Using MLE in R stats4

Question

I have been trying to estimate the MLE for my joint posterior. I'm using R and the package stats4. I have 14 parameters and two of them are $\geq 0$, which I did not know how to implement (and I was creating NaN due to the minus log posterior required in for the mle function) and I just made it return very high value (1000) if either of the parameters were negative. Is this the right way to solve this problem? As I was forced to change my prior each time (because MLE told me that my prior estimates were way to high) and I find these nonnegative parameters going down to were low numbers (0.001 and 0.01) which did not seem right and at each iteration way below my suggested prior.

Also, since I didn't have the exact posterior due to the structure of the model and I tried to scale it such that the point estimate from the mle function plugged in the log joint posterior had the value 0. Is this approximation okay for this function?

Answer 1

Why use maximum likelihood for a Bayesian problem?

Nevertheless, the problem with two nonnegative parameters can be solved in several ways:

• Using a solver which admits restrictions.

• Maybe more practical, reparametrize the parameter, if it is $\theta_0 \ge 0$, represent it in the model as $\theta=\log \theta_0$. That admittedly also avoids the value zero, but it seems that's ok with you.

Answer 2

I had to solve this kind of a problem recently for computing the MLE of a triangle distribution. I also wanted to use the stats4 package so that users of my triangle package could use the related functionality that comes with the stats4::mle object. If you are interested, look here and here.

If you look at the function call for stats4::mle, you notice a couple of things:

> stats4::mle
function (minuslogl, start, optim = stats::optim, 
          method = if (!useLim) "BFGS" else "L-BFGS-B", 
          fixed = list(), nobs, lower, upper, ...)

You are essentially calling the stats::optim function with starting parameters start, a function to optimize minuslogl, a function optim, a method method, and other parameters that are useful for control fixed, lower, upper, ...

So, being a little more specific than in @kjetil-b-halvorsen 's answer:

• You can use "L-BFGS-B" with lower and upper limits to accomplish your desired of some parameters being non-negative.
• You can switch our the stats::optim algorithm for something better like using methods in optimx
• You can re-parameterize your non-negative parameters in the negative log likelihood using exponentials: $f(x_1, \dots,x_{14})$ where $x_1 \ge 0$ changed to $g(z_1, x_2, \cdots, x_{14}) = f(x_1=e^{z_1}, x_2, \dots, x_{14})$
• You can just just run the optimization yourself instead of trying to fit it into stats4::mle. In fact, I found it easier to troubleshoot this way.