An investigation into error propagation in chained models

In this paper we describe several possible approaches for estimating uncertainty in the target output in the chained models. We introduce the approaches from the simple linear model, the nonlinear to the Bayesian modeling method including Markov chain Monte Carlo simulation algorithm. Under several rough assumptions we derive some approximated estimation formulas. The estimated formulas strongly depend not only on the characteristic property of the noises existed in both input pattern and output pattern but also on the given model structure f(x, w) as well as the training dataset.