The paper deals with Bayesian inference in a discretely observed stochastic predator-prey model. The dynamics of the model is described by a system of stochastic differential equations where the noise term summarizes both demographic and environmental stochasticity. We focus on the estimation of a behavioural parameter appearing in the functional response of a predator to the prey abundance when only few observations are available. Latent data are introduced between each pair of observations and are considered as missing data. An MCMC algorithm is used to sample from the posterior distribution of the parameter of interest. The method is then applied to both simulated and real data and results for different numbers of latent data are compared with those obtained following a frequentist approach. As a case study we consider an acarine predator-prey system relevant to biological control problems.

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