Greetings everyone. I am PhD student who has recently started in bayesian statistics and I have some basic questions about using COSMOMC as a MCMC sampler.
I would like to start doing a simple linear regression using the scheme described in this cosmomc lecture http://www.cosmo-ufes.org/uploads/1/3/7 ... torial.pdf by Daniel Boreiro, where the likelihood in the cosmomc sampler is defined as:
At this point my questions are:
A) Is this the default likelihood definition? If not, how was it defined?
B) What is the distribution of this likelihood? From what I have read in the cosmomc notes, parameters are defined with a normal distribution or a n-dimensional guassian distribution, if you provide the covariance matrix. However, according to the definition in the image above, [tex]\chi^2[/tex] is a logaritmic estimate of the probability.... So is this a log-normal probability?
C) Finally, in the case of a normal distribution, is the [tex]\sigma[/tex] in the [tex]\chi^2[/tex] squared formula the [tex]\sigma[/tex] of the distribution.
Thank you in advance for any advice/reference to point me in the right direction
CosmoMC likelihood distribution definition
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