It seems very strange to me to look at e1 and e2 as point values without weights or confidence distributions. Taking no other information about e1 and e2 other than the fact that they both indicate a 999/1000 victory is quite limiting and makes for impossible meta-analysis. Other information could include what you think of both sources.
If you could get an accurate 90% confidence interval for each (or any accurate probability distribution) this could make a lot more sense. This must encompass the expected error in the New York Time’s error margin, especially if they don’t have one. For example, you may find that whenever reference a statistic, 90% of the time it is has at most 15% error compared to the true result (this would be really useful btw, someone should do this). Even if you estimate this number, you could still get a workable value.
If their 90% confidence interval was 0% error, and their reported statistics were always exactly true, then I do not believe you would update at all from e2.
I feel like it is possible to combine two 90% confidence intervals, and my guess is that any two with the same mean would result in higher certainty than at least the worst estimate (the one with the wider 90% confidence interval), possible higher than both. Solving this mathematically is something I’m not too sure about.
It seems very strange to me to look at e1 and e2 as point values without weights or confidence distributions. Taking no other information about e1 and e2 other than the fact that they both indicate a 999/1000 victory is quite limiting and makes for impossible meta-analysis. Other information could include what you think of both sources.
If you could get an accurate 90% confidence interval for each (or any accurate probability distribution) this could make a lot more sense. This must encompass the expected error in the New York Time’s error margin, especially if they don’t have one. For example, you may find that whenever reference a statistic, 90% of the time it is has at most 15% error compared to the true result (this would be really useful btw, someone should do this). Even if you estimate this number, you could still get a workable value.
If their 90% confidence interval was 0% error, and their reported statistics were always exactly true, then I do not believe you would update at all from e2.
I feel like it is possible to combine two 90% confidence intervals, and my guess is that any two with the same mean would result in higher certainty than at least the worst estimate (the one with the wider 90% confidence interval), possible higher than both. Solving this mathematically is something I’m not too sure about.
Yeah, one of the problems of the example is that it seems to take for granted that both, the NYT and WP are 100% reliable.