  The ab initio thermodynamic simulation of correlated Fermi systems is of
central importance for many applications, such as warm dense matter, electrons
in quantum dots, and ultracold atoms. Unfortunately, path integral Monte Carlo
(PIMC) simulations of fermions are severely restricted by the notorious fermion
sign problem (FSP). In this work, we present a hands-on discussion of the FSP
and investigate in detail its manifestation with respect to temperature, system
size, interaction-strength and -type, and the dimensionality of the system.
Moreover, we analyze the probability distribution of fermionic expectation
values, which can be non-Gaussian and fat-tailed when the FSP is severe. As a
practical application, we consider electrons and dipolar atoms in a harmonic
confinement, and the uniform electron gas in the warm dense matter regime. In
addition, we provide extensive PIMC data, which can be used as a reference for
the development of new methods and as a benchmark for approximations.
