Novel artificial neural network (ANN) techniques are giving new development possibilities in many time series applications. Their performance must be compared with other ANN and with non neural models in order to choose the most suitable method for a particular application and data set. These performances are usually measured by the accurracy of the prediction, the computational costs and by other information they might provide.
In this paper we will consider the use of Bayesian ANN in a forecasting task, and compare its performance with other methods. As it is the case in many real world applications the variable to be predicted will have a non linear relation to other variables and might have noise corrupting the data points.
Having a set of data points we can arrange them, using an appropiate windowing, instances 
which are assumed to be the result of:
where 
is a noise term.
Training the network using standard back-propagation techniques
[9],[8] or more complex variations of it [10] we get a network such that given a new input vector 
,
we get an output 
that can be interpreted as an estimate of the regression 
.
In many applications however it is of great importance to quantify the accurracy of these estimations.
In section 1.1, we introduce Bayesian forecasting using neural networks, and in 1.2 the Markov Chain Monte Carlo (MCMC) techniques used to sample the weight space of the neural networks. In section 2 we describe the data sets used based the Mackey Glass series, the neural network architecture and other methodological issues. Section 3 describes the results and compares various backpropagation and neural network algorithms, and Multivariate Adaptive Regression Splines (MARS) to the Bayesian techniques, we show here (sec 3.1) how Bayesian learning performs better than other methods, specially in the noisy data set, the computational expense is high (sec. 3.2), but has the advantage (sec. 3.3) that it can be used to obtain the prediction intervals that describe a degree of belief of the predictions.