  We review the data gathering and analysis procedure used in real
Einstein-Podolsky-Rosen-Bohm experiments with photons and we illustrate the
procedure by analyzing experimental data. Based on this analysis, we construct
event-based computer simulation models in which every essential element in the
experiment has a counterpart. The data is analyzed by counting single-particle
events and two-particle coincidences, using the same procedure as in
experiments. The simulation models strictly satisfy Einstein's criteria of
local causality, do not rely on any concept of quantum theory or probability
theory, and reproduce all results of quantum theory for a quantum system of two
$S=1/2$ particles. We present a rigorous analytical treatment of these models
and show that they may yield results that are in exact agreement with quantum
theory. The apparent conflict with the folklore on Bell's theorem, stating that
such models are not supposed to exist, is resolved. Finally, starting from the
principles of probable inference, we derive the probability distributions of
quantum theory of the Einstein-Podolsky-Rosen-Bohm experiment without invoking
concepts of quantum theory.
