(c) 2022, 2023 Geraint F Lewis, B. J. Brewer
LICENSE: GNU General Public Licence v3
NumPy, matplotlib, scipy, astropy,
DNest4 (compiled with C extensions on)
To run the MCMC, execute python main.py. This will load the data and launch
Diffusive Nested Sampling. Every 100 iterations, the posterior samples are
saved to posterior_sample.txt, and the marginal likelihood is printed to the
screen. The main parameter of interest, n (which describes the dependence of
the quasar timescale on the redshift), is the first column of this text file.
Example output is given below.
Data read and file closed
# Seeding random number generators. First seed = 1234.
# Generating 5 particles from the prior...done.
# Creating level 1 with log likelihood = -4316.61360484.
# Creating level 2 with log likelihood = -3205.8457954.
Sample 100.
log(Z) = -1318.8044390992486
Information = 5.568074435862172 nats.
Effective sample size = 1.000000021225817
log(Z) is the marginal likelihood. For more information about Diffusive Nested
Sampling, see this paper,
but be aware that the version shipped with the paper contains a bug. It is
recommended that you install from the master branch of the
DNest4 git repository.
By default, the model sampled is the favoured one, with the parameter n fixed
to 1. To modify the model, follow the instructions in the comment in
the prior_transform() function in main.py:
def prior_transform(u):
"""Transforms the uniform random variable `u ~ Unif[0., 1.)`
to the parameter of interest `x ~ Unif[1, 5)`."""
x = 1. + 4*u
# This is n set to 1. Change the first term here to set it to another
# value, or comment out this line to let n be free.
x[0] = 1 + 1e-6*(u[0]-0.5)
return x