R: Functions to compute the logarithm of the mean (and...

logMeanExpLogs {BayesFactor} | R Documentation

## Functions to compute the logarithm of the mean (and cumulative means) of vectors of logarithms

### Description

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.

### Usage

    logMeanExpLogs(v)

### Arguments

`v` | A vector of (log) values

### Details

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.

### Value

`logMeanExpLogs` returns a single value, `logCumMeanExpLogs` returns a vector of values of the same length as v, and `logSummaryStats` returns a list of the log mean, log variance, and cumulative log means.

### Author(s)

Richard D. Morey (richarddmorey@gmail.com)

### References

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 and http://www.johndcook.com/blog/standard_deviation/.

### Examples

    # 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)))

[Package BayesFactor version 0.9.12-4.2 Index]