"Find the best fit values of the slope and intercept from the data using MultNest"
First build the MultiNest libraries provided
$ cd MultiNest_v2.18_CMake/build/
$ cmake ../
$ make
Go to the FitALine directory and build the program
$ cd ../../FitALine/build/
$ cmake ../ -DMULTINEST_ROOT_HINT=../../MultiNest_v2.18_CMake/
$ make
The python script create_data.py will create a data with 100 points with slome m=0.7 and intercept c=2.5.
$ cd ../
$ python create_data.py
The data is written to line_data.dat.
Run the fitting program
$ cd build
$ ./fit_a_line.exe
You will see the folowing output
*****************************************************
MultiNest v2.18
Copyright Farhan Feroz & Mike Hobson
Release Aug 2012
no. of live points = 1000
dimensionality = 2
*****************************************************
Starting MultiNest
generating live points
live points generated, starting sampling
Acceptance Rate: 0.999049
Replacements: 1050
Total Samples: 1051
ln(Z): -881697.419099
Acceptance Rate: 0.993677
Replacements: 1100
Total Samples: 1107
ln(Z): -701436.756640
Acceptance Rate: 0.988822
Replacements: 1150
Total Samples: 1163
ln(Z): -591172.468396
Acceptance Rate: 0.981194
Replacements: 1200
Total Samples: 1223
ln(Z): -528077.020677
Acceptance Rate: 0.974279
Replacements: 1250
Total Samples: 1283
ln(Z): -450880.827773
Acceptance Rate: 0.963677
Replacements: 1300
Total Samples: 1349
ln(Z): -391711.172461
Acceptance Rate: 0.950035
Replacements: 1350
Total Samples: 1421
ln(Z): -345986.707547
Acceptance Rate: 0.936455
Replacements: 1400
Total Samples: 1495
ln(Z): -312810.564647
..........................................................
..........................................................
..........................................................
Acceptance Rate: 0.915384
Replacements: 14150
Total Samples: 15458
ln(Z): -65.904609
Acceptance Rate: 0.915433
Replacements: 14159
Total Samples: 15467
ln(Z): -65.901423
ln(ev)= -65.549001951267400 +/- 0.10549400415943505
Total Likelihood Evaluations: 15467
Sampling finished. Exiting MultiNest
All the output files are written to chains directory.
$ cd chains
$ ls -la
-rw-r--r-- 1 sree sree 1552762 Jan 22 12:46 fit_a_line_ev.dat
-rw-r--r-- 1 sree sree 85000 Jan 22 12:46 fit_a_line_live.points
-rw-r--r-- 1 sree sree 89000 Jan 22 12:46 fit_a_line_phys_live.points
-rw-r--r-- 1 sree sree 297075 Jan 22 12:46 fit_a_line_post_equal_weights.dat
-rw-r--r-- 1 sree sree 848519 Jan 22 12:46 fit_a_line_post_separate.dat
-rw-r--r-- 1 sree sree 219 Jan 22 12:46 fit_a_line_resume.dat
-rw-r--r-- 1 sree sree 731 Jan 22 12:46 fit_a_line_stats.dat
-rw-r--r-- 1 sree sree 281 Jan 22 12:46 fit_a_line_summary.txt
-rw-r--r-- 1 sree sree 848517 Jan 22 12:46 fit_a_line_.txt
The posterior samples can be found in fit_a_line_post_post_equal_weights.dat file. The posterior statistics are written to fit_a_line_stats.dat. See the stats using
$ cat fit_a_line_stats.dat
Global Evidence: -0.655490019512673996E+02 +/- 0.105494004159435051E+00
Local Mode Properties
-------------------------------------------
Total Modes Found: 1
Mode 1
Strictly Local Evidence -0.655490019512673996E+02 +/- 0.105494004159435051E+00
Local Evidence -0.655490019512673996E+02 +/- 0.105494004159435051E+00
Dim No. Mean Sigma
1 0.683419243109782415E+00 0.169441339238071767E-01
2 0.278679217846152305E+01 0.194627320053394198E+00
Maximum Likelihood Parameters
Dim No. Parameter
1 0.684161697417490444E+00
2 0.277934384560164460E+01
MAP Parameters
Dim No. Parameter
1 0.659525928528765348E+00
2 0.306564406503305520E+01
Come back to root directory and use the plotting script plot_posterior.py.
$ cd ../../
$ python plot_posterior.py
The plots can be found in the directory plots and are shown below