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Apologies in advance for a very basic question! On Wikipedia, I see that the Bayesian Information Criterion evaluates a model using $$ BIC = k\ln(n)- 2\ln(L) $$ where $k$ is the number of parameters, $n$ the sample size and $L$ the (maximised) likelihood. In the original paper, however, I see instead the expression $$ BIC = k\log(n)- 2\log(L) $$ Can I check that 'log' here means 'ln' (i.e. base $e$ not say base $10$)? Or does it somehow not matter?

afreelunch
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    It is from an exponential distribution family, so I believe it is log base-e. There are only 2 others in common use: base 10 by engineers, and base 2 by computer scientists. – EngrStudent Feb 19 '21 at 19:28

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It is a natural logarithm (log base of e). But, no matter what the log is, the most important thing you need to remember is to compare models under a consistent kind of logarithm.

Vuong Chu
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  • "the most important thing you need to remember is to compare models under a consistent kind of logarithm". Should I take this to mean that I can use a different base provided that the base I use is the same for all models? – afreelunch Feb 20 '21 at 14:46
  • Yes, that is what I want to say. – Vuong Chu Feb 20 '21 at 15:24