Parametric Bootstrapping using the Negative Log Likelihood function

tMinnx — Thu, 17 Oct 2024 07:48:43 GMT

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.

Re: Parametric Bootstrapping for the parameter estimates from the Negative Log Likelihood function

tMinnx — Mon, 07 Oct 2024 11:35:00 GMT

topic Re: Parametric Bootstrapping for the parameter estimates from the Negative Log Likelihood function in Discussions

Parametric Bootstrapping using the Negative Log Likelihood function

Re: Parametric Bootstrapping for the parameter estimates from the Negative Log Likelihood function