Timeline for Estimate accuracy of an estimation on Poisson binomial distribution
Current License: CC BY-SA 3.0
8 events
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| Aug 8, 2015 at 16:48 | history | bounty ended | axiac | ||
| Aug 4, 2015 at 15:10 | comment | added | Sean Easter |
@axiac You've caught two errors on my part. First, yes, use ppf. Choose the two inputs based on what you want percentage of the posterior distribution you want captured within the two values. For example, it's common to use a 95% interval, in which case you'll want $\frac{1 - .95}{2} = 0.025$ in each tail of the distribution. Thus, you'll want to use ppf(0.025) and ppf(0.975). For the parameters, $alpha should be approved + 1; for $beta , declined + 1.
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| Aug 4, 2015 at 14:58 | comment | added | axiac |
Hmm... Or maybe I have to compute ppf(0.0275) and ppf(0.9725)? It says on ppf(): "returns the percent-point function, the inverse of the cdf".
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| Aug 4, 2015 at 14:16 | comment | added | axiac |
Why 0.0275 and 0.0975? Are these values fixed or they depend on the input data? If they are fixed, shouldn't it be 0.9725 (i.e. 1-0.0275)? And what values to use as object's constructor arguments ($alpha, $beta)?
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| Aug 4, 2015 at 13:17 | comment | added | Sean Easter |
@axiac Ah, now that's another challenge entirely :) From the looks of the source code you linked, getPdf() will return the density, which is what I graphed above. If you'd like a quick way to get credible ranges, I would run something like getCdf(0.0275) and getCdf(0.0975). (This is not a highest-density interval, since the beta distribution has some skew to it, but should be a suitable approximation in many applications.)
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| Aug 4, 2015 at 12:57 | comment | added | axiac | I have found this PHP library for statistics. Is it possible to compute the uncertainty using the methods it provides in class Beta? How? | |
| Aug 4, 2015 at 12:27 | comment | added | axiac | Thank you for your answer. While it puts me on the right track from the statistical point of view, it still leaves me in the dark on the practical side (coding). This is because I don't know how to translate the concepts into formulas (and I don't even know what these concept mean, in the first place). Could you please add some references where I could find how to compute the values? (I use PHP which is not one of the favorite languages of the statisticians; therefore there are not many libraries for statistic computations written in PHP. I have to implement the formulas myself.) | |
| Aug 2, 2015 at 14:44 | history | answered | Sean Easter | CC BY-SA 3.0 |