What is the syntax for assigning different elements of a multivariate distribution to different parameters in a Monte Carlo simulation? For example, how do I do something like:
coeff_alpha, coeff_beta = MvNormal(mu, vcv)
James, what is the intended effect of this example? There is no direct support for this right now, but there could be once I understand what it should do.
There is currently support for rank correlation among random variables, if that’s the intention.
No, this wouldn’t be rank correlation, just normal covariance.
The use case is as follows. There’s a lot of interest currently in updating the IAMs with results from the empirical literature-- in fact, PAGE is already using an empirical calibration for its damage function. These results almost exclusively use regressions as the calibration technique. The uncertainty of regression calibrations is represented by a multivariate Gaussian.
For example, suppose that we estimate a quadratic damage function, which has two coefficients, alpha and beta, on the two terms of the quadratic. Generally, the uncertainty in alpha and beta will be correlated (e.g., if the coefficient alpha is higher, then the coefficient beta will be lower, to continue to fit the data).
So, we will have the point estimate of all of the coefficients, and the variance-covariance matrix, but will need to determine values from all of the values from a single draw of the uncertainty distribution.
@jrising @plevin any further questions on this or are you good to go for now? It seems the next step would be to consider adding this feature and making an Issue for it?
Okay, I can make an issue for this.