A MATLAB example of approximate Bayesian computation (ABC) MCMC algorithm to estimate parameters of a g-and-k distribution. See also my slides http://goo.gl/ypAOjs

We implement the example in Allingham et al 2009, except that we use our own custom summary statistics (see gk_summaries) and use a Gaussian kernel to compare summary statistics for simulated and actual data.

Content:

• gk_run, the script running the example
• gk_summaries, defines the summary statistics
• gk_ prior, defines the prior distributions for the parameters to be estimated
• gk_modelsimulate, produces a realization from the g-and-k distribution
• abcmcmc, the ABC-MCMC algorithm. Uses a Gaussian kernel to compare summary statistics for simulated and actual data. Parameters are proposed using the (on-line) adaptive Gaussian Metropolis random walk of Haario et al. 2001.
• cov_update, on-line covariance matrix update for the adaptive MCMC
• param_mask, param_unmask, utilities that extract free parameters from the vector of complete parameters and insert them back in the compete vector of parameters.

• Allingham, King and Mengersen 2009, "Bayesian estimation of quantile distributions", Stat Comput 19.
• Haario, Saksman and Tamminen 2001, "An adaptive Metropolis algorithm", Bernoulli Volume 7, 223-242.