CosmoMC: Parameter input option

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Rita Sinha
Posts: 3
Joined: September 29 2004
Affiliation: IUCAA, Pune, India

CosmoMC: Parameter input option

Post by Rita Sinha » November 07 2005

Hi,
This is regarding the temperature setting in the params.ini file. As I read from the readme file, "the temperature setting allows one to sample from P^(1/T) rather than P which is good for exploring the tails of distributions, discovering other local minima, and for getting more robust high-confidence error bars."
Could someone please elaborate more on this i.e. how does it exactly affect the likelihood values quantitatively. At present I am running cosmoMC with a new set of inflationary parameters for my model P(k) and evaluating the likelihoods keeping the temperature setting as 1 using both metropolis and slice sampling. I get reasonably good likelihood values. Increasing 'temperature' even slightly to say 1.1/1.05 improves the likelihood value. Increasing temperature further gives me an even lower Chi^2 minimum. How do I know where to stop (i.e. what value of temp shd I use) and whether I need to change the temperature setting at all for my case.
Is it more relevant for postprocessing?

Thanks.

Regards
Rita

Anze Slosar
Posts: 183
Joined: September 24 2004
Affiliation: Brookhaven National Laboratory
Contact:

Re: Parameter input option

Post by Anze Slosar » November 07 2005

Rita Sinha wrote:Increasing 'temperature' even slightly to say 1.1/1.05 improves the likelihood value. Increasing temperature further gives me an even lower Chi^2 minimum. How do I know where to stop (i.e. what value of temp shd I use) and whether I need to change the temperature setting at all for my case.
Well, raising temperature to infinity will give you zero chi^2... :) Temperature is just a trick for sampling difficult posteriors, if you raise your temperature by two, effectivelly all chi^2 are going to be divided by two giving you posterior ranges twice as large. You then correct for this in the post-processing when you correctly reweight your samples. It is useful, for example, if you have two islands of probability and chains have trouble jumping between the two, leaving you with something that converges very slowly: then you raise temperature enough so that islands merge, sampling goes ok and then you post-process back to two separate islands. So, unless you are doing something complicated just leave it at one.

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