pred.mle: Estimate of predictive interval of 'T|data' using Monte Carlo...

In queelius/algebraic.mle: Algebraic Maximum Likelihood Estimators

Estimate of predictive interval of 'T|data' using Monte Carlo integration.

Description

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 class '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

queelius/algebraic.mle documentation built on Jan. 29, 2025, 3:23 p.m.