## CosmoMC likelihood distribution definition

Use of Healpix, camb, CLASS, cosmomc, compilers, etc.
vital fernandez
Posts: 1
Joined: August 10 2015
Affiliation: INAOE

### CosmoMC likelihood distribution definition

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, $\chi^2$ 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 $\sigma$ in the $\chi^2$ squared formula the $\sigma$ of the distribution.

Thank you in advance for any advice/reference to point me in the right direction