Often, in dynamical systems such as farmer’s crop choices, the dynamics are driven by external non-stationary factors, such as rainfall, temperature and agricultural input and output prices. Such dynamics can be modelled by a non-stationary Markov chain, where the transition probabilities are multinomial logistic functions of such external factors. We extend previous work to investigate the problem of estimating the parameters of the multinomial logistic model from data. We use conjugate analysis with a fairly broad class of priors, to accommodate scarcity of data and lack of strong prior expert opinion. We discuss the computation of bounds for the posterior transition probabilities. We use the model to analyse some scenarios for future crop growth.