Bayesian prediction is analyzed in the I.I.D case. In a search for robust methods we combine non parametric methods - trough Dirichlet processes - and Least- Squares Approximations. Autoprediction is first analyzed as a starting point. Then we consider the prediction of a variable when we are provided with observations of other assoiated variables. we first show the difficulties in conditionning in Dirichlet processes and thereafter propose various approximations for the posterior predictive conditional expectation.
Mouchart, M., & Simar, L. (1984). Bayesian Prediction : Nonparametric Methods and Least Squares Approximations. In Florens, J. P.; Mouchart, M.; Raoult, J. P.; Simar, L. (ed.), Alternatives approaches to time series analyssis : Proceeddings of the 3rd Franco-Belgian meetng of statistician (p. p. 11-28). Publications des Facultés Universitaires Saint-Louis. https://hdl.handle.net/2078.5/208567