Estimate of predictive interval of `T|data` using Monte Carlo integration.

Let `T|x ~ f(t|x)`` be the pdf of vector `T` given MLE `x` and `x ~ MVN(params(x),vcov(x))`` be the estimate of the sampling distribution of the MLE for the parameters of `T`. Then, `(T,x) ~ f(t,x) = f(t|x) f(x) is the joint distribution of `(T,x)`. To find `f(t)` for a fixed `t`, we integrate `f(t,x)` over `x` using Monte Carlo integration to find the marginal distribution of `T`. That is, we:

Usage

# S3 method for mle
pred(x, samp, alpha = 0.05, R = 50000, ...)

Arguments

x

an `mle` object.

samp

The sampler for the distribution that is parameterized by the MLE `x`, i.e., `T|x`.

alpha

(1-alpha)-predictive interval for `T|x`. Defaults to 0.05.

R

number of samples to draw from the sampling distribution of `x`. Defaults to 50000.

...

additional arguments to pass into `samp`.

Details

1. Sample from MVN `x` 2. Compute `f(t,x)` for each sample 3. Take the mean of the `f(t,x)` values asn an estimate of `f(t)`.

The `samp` function is used to sample from the distribution of `T|x`. It should be designed to take