  We induce quantum jumps between the hyperfine ground states of one and two
Cesium atoms, strongly coupled to the mode of a high-finesse optical resonator,
and analyze the resulting random telegraph signals. We identify experimental
parameters to deduce the atomic spin state nondestructively from the stream of
photons transmitted through the cavity, achieving a compromise between a good
signal-to-noise ratio and minimal measurement-induced perturbations. In order
to extract optimum information about the spin dynamics from the photon count
signal, a Bayesian update formalism is employed, which yields time-dependent
probabilities for the atoms to be in either hyperfine state. We discuss the
effect of super-Poissonian photon number distributions caused by atomic motion.
