The article seems to be well written, clearly structured, honest with no weasel words, with concrete examples and graphs—all symptoms of a great post. In the same time, I am not sure what it is precisely saying. So I am confused.
The initial description of EEV seems pretty standard: calculate the expected gain from all possible actions and choose the best one. Then, the article criticises that approach as incorrect, giving examples like this:
It seems fairly clear that a restaurant with 200 Yelp reviews, averaging 4.75 stars, ought to outrank a restaurant with 3 Yelp reviews, averaging 5 stars.
It doesn’t seem much clear to me, but let’s take it for granted that the statement is correct. The problem is: does EEV necessarily favour the new restaurant over the other one? What is tacitly assumed is that the person using EEV calculates his expected utility taking the review average at face value. But, are there people who advocate such an approach?
The method described in the following is in fact a standard Bayesian way. Let’s call the Yelp average rating a measurement. The Bayesian utility calculations don’t use a delta-distribution centered on the measured value M, but rather an updated distribution made from the prior P(x) and the distribution P(M|x), while the latter contains the fuzziness of the measurement which influences the posterior distribution. It is precisely what the graphs illustrate.
Now it is possible that I am responsible for the misinterpretations, but there are few comments which seem to (mis)understand the message in the same way I did after the first reading. The clearly valid and practically important advice, which should read
always take into account your priors and update correctly, don’t substitute reported values (even if obtained by statistical analysis) for your own probability distribution
did come out rather like more problematic
don’t trust expected value calculations, since they don’t take into account measurement errors, you should make some additional adjustments which we call Bayesian and have something to do with log-normal distributions and utilities; also, always check it by common sense.
And I am still not entirely sure which one is the case.
Now it is possible that I am responsible for the misinterpretations...
I don’t have a clear understanding of the difference between the two italicized statements. Your first paragraphsing doesn’t address three crucial (and in my opinion valid) points of the post that your second paraphrasing does:
The degree to which one should trust one’s prior over the new information depends on the measurement error attached to the new information.
Assuming a normal/log-normal distribution for effectiveness of actions, the appropriate Bayesian adjustment is huge for actions with prima facie effectiveness many standard above the mean but which have substantial error bars.
Humans do not have conscious/explicit access to most of what feeds into their implicit Bayesian prior and so in situations where a naive Fermi calculation yields high expected value and where there’s high uncertainty, evolutionarily & experientially engrained heuristics can be a better guide to assessing the value of the action than attempting to reason explicitly as in the section entitled “Applying Bayesian adjustments to cost-effectiveness estimates for donations, actions, etc.”
The first paraphrasing certainly addresses your first point. Assuming the prior has normal distribution with variance σ0^2 and mean μ0 and you measure μ, assuming that errors are normally distributed with variance σ^2, the updated mean is (μ σ0^2 + μ0 σ0^2)/(σ0^2 + σ0^2). The higher σ, the less the updating moves the estimate. This is standard Bayes.
I can’t parse your second point.
It is indeed possible that evolutionarily engrained heuristics are a better guide than a more formal approach. But is is also possible that they aren’t, especially applied to situations which are rare and so didn’t exert selection pressure during human evolution. Many times I have seen common sense declared superior over formal analysis, but almost never had such declaration been supported by good arguments.
I agree that the Pascalesque arguments that appear on LW now and then, based on Fermi calculations and astronomical figures, such as
Even then the expected lives saved by SIAI is ~10^28.
are suspicious. But the problem lies already in the outlandish figure—the author should have taken the Fermi calculation, considered its error bars and combine it with his prior; presumably the result would be much lower then. If the HoldenKarnofsky’s post suggests that, I agree. Only I am not sure whether the post doesn’t rather suggest to accept that the expected value is unknowable and we should therefore ignore it, or even that it really may be 10^28, but we should ignore it nevertheless.
Re: #1, okay, it was unclear to me that all of that was packaged into your first paraphrasing.
Re: #2, not sure how else to explain; I had in mind the Pascal Mugging portion of the post.
Re: #3, as I mentioned to benelliott I would advocate a mixed strategy (heuristics together with expected value calculations). Surely our evolutionarily engrained heuristics a better guide than formal reasoning for some matters bearing on the efficacy of a philanthropic action.
But the problem lies already in the outlandish figure—the author should have taken the Fermi calculation, considered its error bars and combine it with his prior; presumably the result would be much lower then. If the HoldenKarnofsky’s post suggests that, I agree.
All but the final section of the post are arguing precisely along these lines.
Only I am not sure whether the post doesn’t rather suggest to accept that the expected value is unknowable and we should therefore ignore it, or even that it really may be 10^28, but we should ignore it nevertheless.
Not sure what Holden would say about this; maybe he’ll respond clarifying.
All but the final section of the post are arguing precisely along these lines.
