  Stochastic kinetic models are often used to describe complex biological
processes. Typically these models are analytically intractable and have unknown
parameters which need to be estimated from observed data. Ideally we would have
measurements on all interacting chemical species in the process, observed
continuously in time. However, in practice, measurements are taken only at a
relatively few time-points. In some situations, only very limited observation
of the process is available, such as when experimenters can only observe noisy
observations on the proportion of cells that are alive. This makes the
inference task even more problematic. We consider a range of data-poor
scenarios and investigate the performance of various computationally intensive
Bayesian algorithms in determining the posterior distribution using data on
proportions from a simple birth-death process.
