logMeanExpLogs: Functions to compute the logarithm of the mean (and...
In BayesFactor: Computation of Bayes factors for common designs

Description Usage Arguments Details Value Author(s) References Examples

Given a vector of numeric values of real values represented in log form, logMeanExpLogs computes the logarithm of the mean of the (exponentiated) values. logCumMeanExpLogs computes the logarithm of the cumulative mean.

1	logMeanExpLogs(v)

`v`	A vector of (log) values

Given a vector of values of log values v, one could compute log(mean(exp(v))) in R. However, exponentiating and summing will cause a loss of precision, and possibly an overflow. These functions use the identity

log(e^a + e^b) = a + log[ 1 + e^(b-a) ]

and the method of computing log(1+e^x) that avoids overflow (see the references). The code is written in C for very fast computations.

logMeanExpLogs returns a single value; logCumMeanExpLogs returns a vector of values of the same length as v.

Richard D. Morey (richarddmorey@gmail.com)

For details of the approximation of log(1+e^x) used to prevent loss of precision, see http://www.codeproject.com/Articles/25294/Avoiding-Overflow-Underflow-and-Loss-of-Precision.

# Sample 100 values
y = log(rexp(100,1))

# These will give the same value,
# since e^y is "small"
logMeanExpLogs(y)
log(mean(exp(y)))

# We can make e^x overflow by multiplying
# e^y by e^1000
largeVals = y + 1000

# This will return 1000 + log(mean(exp(y)))
logMeanExpLogs(largeVals)

# This will overflow
log(mean(exp(largeVals)))