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Comment by carbocation | Hacker News Reader

They are describing a basic Monte Carlo simulation. It shows you that, given a certain distribution, some subset of trials will exceed some arbitrary cutoff. But, well, of course! This must be topical in Britain - is there some flap about death rates going on there? Perhaps there is some concern about too-stringent cutoffs being used there to try to catch bad physicians?

The real take-home here is that if you set your 'warning' threshold to be too low, you'll get a lot of warnings. Here, they used an arbitrary cutoff of 8 as their warning threshold. A fairer move would have been to allow some data to come back, try to infer a distribution and it's parameters, and then set future cutoffs based on those parameters. One could even continuously recalculate based on incoming data.

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>They are describing a basic Monte Carlo simulation. It shows you that, given a certain distribution, some subset of trials will exceed some arbitrary cutoff. But, well, of course!

Of course for you and me maybe, but many people wouldn't think of that.

I don't think there's anything particularly topical about death rates here in the UK right now. The author together with Michael Dilnot presented a radio show "More or Less" which covered lots of topics of this sort, showing how maths can aid an understanding of the world in general and current affairs in particular.

Their book "The Tiger That Isn't" (http://www.amazon.co.uk/Tiger-That-Isnt-Through-Numbers/dp/1...) is excellent and includes some other examples around sample size and regression to mean.

One thing that struck me from the article was how computers and Monte Carlo simulations have lowered the barrier to entry for statistical understanding. It seems much simpler to run this sort of simulation than to understand the intricacies of different probability distributions.

I agree, but understanding probability distributions is actually key to this simulation that they've performed. The results would differ, greatly, by running it with a uniform vs normal vs binomial distribution, or by tuning their parameters.

I was thinking that they probably just simulated each individual patient by picking a random number and seeing if it's less than the death rate.

So the number of deaths in a hospital is just

  sum([random()<deathRate for i in range(numPeople)])

and they can do the analysis without needing to know what a Bernouilli or Binomial distribution is, even though these both feature in the problem.

Again, the "random number" comes from a distribution. You can have a random number from the binomial, normal, etc distribution, and the output will look quite different. Also, there are clearly bounds on the distribution. Etc. They absolutely do need to understand how their pseudorandom number generator works in order to understand the properties of their simulation.

I can't tell if we're disagreeing or just at cross purposes.

In the code above the random number is uniform(0,1), the standard random number in most languages. So each individual death is Bernouilli, although you don't need to know the word Bernouilli. Then this leads to a binomial distribution for a hospital as a whole.

But the binomial assumption doesn't need to be known or explicitly built into the model. It's effectively an emergent property of the individual deaths.

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