What if you change it to 1 or 0.1?

Good question. Then your data wouldn’t have unit variance (prob. doesn’t matter much in practice, you can maybe think of the spread of the distribution as a tuning param)

the logvar variable, which is the variance vector $\sigma^2$ of the covariance matrix $\Sigma = \sigma^2 * I$ is multiplied by 0,5.


What is the theoretical reason to do that?

Main reason is we work with the log for stability reasons. Hence, you have have
logVariance = log($\sigma^2$) = 2 * log(sigma)
To get the log standard deviation, you then basically divide by two
logStdDev =  2 * log(sigma) / 2 = 0.5 *  2 * log(sigma)  = log(sigma)