## 5.1 Introduction

As cosmology becomes nowadays increasingly dominated by results emerging from large-scale
observational programmes, it is imperative to be able to justify that resources are being deployed as
effectively as possible. In recent years it has become standard to quantify the expected outcome of
cosmological surveys to enable comparison, a procedure exemplified by the Figure of Merit (FoM)
introduced by [470] and later used in the influential Dark Energy Task Force (DETF) report about
dark-energy surveys [21, 22].
The idea is to be able to capture in one single number the scientific return of a future mission, in order
to be able to rank competing proposals and to forecast their ability to answer relevant scientific questions,
such as: is dark energy a cosmological constant or does it evolve with time? Is it an expression of modified
gravity? How well can a time-evolution of dark energy be constrained?

Encapsulating the entire value of a proposed cosmological survey in one single number is of course highly
reductive, and the ensuing conclusions should therefore be taken with a large grain of salt.
Having said that, work in recent years has focused on attempts to devise Figures of Merit (FoMs)
that represent in an increasingly realistic way future missions. It is perhaps obvious that, to
a certain extent, the assessment of a future probe will depend on the scientific question one
is most interested in: parameter constraints, model selection, robustness to systematics are
but a few examples of the different levels on which a proposed mission can be evaluated and
optimized.

This part gives an overview of some of the approaches recently adopted in the field, and used elsewhere
in this document to produce forecasts for Euclid. Useful references and background material to some of the
concepts discussed below are: [897, 439] for an introduction to Bayesian methods in cosmology, [839, 607]
for introductions to the Bayesian approach in data analysis, [396] for an introduction to Markov Chain
Monte Carlo (MCMC) methods.