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Math Help - How can I determine the accuracy of some predictions?

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    How can I determine the accuracy of some predictions?

    How can I determine the accuracy of some predictions? Take the example of weather forecasts. Each day weather.com has a predicted probability it will rain. Over a week then, we know the predicted
    chance it would rain, and whether it rained on each day. How do I determine how accurate the predictions were over the past week?

    For instance, for Sunday-Saturday of one week, here's the predictions and the actual results:

    Day of week: Predicted Chance of Rain - Actual result (1 = it rained, 0 = it didn't rain)

    S: .72 - 1
    M: .31 - 0
    T: .08 - 0
    W: .01 - 0
    T: .24 - 1
    F: .51 - 1
    S: .98 - 1

    So given this, how do I determine the accuracy of the prediction percentages?
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    Quote Originally Posted by TheAndruu View Post
    How can I determine the accuracy of some predictions? Take the example of weather forecasts. Each day weather.com has a predicted probability it will rain. Over a week then, we know the predicted
    chance it would rain, and whether it rained on each day. How do I determine how accurate the predictions were over the past week?

    For instance, for Sunday-Saturday of one week, here's the predictions and the actual results:

    Day of week: Predicted Chance of Rain - Actual result (1 = it rained, 0 = it didn't rain)

    S: .72 - 1
    M: .31 - 0
    T: .08 - 0
    W: .01 - 0
    T: .24 - 1
    F: .51 - 1
    S: .98 - 1

    So given this, how do I determine the accuracy of the prediction percentages?
    I can partially answer your question. This is basically a situation for expected value. Assuming the predictions are fairly accurate, we would think that the following holds (but generally for larger sample size)

    0.72 + 0.31 + 0.08 + 0.01 + 0.24 + 0.51 + 0.98 \approx \frac{1+0+0+0+1+1+1}{7}

    I'm guessing that a reasonable way to quantify the error here (which would reflect accuracy/precision) is to take the absolute difference of the LHS and RHS and divide by sample size, but this is a bit of "original thinking" on my part.

    It's a good question. I hope that if my answer is inadequate someone will provide a better one.
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