This video just has a plain transcript, not time-aligned to the videoTHIS IS AN UNCORRECTED AUTOMATIC TRANSCRIPT. IT MAY BE CORRECTED LATER IF TIME PERMITSfrequent practical point, which will come up in the practical.All of this probability stuff seems to involve a lot of multiplying.One probability, by another likelihood by a prior probabilities, are numbers less than one multiplied together.Lots and lots of numbers.Less than one gets smaller and smaller and smaller numbers and then the computer.That's a problem, because the number of decimal places essentially fixed we have some sort of precision on will just fall off the end.It'll just become zero.Things will get something called under Flo.So to avoid that and avoid precision problems because it's hard to precisely represent very tiny numbers, we just work in terms of the log of the probability.So instead of writing things down like these tiny probabilities here we write the log of it.Because it's a number less than one belongs a negative number.It's okay.Multiplication in the probability domain just turns into what in the log to Maine edition, Good people logs.That's why larger invented to turn hard modifications into easy editions.And so all those numbers coming of age day care, long probabilities.That's why there are weird things, like minus 3605.And that's something like having 0.3000 zeros.Okay, you see what we do long? Try it yourself.Get your pocket calculator out.Just 2.1 and multiply myself enough times and eventually just fall off the bottom.Okay, If you longer 0.1 and just added together, you could keep much, much longer.
Numerical issues
Probabilities can get very small, so we must take care when storing and computing with them. The most common operation on probabilities is multiplying them. That turns into addition of log probabilities - how convenient!
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