CosmoMC: Finding the best fit Log likelihood

Use of Healpix, camb, CLASS, cosmomc, compilers, etc.
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gongbo zhao
Posts: 71
Joined: January 04 2005
Affiliation: ICG, Portsmouth

CosmoMC: Finding the best fit Log likelihood

Post by gongbo zhao » October 26 2005

Dear all:
I want to find the best fit -Log(Like) value of a given cosmological model using some datasets.I set action = 2 in params.ini since MCMC cannot provide accurate best fit values. Testing with \Lambda CDM model using WMAP-only data , I found the same result using two different initial seeds as follows:
Random seeds: 4321, 9373 rand_inst: 0
Random seeds: 12345, 9373 rand_inst: 0

Computing tensors: F

Doing CMB lensing: F

lmax = 2100

Number of C_ls = 3

Varying 6 parameters ( 2 fast)

reading: params_CMB.covmat

Finding max-like point

reading WMAP data

WMAP read

Change in F is less than 0.10000000 after 4 iterations

Found minimum value of -Log(Like) = 717.2668

Converged sucessfully (loglike changes by less than 0.1000000 )

after 4 iterations

Best fit parameters values:

1 : 2.3866521E-02

2 : 0.1122643

3 : 1.049735

4 : 0.1119891

8 : 0.9966581

11 : 3.118499

Have estimated the minimum, now exiting since action=2

Wrote the minimum to file chains/test2.minimum

I used all the default setting in params.ini except
delta_loglike = 0.1
use_CMB = T
use_HST = F
use_mpk = F
use_clusters = F
use_BBN = F
use_Age_Tophat_Prior = F
use_SN = F
use_min_zre = 0
The best-fit -Log(Like)=717.2668 is larger than the other published fitting results ( around 714 ),I have tested by setting delta_loglike = 1,2 ,the best-fit -Log(Like) got larger. Did I make any mistakes ? Any comments and suggestion on that ?
Thanks in advance .

Gongbo Zhao

Sarah Bridle
Posts: 144
Joined: September 24 2004
Affiliation: University College London (UCL)

CosmoMC: Finding the best fit Log likelihood

Post by Sarah Bridle » October 26 2005

The minimiser in fact does not use the random seed generator.
The minimiser finds the gradient at the initial values of the cosmological parameters, as set in the params.ini file, and then uses the conjugate gradient algorithm as in Numerical Recipes (using bracketing around gradient=0 to find the minimum in each direction).
It chooses to stop refining the search when the change in the likelihood is less than delta_loglike.
Therefore for most problems, the log likelihood at the best fit point will be correct to very roughly +/- delta_loglike, but this depends on the geometry of the probability surface around the best fit point.
Decreasing delta_loglike to e.g. 0.1 would continue the search for longer, and therefore get closer to the true local minimum.
You could also consider changing the starting position for the search, by changing the cosmological parameter values in the first column in params.ini.
Hope this makes more sense than my previous message,

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