Navneeth: I am afraid I am not very qualified for answering this query. When we wrote Bayesian Core, we thought we had a basic introduction to Bayesian Statistics, but the main criticisms were that the book was “too” mathematical!

]]>Thanks, Keith.

Yes indeed, I had not looked close enough: the likelihood is clearly replaced with a Gaussian approximation for both the empirical mean and more controversially the empirical variance [top of p.119], Or the median and the inter-quartile range (p.122), with no detail on the derivation of the associated variance. This is most curious indeed, since it ends up as a crude version of Laplace’s approximation and not at all related with “our” ABC methods.

]]>Opps, had a look at the ABC entry which does not seem to be ABC as there is no rejection step based on the observed summaries but rather (an motivated) a substitution of a quadratic likelihood for the true likelihood…

Weird given the ABC wiki page is so clear https://en.wikipedia.org/wiki/Approximate_Bayesian_computation#Summary_statistics

Maybe some other idea of approximate?

Keith O’Rourke

]]>One can go further to more realistic problems (e.g. using some simple importance sampling ideas as demonstrated in R code here https://phaneron0.wordpress.com/2012/11/23/two-stage-quincunx-2/ in the BinaryABC link ).

As for how much understanding people can achieve with just this approach, only time will tell.

One important question might be: could their be a group of _competent_ Bayesian analysts that never have to learn MCMC?

Keith O’Rourke

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