Speaker
Description
Numerically approximating multidimensional posterior distributions can be very expensive
when evaluating the likelihood function involves expensive numerical computation.
At the same time many likelihoods in physics show a "speed hierarchy"
between the different dimensions of the parameter space which means that recomputing
the likelihood function is much more expensive when changing some parameters
than others. This naturally arises when some of these parameters come from theoretical
models while others are associated to the data. Recently some attempts have
been made at fast Bayesian inference using Bayesian quadrature to reduce
the number of samples required for mapping the posterior distributions drastically.
While this approach works well in low dimensions it becomes prohibitively expensive
if the number of dimensions exceeds d~10. Additionally these approaches
cannot take advantage of the aforementioned speed hierarchy in the likelihood. In
this thesis we develop an algorithm which mitigates these problems and improves
on the current state of the art by (i) introducing a novel acquisition function which
is well suited to performing Bayesian quadrature of log-probability distributions (ii)
accelerating the Kriging believer batch acquisition algorithm with blockwise matrix
inversion and (iii) Proposing an algorithm which can take advantages of
speed hierarchies by marginalizing nuisance parameters with the PolyChord nested
sampling algorithm. We test these algorithms on gaussian toy likelihoods and
real cosmological likelihoods and report a decrease in wall clock time of up to several
orders of magnitude for mapping the posterior space.
