Interactive material

Basic mathematics

• Derivative
• Riemann integral
• Second derivative and function curvature

Descriptive Statistics

• Choosing the bins in a histogram
• Robustness of mean and median to outliers

Probability

• Normal and Poisson approximations of the Binomial distribution
• Normal approximation of the sampling distribution for a proportion
• Law of large numbers
• Central limit theorem
• Distributions on the unit simplex
• Kullback-Leibler divergence for continuous distributions
• Tails and distribution of the maximum

Statistical distributions

• Nearly 50 different statistical distributions

Basic statistics in Swedish

• List with notebooks for the SDA1 course

Confidence intervals

• Confidence interval for a proportion
• Confidence interval for a mean
• Coverage of intervals for a proportion

Hypothesis testing

• Hypothesis test for a mean
• Type I and II errors in hypothesis testing

Likelihood estimation

• Maximum likelihood - Bernoulli model
• Maximum likelihood - Poisson model
• Maximum likelihood - Poisson regression
• Sampling distribution and likelihood function - Bernoulli model

Bayesian Learning

• Bayes’ theorem for events
• Bayesian inference for Bernoulli data
• Bayesian inference for normal data with known variance
• Bayesian inference for normal data with unknown variance
• Bayesian inference for counts
• Bayesian inference for exponential data
• Bayesian inference for multinomial data
• Bayesian credible intervals
• Prior predictive distribution for Poisson model
• Bayesian linear regression
• Normal posterior approximation for Beta model
• Frequentist coverage of credible intervals for a proportion
• Bayesian test for a mean
• Priors for AR process

Time series

• AR processes - simulation and autocorrelation function
• Seasonal ARMA(p,q) - simulation and autocorrelation
• Spectral density - ARMA(p,q) process
• Spectral density of a seasonal ARMA(p,q)×(P,Q) process
• ARTFIMA - tempered fractional differencing
• ARTFIMA - spectral density

Time-varying parameter models and state-space models

• Piecewise constant model for time series
• Local level model
• Local trend model
• Time-varying regression
• Poisson time series model
• Stochastic volatility model
• Kalman filtering on simulated data from local level model
• Kalman filtering for Nile river data
• Identification of the mean in the AR(1) process
• Local level model with dynamic shrinkage process prior

Interactive notebooks for research

• Time-varying spectral density for US industrial production data from the paper Time-Varying Multi-Seasonal AR Models