sumlog: Log-sum from log data
In snipEM: Snipping Methods for Robust Estimation and Clustering

Description Usage Arguments Details Value Author(s) References Examples

Obtain log(sum(x)) from log(x), without passing to exponentials. It is based on the fact that log(a + b) = log(a) + log (1 + exp(log(b) - log(a))).

1	sumlog(x,lower=-745,upper=709)

`x`	Vector of log-values
`lower`	Value such that exp(lower-epsilon)=0
`upper`	Value such that exp(upper+epsilon)=Inf

This function computes the logarithm of the sum of exp(x), without passing through exponentials. It shall be used to avoid under/over flow. It has proven useful in computing the likelihood of finite mixture models, normalization constants, importance sampling, etc. It is described in the appendix of Farcomeni (2012).

A scalar equal to log(sum(exp(x))).

Alessio Farcomeni alessio.farcomeni@uniroma1.it, Andy Leung andy.leung@stat.ubc.ca

Farcomeni, A. (2012) Quantile Regression for longitudinal data based on latent Markov subject-specific parameters. Statistics and Computing, 22, 141-152

# complete underflow without sumlog 
x <- c(-750,-752)
log(sum(exp(x)))
sumlog(x)

# imprecise sum 
x <- c(-745,-752)
log(sum(exp(x)))
sumlog(x)

# no issues 
x <- c(log(3),log(2))
log(5)
log(sum(exp(x)))
sumlog(x)

Loading required package: Rcpp
Loading required package: mvtnorm
Loading required package: MASS
[1] -Inf
[1] -749.8731
[1] -744.4401
[1] -744.9991
[1] 1.609438
[1] 1.609438
[1] 1.609438