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[Linkpost] “Histograms are to CDFs as calibration plots are to...” by Optimization Process
This is a link post.
As you know, histograms are decent visualizations for PDFs with lots of samples...
10k predictions, 20 bins
...but if there are only a few samples, the histogram-binning choices can matter a lot:
10 predictions, 4 binssame 10 predictions, 7 binsThe binning (a) discards information, and worse, (b) is mathematically un-aesthetic.
But a CDF doesn't have this problem!
same 10 predictions, every data point precisely representedIf you make a bunch of predictions, and you want to know how well they're calibrated, classically you make a graph like this:
source: SSC's 2019 prediction gradingBut, as with a histogram, this depends on how you bin your predictions.
100 predictions, 10 binssame 100 predictions, 30 binsIs there some CDF-like equivalent here? Some visualization with no free parameters?
I asked that question to several people at Arbor Summer Camp. I got three answers:
- "You get from a PDF to [...]
---
First published:
June 5th, 2025
Source:
https://www.lesswrong.com/posts/LFGgwitjertJqch7J/histograms-are-to-cdfs-as-calibration-plots-are-to
Linkpost URL:
https://optimizationprocess.com/calibration-cdf/
---
Narrated by TYPE III AUDIO.
---
Images from the article:
Apple Podcasts and Spotify do not show images in the episode description. Try Pocket Casts, or another podcast app.
View all episodes
By LessWrongThis is a link post.
As you know, histograms are decent visualizations for PDFs with lots of samples...
10k predictions, 20 bins
...but if there are only a few samples, the histogram-binning choices can matter a lot:
10 predictions, 4 binssame 10 predictions, 7 binsThe binning (a) discards information, and worse, (b) is mathematically un-aesthetic.
But a CDF doesn't have this problem!
same 10 predictions, every data point precisely representedIf you make a bunch of predictions, and you want to know how well they're calibrated, classically you make a graph like this:
source: SSC's 2019 prediction gradingBut, as with a histogram, this depends on how you bin your predictions.
100 predictions, 10 binssame 100 predictions, 30 binsIs there some CDF-like equivalent here? Some visualization with no free parameters?
I asked that question to several people at Arbor Summer Camp. I got three answers:
- "You get from a PDF to [...]
---
First published:
June 5th, 2025
Source:
https://www.lesswrong.com/posts/LFGgwitjertJqch7J/histograms-are-to-cdfs-as-calibration-plots-are-to
Linkpost URL:
https://optimizationprocess.com/calibration-cdf/
---
Narrated by TYPE III AUDIO.
---
Images from the article:
Apple Podcasts and Spotify do not show images in the episode description. Try Pocket Casts, or another podcast app.
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