# Large disparity between sensitivity of model parameters

Hello,

I am trying to estimate the values of a number parameters. The sensitivity of the parameters with respect to the model output varies by several orders of magnitude. By sensitivity I am referring to the partial derivate of my cost function SE with respect to each parameter. See below image for parameter sensitivity magnitudes.

Notice that, for example, the sensitivity of parameter \beta is 1.8e5 while parameter \rho C_{pF} has a sensitivity of only 8.6e-1.

My questions are the following:

• Can the NUTS sampler handle this level of disparity between parameter sensitivities?
• If not, are there any tricks to help the sampler for this kind of model?

Re-parameterising is difficult as each parameter has a very specific and individual purpose (they are material coefficients in the heat equation which is solved using the Forward Euler Finite Difference method).

Thanks!