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24th February 2020, 08:44 #1
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Probabilistic inference vs statistical inference
I wanted to understand when do we need probability and statistics together and when either probability or statistics can be used independently to derive inference

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23rd March 2020, 13:19 #2
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Re: Probabilistic inference vs statistical inference
i will make an attempt at your question
i am not an expert in either probability or statistics
statistics are derived from data
an example is test scores
your class takes a test, from that, a variety of statistics may be produced:
maximum score
minimum score
mode (most common score)
mean (or average) score
median (the middle score found by eliminating the highest and lowest and repeating until one (or two) scores are left
standard deviation (+/ range for about 67% of the grades)
there are a lot of other statistics available that measure other qualities of the data
probability is derived from speculation
an example is picking a card from a standard deck of playing cards (solitaire, bridge or poker, not euchre)
probability is measured on a scale of 0 to 1
you pick one card from the deck
what is the probability that:
it will be a club? 13 out of 52 or 1/4
it will be a 9? 4 out of 52 or 1/13
it will be a 9 of clubs? 1 out of 52 or 1/52
it will be a card? 52 out of 52 or 1
as to your question, we can clearly use probability and statistics separately
they inform each other
you can find the results of picking cards by inferring from the nature of the deck of cards
or you can do the experiment and get statistics
some things, like cards, are relatively easy to calculate probabilities
some things, require looking at the available data, like test scores
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