  Single-molecule force spectroscopy experiments, as well as a number of other
physical systems, are governed by thermally activated transitions out of a
metastable state under the action of a steadily increasing external force. The
main observable in such experiments is the distribution of the forces, at which
the escape events occur. The challenge in interpreting the experimental data is
to relate them to the microscopic system properties. We work out a maximum
likelihood approach and show that it is the optimal method to tackle this
problem. When fitting actual experimental data it is unavoidable to assume some
functional form for the force-dependent escape rate. We consider a quite
general and common such functional form and demonstrate by means of data from a
realistic computer experiment that the maximum number of fit parameters that
can be determined reliably is three. They are related to the force-free escape
rate and the position and height of the activation barrier. Furthermore, the
results for the first two of these fit parameters show little dependence on the
assumption about the manner in which the barrier decreases with the applied
force, while the last one, the barrier height in the absence of force, depends
strongly on this assumption.
