Use log/exp transformation to make the log likelihood computation of a simple mixture model more robust.

robust_mixture.R

# making mixture models numerically robust
set.seed(4)
rm(list = ls())

nobs = 1000
alpha = 0.1
p = runif(nobs, min = 0.0, max = 1.0)
q = runif(nobs, min = 0.0, max = 1.0)

# naive computation of log-likelihood contribution
log(alpha * prod(p) + (1-alpha) * prod(q))

# sum up the logs
psum = sum(log(c(alpha, p)))
qsum = sum(log(c(1 - alpha, q)))

# use exp/log transformation
const = 1 - max(c(psum, qsum))

# put it back together
log(exp(psum + const) + exp(qsum + const)) - const