STATISTICAL METHODS IN DATA SCIENCE AND LABORATORY II
Prof. L. Tardella
semester II
6 credits
List of topics:
- introduction to the basics of Bayesian inference
- introduction to Monte Carlo methods as approximation strategy
- Monte Carlo methods for Bayesian inference
- pseudo-random number generation
- uniform distributions and common classes of parametric distributions
- general classes of algorithms for simulating from a known density
- classical asymptotic theorems and Monte Carlo methods: convergence and error control
- importance sampling techniques
- other techniques for improving error control: antithetic variates, control variates
- Monte Carlo strategies for approximating marginal likelihood and Bayes Factor
- introduction to Markov chains on a finite state space
- introduction to Markov chains on general state spaces
- transition kernels and transition densities
- Markov chains, stationarity, invariant measures,
- limiting distributions and rate of convergence
- general algorithms for Markov chain simulation with a prescribed invariant distribution
- Gibbs sampling
- Metropolis Hastings
- MH, alternative proposal distributions, tuning
- basic examples of GS
- basic examples of MH
- reversibility
- hybrid methods: kernel composition, kernel mixtures
- GS and MH implementation on real data examples
- Bayesian hierarchical linear models, generalized linear model (logistic and probit)
- finite mixture models
- model choice and model averaging; transdimensional methods
- ergodic theorems for MCMC
- error control and variance estimation of ergodic Markov Chains, effective sample size
- convergence monitoring
- software tools for MCMC implementation: R packages and BUGS
- sequential methods and particle filters (*)
- ABC (Approximate Bayesian Computation) (*)
- dynamic linear models (*)
- introduction to the basics of Bayesian inference
- introduction to Monte Carlo methods as approximation strategy
- Monte Carlo methods for Bayesian inference
- pseudo-random number generation
- uniform distributions and common classes of parametric distributions
- general classes of algorithms for simulating from a known density
- classical asymptotic theorems and Monte Carlo methods: convergence and error control
- importance sampling techniques
- other techniques for improving error control: antithetic variates, control variates
- Monte Carlo strategies for approximating marginal likelihood and Bayes Factor
- introduction to Markov chains on a finite state space
- introduction to Markov chains on general state spaces
- transition kernels and transition densities
- Markov chains, stationarity, invariant measures,
- limiting distributions and rate of convergence
- general algorithms for Markov chain simulation with a prescribed invariant distribution
- Gibbs sampling
- Metropolis Hastings
- MH, alternative proposal distributions, tuning
- basic examples of GS
- basic examples of MH
- reversibility
- hybrid methods: kernel composition, kernel mixtures
- GS and MH implementation on real data examples
- Bayesian hierarchical linear models, generalized linear model (logistic and probit)
- finite mixture models
- model choice and model averaging; transdimensional methods
- ergodic theorems for MCMC
- error control and variance estimation of ergodic Markov Chains, effective sample size
- convergence monitoring
- software tools for MCMC implementation: R packages and BUGS
- sequential methods and particle filters (*)
- ABC (Approximate Bayesian Computation) (*)
- dynamic linear models (*)