Can JMP estimate the uncertainties of the coefficients of the models<meta http-equiv="Content-Type" content="text/html; charset=UTF-8" />A customer is asking:
Consider a y variable (mesure) for which a model was obtained by multiple linear regression is of the form y_mod = a1 * cement +
a2 * water+ a3 * air
Now consider as deterministic input parameters cement, water and air, can we go back with JMP on the uncertainties of the coefficients a1, a2 and a3 if a covariance y_mod is fixed? The customer heard about inference or Bayesian updating to approach this ...
Thanks in advance,
Valerie
Re: Can JMP estimate the uncertainties of the coefficients of the modelsHi Valerie,
This does sound a lot like the Bayesian approach to building models. Software like WinBUGS and OpenBUGS (BUGS = Bayesian inference Using Gibbs Sampling) use Markov Chain Monte Carlo algorithms to sample different coefficients for each parameter in the model. Once the chains have stabilised, the distribution of values for each coefficient can be used to give "credible intervals": a measure of the uncertainty, equivalent to confidence intervals.
However, it is not possible to do any of this directly in JMP. I think it would be possible to interface with R to do the Bayesian inference. Or you could use JMP to visualise and analyse the output of WinBUGS (there is a blog post about this: Using JMP to evaluate MCMC diagnostics).
It depends why the customer wants to do this. If they have built a model using least squares regression they can get confidence intervals for each coefficient by right clicking on the Parameter Estimates table > Columns > Lower 95%, Upper 95%. Alternatively if they have Pro they can right click on the Estimate within the table and Bootstrap to estimate the uncertainty. Why do they want to use Bayesian inference?
Regards,
Phil
