Estimation of parameter distributions in a model of magnesium dynamics in cows to predict the risk of tetany in dairy herds

Abstract

The onset of tetany, when dairy cattle have insufficient magnesium, has a huge impact both economically and on animal welfare. We have previously adapted a model of magnesium dynamics in sheep (Robson et al. 1997) for use with dairy cattle as an aid to understanding aspects of magnesium metabolism which influence the risk of animals contracting tetany (Bell et al. 2005). To estimate this risk in a dairy herd, we carried out Monte-Carlo simulations in which model parameters for individual animals in the herd were varied randomly according to their statistical distributions (McKinnon et al. 2003). In this approach the choice of parameter distributions can significantly influence the risk estimates. In some cases the distributions are available from the literature, but in other cases they must be obtained using some sort of parameter refinement process to estimate the parameter distributions from measured data corresponding to a model output. In this paper we present an overview of a generalised algorithm which was developed to improve the accuracy of a priori parameter distribution estimates obtained from literature data using an iterative refinement process. At each iteration a response distribution for the current parameter distribution estimate is evaluated using the Monte-Carlo method and compared with a corresponding experimental sample response distribution. A parameter filter is constructed using the iterative parameter estimates and response distributions so that the filter entries form an approximate solution space of the desired refined state. This permits estimates of the parameter distributions to be calculated from the parameter filter.