Parameter Identification and Forecast with a Biased Model

A well known practical issue is to ascertain how well the parameters of a model can be identified so as to allow a legitimate inference. In most cases, models are biased and may not contain all the necessary features needed to fit the data well. Employing the simplest Ross model as an example, we illustrated that parameter identifiability can be a problem of three factors: model specification, noisy data and partially observed model. Kalman filtering technique was employed in order to produce an optimal estimate of the evolving state of the system based on the model and other information such as rainfall, while simultaneously estimating the model parameters using the Kalman filter likelihood. Markov Chain Monte Carlo (MCMC) was employed as a general tool to diagnose parameter identifiability. To show the performance of the methods, an illustrative example was given with malaria data from Kalangala district, Uganda. In the end, the parameters were more or less well identified although the posterior is larger than when a synthetic data was used.