Hello,

I fit the negative log-likelihood function for a Poisson distribution (green highlighted column in the *attached .jmp file*) to my observed data and get the mean estimates for 10 unknown parameters (screenshot below).

My problem is bootstrapping these 10 parameters using the __parametric__ method. The one-button "**bootstrap**" function in jmp (after right-click on the column "Estimate") gives me 1000 sets of 10 unknown parameters I need to construct the 95% CI. However that function uses the non-parametric method, and I want to use the parametric one. I am aware that the parametric bootstrap can be done by using the one-button "**simulate**" function in jmp. However, I could not understand the steps in the example from the jmp documentation that uses Design of Experiments (DOE), especially the part where one column has to be swapped. I do not know how to construct a column to switch in that is appropriate for my Neg Log-likelihood function. I want to get 1000 sets of parameters similar to the non-parametric method.

Is there any additional guidance I can use to do parametric bootstrapping for the parameter estimates from the Negative Log likelihood function? I am using JMP Pro 17.0.0. Many thanks for your time and help in advance.

Edit 1 (Oct 4): I tried Copilot and chatGPT to get guidance, but I still don't know how to address the problem myself.

Edit 2 (Oct 4): TLDR: How do I use the "simulate" feature from the Solution window (screenshot) that contains parameter estimates from using the Negative Log Likelihood function following a Poisson distribution?

Edit 3 (Oct 7): I tried making a column that includes the formula for the expected value with a random normal component. then I used that column to switch in during the simulate function. However, this only gave me multiple simulate samples with the same parameter estimates I got from the loss function fitting.