https://daynefiler.com/categories/statistics/ Recent content in statistics on Dayne Filer, MD, PhD | Research Software & Scientific Computing Hugo -- gohugo.io en-US Thu, 10 Oct 2019 11:29:37 -0400 https://daynefiler.com/blog/log-sum-exp/ Thu, 10 Oct 2019 11:29:37 -0400 https://daynefiler.com/blog/log-sum-exp/ To formulate the problem, consider calculating the posterior probability given a series of weighted likelihoods. Let \[ x_i \] be the likelihood for observation i. We wish to calculate the posterior probability as: \[ p_i = \frac{x_i}{\sum_j x_j} \] As Robert Eisele very nicely discusses in his blog post, we can run into underflow issues. Suppose you have the following vector of logged likelihoods. x <- c(-9000, -3000, -1000) exp(x)/sum(exp(x)) # [1] NaN NaN NaN As we can see, all the values will be zero.