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> I have no idea what you just said.
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Sorry. Lots of mathematics.
Say you run a test, it says 25% chance of a gaffed machine.
This is usually not quite accurate, because it assumes "random
dataset" and "everything else being equal".
To paraphrase Frank's concern, when you run a test on "old data",
often you have selective memory, and are remembering a particularly
"bad" or "good result".
...so the "25% of a gaffed machine" may actually be "5%".
If I'm in Las Vegas where I strongly believe the machines are fair, I
may chalk up the "25%" result to bad luck, and still believe in a
"<1%" chance of a bad machine.
If I'm in an Indian casino whether there been rumors/stories of bad
machines, I may believe there is a "90%" chance of a bad machine.
Hope this helps.
Mitchell
P.S. Bayesian inference is one of the math techniques to combine
knowledge from multiple sources.
1) old data, new data, data not randomly created
2) reliability of Las Vegas machines (which are regulated)
3) rumors/stories from other people
If John believes 50% in bad machines at Casino A, Mark believes 25%,
we have multiple data sets, and run some tests.
Bayesian creates a network of nodes, with arrows connecting the nodes,
and propagation rules to send the information/calculations back and
forth.
What Bayesian analysis did, is show mathematicians that we usually
double-counted, overcompensated, or undercompensated
for multiple information sources, when they interconnect with each
other, and we try manually to calculate the overall probability.
The basic P(A or B) = P(A) + P(B) - P (A and B) is unchanged in
Bayesian analysis.
It's the messy combining everything together which changed.
