logmeanexp function

The log-mean-exp trick

logmeanexp computes [REMOVE_ME]$\log\frac{1}{n}\sum_{i=1}^n\!e^{x_i},log(mean(exp(x))), [REMOVE_ME_2]$

avoiding over- and under-flow in doing so. It can optionally return an estimate of the standard error in this quantity.

logmeanexp(x, se = FALSE, ess = FALSE)

Arguments

• x: numeric
• se: logical; give approximate standard error?
• ess: logical; give effective sample size?

Returns

log(mean(exp(x))) computed so as to avoid over- or underflow. If se = TRUE, the approximate standard error is returned as well. If ess = TRUE, the effective sample size is returned also.

Description

logmeanexp computes

avoiding over- and under-flow in doing so. It can optionally return an estimate of the standard error in this quantity.

Details

When se = TRUE, logmeanexp uses a jackknife estimate of the variance in $log(x)$.

When ess = TRUE, logmeanexp returns an estimate of the effective sample size.

Examples

# takes too long for R CMD check
  ## an estimate of the log likelihood:
  ricker() |>
    pfilter(Np=1000) |>
    logLik() |>
    replicate(n=5) -> ll
  logmeanexp(ll)
  ## with standard error:
  logmeanexp(ll,se=TRUE)
  ## with effective sample size
  logmeanexp(ll,ess=TRUE)

Author(s)

Aaron A. King