisher exact test
• Analysis of variance (ANOVA)
• Tests for normality
• Kolmogorov-Smirnov test
• Hotelling's T-test

Regression & Survival Analysis

(GLM and Survival packages)

• Principles of linear regression and exponential family
• Linear regression
• Generalized linear models (GLMs)
  • Logistic regression
  • Poisson regression
  • Gamma regression
  • Other GLM models
• Survival analysis
  • Events
  • Kaplan-Meier estimator
  • Nelson-Aalen estimator
  • Cox proportional hazards model

Distances

(Distances package)

• Definition of a distance metric
• Euclidean distance
• Cityblock (Manhattan) distance
• Cosine similarity
• Correlation distance
• Mahalanobis distance
• Hamming distance
• Mean absolute deviation (MAD)
• Root mean square (RMS) error
• Mean squared deviation

Multivariate Statistics

(MultivariateStats, Lasso, and Loess packages)

• Ridge regression
• Lasso regression
• Local regression (Loess)
• Linear discriminant analysis
• Principal Component Analysis (PCA)
  • Linear PCA
  • Kernel PCA
  • Probabilistic PCA
  • Independent component analysis (ICA)
• Principal Component Regression (PCR)
• Factor Analysis
• Canonical Correlation Analysis
• Multidimensional scaling

Clustering

(Clustering package)

• K-means clustering
• K-medoids clustering
• Density-based spatial clustering of applications with noise (DBSCAN)
• Hierarchical clustering
• Markov Cluster Algorithm
• Fuzzy C-means clustering

Bayesian Statistics & Probabilistic Programming

(Turing package)

• Markov Chain Monte Carlo (MCMC)
• Hamiltonian Monte Carlo
• Gaussian mixture models
• Bayesian linear regression
• Bayesian exponential family regression
• Bayesian neural networks
• Hidden Markov models
• Particle filtering
• Variational inference