Many models of complex phenomena (physics, molecular dynamics, etc.) have no
global analytical expressions but admit implementations in silico in form of
forward simulators. In turn, forward simulations are used to solve inverse
problems: given observations of the phenomena find its initial conditions
viewed as input parameters of the simulator.
In statistical terms solving such an inverse problem corresponds to sampling
from a (bayesian) posterior distribution with the implicit likelihood given by the
simulator - this provides (at least) an answer to the problem with
error bounds in form of uncertainty estimates. High dimensionality and/or
computational load hinder use of simple classical methods (like ABC or
Kernel Density Estimator) and lead to construction of surrogates that approximate
the intractable likelihood coupled with amenable schemes for posterior sampling.
Recent advances in Automatic Differentiation models allow construction of
such surrogates which are yet in their early development. In this thesis
we aim to study and develop new ways to construct differentiable surrogates
and apply them on a number of realistic problems starting
with a number of applications in nuclear imaging.