177
edits
Aggregation of Non-Binary Predictions: Difference between revisions
Create first article draft
(Created page with "{{Banner|help wanted}}<!--- Change 'Help wanted' to 'WIP' if you don't want others to edit, then 'Review wanted' when you want feedback and approval, remove banner when review is passed.---> Combining several predictions from several forecasters or models consistently improves the accuracy of forecasts. Methods may differ depending on whether forecasts are for a binary (yes/no) or a non-binary target (like world GDP in year X). This page only deals with aggregating prob...") |
(Create first article draft) |
||
Line 7:
[[File:Combination of the CDF of different forecasts.png|thumb|Combination of the CDF of different forecasts]]
Probability distributions can be combined either based on their probability density functions (PDF) or their cumulative density functions (CDF). Usually, forecasts are combined using the CDF.
A horizontal combination of several CDF is equal to a combination of the quantiles of the CDF. A vertical combination of the CDF is equal to a mixture distribution that combines the cumulative densities of the individual forecasts. ▼
▲Several CDF can be either combined horizontally or vertically. A horizontal combination of several CDF is equal to a combination of the quantiles of the CDF. A vertical combination of the CDF is equal to a mixture distribution that combines the cumulative densities of the individual forecasts.
When combining forecasts based on their PDF, then only a vertical combination is sensible. When combining using the mean, then it does not matter whether we combine functions based on their PDF or CDF, as the sum of integrals is the same as the integral of a sum of two distributions. For combinations based e.g. on the median of the cumulative or non-cumulative density at a given point, differences may occur.
| |||