# logMeanExpLogs: Functions to compute the logarithm of the mean (and... In BayesFactor: Computation of Bayes Factors for Common Designs

## 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

 `1` ```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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ```# 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))) ```

BayesFactor documentation built on May 2, 2019, 7 a.m.