Research in physics often starts from a mechanistic model
and then aims to understand how different parameter regimes are related
to certain features in the data. This type of research focuses on the
model and views features in the data as emergent properties. Statistics
follows the opposite direction: given the data, the aim is to find, or
"infer", the parameters of the model that are most consistent with the
observations. In this talk I will focus on three different applications
in which statistical inference is computationally challenging for
various reasons and I will show how state-of-the-arr methods from
computational statistics can come to our rescue. First, I will discuss
optimising physiological parameters of a bio-mechanical model of the
left ventricle for which standard gradient-based optimisation schemes
are prohibitively time consuming. Second, I will talk about a stochastic
system describing cell movement with the outputs of the associated
simulator being very high-dimensional. Third, I will speak about risk
evaluation, or estimating the probability of a rare event, for which
simulating from the model directly typically does not lead to improved
insights on the event in question.