Hi, I'm a bit confused about this and would like to ask a few questions:
When can we use an analytical method and when must we use sampling simulation? For example, I have an introductory Statistics book and it provides formulae (though with no real explanation or examples), for calculating the posterior means SD's and CI's given the prior (data) and actual data. These formulae are; mean b = n0*b0 +nb/n0+n SE b = (sigma/sigmaX)/sqr(n0+n) 95% CI b =(n0b0+nb)/(n0+n)+-1.96(SE b) where the suffix 0 specifies prior data and n0 = (sigma/sigmaX)^2/sigma0^2 is called the size of the "quasi-sample". So, if I have prior data, can I just perform a linear regression on this data to get b0 and sigma0, and again on the test data, then combine using the above formulae to get the posterior value for b? Can I extend this to a quadratic example, but still linear in the parameters like y=a+(b1)x+(b2)x^2 and use the same formulae for a, b1 and b2 to achieve the posterior values for the parameters? So, if we can do the above by analytical methods why do we need simulation, or is it just required for multiple rather than simple linear regression? Further, the 'impact' of the prior data is weighted by the size of the quasi-sample above. How does this work in a simulation? Is it just given by the sd of the prior, which doesn't seem the same thing? Finally, could someone provide a worked example(s) (or links to) so that I can check that I know what I'm doing! I am particularly interested in using an informative prior (which has been derived from its own data set) and the quadratic form of the linear model. An analytic worked example and a simulation example would be great. I have access to matlab and Winbugs though any code or workings would be great. Thanks . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
