Producing a confidence interval for a percentile estimate (not the median) #293
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Hello, I wish to predict a specific percentile of time-series data over time and put a confidence interval on my prediction. In the examples I have read with MAPIE so far it seems that people are predicting the median and adding a 90% prediction interval by calculating the 5th and 95th percentiles of the data. This seems different to what I am trying to do (build a confidence interval around a specific percentile of the data). Is what I am trying to do reasonable? Possible with MAPIE? Thank you for your time, and bearing with my probably basic question :) |
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Replies: 1 comment 1 reply
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Helo @LukeAFullard, I think what you are trying to do is not possible with MAPIE. Indeed, with conformal prediction framework, we are looking for this statement: If I rephrase your proposal, you are looking for: I hope my answer will help you find a solution to your problem :) |
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That is clear, thank you very much for your reply :) |
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Helo @LukeAFullard,
Not at all, your question is interesting and makes sense! Your request is clear and you understand how MAPIE for TimeSeries works.
I think what you are trying to do is not possible with MAPIE. Indeed, with conformal prediction framework, we are looking for this statement:$p[Y \in C(X)] \leq 1-\alpha$ (see this gentle introduction for more details). In other words, we are trying to find a $1-\alpha$ confidence interval around the mediane prediction $\hat Y$ .
If I rephrase your proposal, you are looking for:$p[Q(Y,p) \in C(X)] \leq 1-\alpha$ where $Q(Y,p)$ corresponds to the p-th percentile of the probabilistic distribution of the random variable $Y$ . In other words, y…