Summarised lecture notes of the course CS-E5795 Computational Methods in Stochastics taught at Aalto University.
- Random variables and distributions
- Random variables
- Expectation of RVs
- Join didstributions, independency, and conditionality
- Central limit theorem
- Stochastic simulation
- Monte Carlo
- Transformation methods
- Conditionality and Markov processes
- Markov chain properties
- Markov chains in continuous time
- Sampling an inhomogeneous Poisson process
- MCMC and Bayesian inference
- Gibbs sampler
- Metropolis-Hastings algorithm
- Hamiltonian Monte Carlo
- Hamiltonian dynamics
- Discretization of Hamilton's equations