  We develop a statistical toolbox for a quantitative model evaluation of
stochastic reaction-diffusion systems modeling space-time evolution of
biophysical quantities on the intracellular level. Starting from space-time
data $X_N(t,x)$, as, e.g., provided in fluorescence microscopy recordings, we
discuss basic modelling principles for conditional mean trend and fluctuations
in the class of stochastic reaction-diffusion systems, and subsequently develop
statistical inference methods for parameter estimation. With a view towards
application to real data, we discuss estimation errors and confidence
intervals, in particular in dependence of spatial resolution of measurements,
and investigate the impact of misspecified reaction terms and noise
coefficients. We also briefly touch implementation issues of the statistical
estimators. As a proof of concept we apply our toolbox to the statistical
inference on intracellular actin concentration in the social amoeba
Dictyostelium discoideum.
