# what is the best theory/model to use for prediction in multivariate data?

I use a software for pollutant propagation on rivers that takes as input a set of parameters (p1, p2, ...pn) and creates an output file which is basically a matrix where on each row there is represented the concentration of pollutant in various places along the river at a given timestamp.

\begin{array} {|r|r|r|r|r...|r|} \hline TIME &500m&1000m&1500m&2000m&2500m&...&25000m \\ \hline 2015/12/07 - 4:50:00&0.75&0.71&0.6&0.58&0.55&...&0.12 \\ \hline \hline 2015/12/07- 4:55:00&0.71&0.70&0.58&0.56&0.51&...&0.10 \\ \hline \end{array}

My question is: what models/theories are suitable to be used to predict, based on a set of given INPUT parameters, to predict the OUTPUT that would be closest to what the software will give as result? And how many pairs INPUT/OUTPUT will I need to have in order to minimize the error?

P.S: If this is not the right forum to post this please redirect me to the proper one.

Thank you. Regards, Sorin

• Perhaps better on Computational Science? Community opinions? – David Richerby Oct 29 '15 at 8:58
• I doubt that this can be answered anywhere, since this table is unlikely to hold enough (domain) information to pick a fitting model. – Raphael Oct 29 '15 at 17:38
• This does not appear to be a question about computer science, but a question about pollutant propagation in rivers: only someone who is expert in the latter could reasonably be expected to answer this. Or, worse, it's a question about that specific unnamed software package. Either way, it seems off-topic here (community votes?). I don't know whether there is any Stack Exchange site where this would be on-topic; some questions just don't fit anywhere on the Stack Exchange network, I'm afraid. – D.W. Oct 30 '15 at 0:18
• I did not intend to make the question domain specific, as I think is not relevant. The problem, you can think as general case where you have N sets of [input,output] where input is a set of m parameters and output is another set of n parameters. Now, suppose someone gives you an input i and ask you for the best prediction you can made of the output o based on the N sets [input,output], what theory/model could be used? – Sorin Ciolofan Oct 30 '15 at 18:13
• There is no "best" model to use for prediction across all scenarios. Obviously the "best" would be whatever the actual underlying model is in that context. Since it is highly unlikely that we will know what that is, we tend to make simplifying assumptions (e.g., linear model with fixed effects, linear model with random effects, linear after some kernel transform, etc.). To make matters worse, saying what is "best" is already difficult. Do you use likelihoods, AIC/BIC, or some other measure of "goodness of fit"? All of these should be taken into considering when investigating these issues – Nicholas Mancuso Nov 3 '15 at 6:27