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  1. #1
    Member level 3
    Points: 440, Level: 4

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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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  2. #2
    Advanced Member level 2
    Points: 3,155, Level: 13

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    Jan 2019
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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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