MARS regression I have a question about MARS, If I have for example 50 observations of 5 sensors with 5 signals and I tried to do regression with MARS. I found the model eliminate the 5th sensor readings as it is so near. So, the model is function of 4 sensor variables and does not be affected by the 5th one and I use this model for prediction. But if suddenly and for any reason happen that I get an observation that has a reading of the 5th sensor which is too high than that I had before so the model will not sense that however this is an indication for a fault. So, now I wonder what shall I do to keep the model at least sense that there is a problem or something like that.
 A: One of the advantages of MARS, is that it automatically performs variable selection. This can also be viewed as a disadvantage in certain applications, when you know that the response variable is a function of all parameters.
Would a Bayesian approach be acceptable to you? The BASS package in R offers a fast implementation of Bayesian MARS, with at least two advantages (in my opinion) for you.

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*By working with the posterior, even a non-important predictor variable (like your fifth sensor) is unlikely to be dropped from the model completely. At least some of the posterior samples are bound to include this predictor.

*The BASS package will also compute Sobol Decompositions for you, which are available in closed form for a Bayesian MARS model. Sobol Decompositions are a useful tool for sensitivity analysis which will allow you to better understand the effect of the predictor variables on the response. See this paper for more details.

Alternatively, you can tune the fitting algorithm to include more basis functions. This can be done in both MARS and Bayesian MARS. In the BASS package, for example, you can do this by changing the h1 and h2 parameters (altering the prior on the number of basis functions). Be careful however, as you can end up with an overfit model if you incorporate too many basis functions.
