Substitute for experimental design I have a set of biological systems optimizing biomass growth. I would like to know the best values for a set of variables affecting the response (biomass). But it is quite expensive to conduct a systematic experimental design, is there a way around this?
I have sensors; temperature, nutrient concentration etc which monitors the system. Can I use these values somehow, even though the values will probably differ by a small amount? 
 A: Not realistically - unless you only ever would make the tiniest of changes (even then - are some changes caused by the others?) - with a standard regression model. Even if you allow covariates to enter you model in a non-linear fashion (over small changes their effect would likely seem linear anyway).
Extrapolating beyond your data is hard, especially if your model is only your model, because it approximately fits your data.
With a model based more on a detailed understanding of the system in terms of say a set of linked differential equations and solicited expert knowledge on some system parameters, perhaps you could do better. However, you would still not know when your model would break down (after all, it will still only be an approximation to reality). And it may turn out that you will not learn a lot about the parameters describing the system, because you more or less have just a lot of observations under one stable condition. In that case almost everything will hinge on the priors you obtained.
