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