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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?

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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.

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  • $\begingroup$ Alright, good points. I think I'm within the optimal range of the values for the variables, collected from the litterature. So small incremental steps of finding the absolute optimum would be needed.. Is there some way of using experimental design with large intervals and combine it with data from the production systems? Also, I have no analytical equation or the like. The field is quite new and so noone have identified an equation based on the amount of variables that I have.. $\endgroup$ – Lennart Apr 27 '17 at 6:28
  • $\begingroup$ Yes, I do not see why you could not combine the production data (after all, there is a bunch of settings you have for that) with experimental data. Particularly, if the data were all generated under the same circumstances. It could be a problem for doing that (but really in general for how the experimental data applies to the production system), if you e.g. got your experimental data from e.g. a smaller scale version of the system, an old version, from too short a period of time for the system to settle down etc. (you problem understand better than me what other things could be a problem). $\endgroup$ – Björn Apr 27 '17 at 8:41

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