Bayesian Computing
Bayesian Computing Problems
Laplace Approximation
Quadrature
IID Monte Carlo
Importance Sampling
Markov chain Monte Carlo
Concluding
Example 1:
Inferring Poisson rate from count data
Example 2:
SImple linear regression
Keywords to search
conditional distribution
Bayesian Computational problems:
Marginal and joint distribution
Posterior predictive distribution
Comparing evidence for different models
There are alternatives to integration for the posterior, but integration is much better
Useful algorithms for integration
Numerical approximation
Monte carlo methods
idea
use a Taylor series approximation so that the posterior is approximated by a normal distribution
mean=mode of the posterior
Covariance = curvature at the mode
New math for me
approximating integrals with summing (like trapezoid)
related methods
quasi-Monte-Carlo