That seems probable, and therefore I haven’t said that I disagree with the post, but that I am confused about what it suggests. But I have some problems with the non-final sections, too, mainly concerning the terminology. For example, the phrases “estimated value” and “expected value”, e.g. in
The crucial characteristic of the EEV approach is that it does not incorporate a systematic preference for better-grounded estimates over rougher estimates. It ranks charities/actions based simply on their estimated value, ignoring differences in the reliability and robustness of the estimates.
are used as if it simply meant “result of the Fermi calculation” instead of “mean value of probability distribution updated by the Fermi calculation”. It seems to me that the post nowhere explicitly says that such estimates are incorrect and that it is advocating standard Bayesian reasoning, only done properly. After first reading I rather assumed that it proposes an extension to Bayes, where the agent after proper updating classifies the obtained estimates based on their reliabilities.
Also, I was not sure whether the post discusses a useful everyday technique when formal updating is unfeasible, or whether it proposes an extension to probability theory valid on the fundamental level. See also cousin_it’s comments.
As for #2, i.e.
Assuming a normal/log-normal distribution for effectiveness of actions, the appropriate Bayesian adjustment is huge for actions with prima facie effectiveness many standard above the mean but which have substantial error bars.
mostly I am not sure what you refer to by appropriate Bayesian adjustment. On the first reading I interpreted is as “the correct approach, in contrast to EEV”, but then it contradicts your apparent position expressed in the rest of the comment, where you argue that substantial error bars shoul prevent huge updating. The second interpretation may be “the usual Bayes updating”, but then it is not true, as I argued in #1 (and in fact, I only repeat Holden’s calculations).
For example, the phrases “estimated value” and “expected value” [...] are used as if it simply meant “result of the Fermi calculation” instead of “mean value of probability distribution updated by the Fermi calculation”. It seems to me that the post nowhere explicitly says that such estimates are incorrect and that it is advocating standard Bayesian reasoning, only done properly.
I’m very sure that in the section to which you refer “estimated value” means “result of a Fermi calcuation” (or something similar) as opposed “mean value of probability distribution updated by the Fermi calculation.” (I personally find this to be clear from the text but may have been influenced by prior correspondence with Holden on this topic.)
The reference to “differences in the reliability and robustness of the estimates” refers to the size of the error bars (whether explicit or implicit) about the initial estimate.
Also, I was not sure whether the post discusses a useful everyday technique when formal updating is unfeasible, or whether it proposes an extension to probability theory valid on the fundamental level. See also cousin_it’s comments.
Here too I’m very sure that the post is discussing a useful everyday technique when formal updating is unfeasible rather than an extension to probability theory valid on a fundamental level.
On the first reading I interpreted is as “the correct approach, in contrast to EEV”, but then it contradicts your apparent position expressed in the rest of the comment, where you argue that substantial error bars shoul prevent huge updating. The second interpretation may be “the usual Bayes updating”, but then it is not true, as I argued in #1 (and in fact, I only repeat Holden’s calculations).
Here we had a simple misunderstanding; I meant “updating from the initial (Fermi calculation-based) estimate to a revised estimate after taking into account one’s Bayesian prior” rather than “updating one’s Bayesian prior to a revised Bayesian prior based on the initial (Fermi calculation-based) estimate.”
I was saying “when there are large error bars about the initial estimate, the initial estimate should be revised heavily”, not “when there are large error bars about the initial estimate, one’s Bayesian prior should be revised heavily.” On the contrary, larger the error bars about the initial estimate, the less one’s Bayesian prior should change based on the estimate.
I imagine that we’re in agreement here. I think that the article is probably pitched at someone with less technical expertise than you have; what seems obvious and standard to you might be genuinely new to many people and this may lead to you to assume that it’s saying more than it is.
The article seems to be well written, clearly structured, honest with no weasel words, with concrete examples and graphs—all symptoms of a great post. In the same time, I am not sure what it is precisely saying. So I am confused.
The initial description of EEV seems pretty standard: calculate the expected gain from all possible actions and choose the best one. Then, the article criticises that approach as incorrect, giving examples like this:
It doesn’t seem much clear to me, but let’s take it for granted that the statement is correct. The problem is: does EEV necessarily favour the new restaurant over the other one? What is tacitly assumed is that the person using EEV calculates his expected utility taking the review average at face value. But, are there people who advocate such an approach?
The method described in the following is in fact a standard Bayesian way. Let’s call the Yelp average rating a measurement. The Bayesian utility calculations don’t use a delta-distribution centered on the measured value M, but rather an updated distribution made from the prior P(x) and the distribution P(M|x), while the latter contains the fuzziness of the measurement which influences the posterior distribution. It is precisely what the graphs illustrate.
Now it is possible that I am responsible for the misinterpretations, but there are few comments which seem to (mis)understand the message in the same way I did after the first reading. The clearly valid and practically important advice, which should read
always take into account your priors and update correctly, don’t substitute reported values (even if obtained by statistical analysis) for your own probability distribution
did come out rather like more problematic
don’t trust expected value calculations, since they don’t take into account measurement errors, you should make some additional adjustments which we call Bayesian and have something to do with log-normal distributions and utilities; also, always check it by common sense.
And I am still not entirely sure which one is the case.
See my response to Michael Vassar.
I don’t have a clear understanding of the difference between the two italicized statements. Your first paragraphsing doesn’t address three crucial (and in my opinion valid) points of the post that your second paraphrasing does:
The degree to which one should trust one’s prior over the new information depends on the measurement error attached to the new information.
Assuming a normal/log-normal distribution for effectiveness of actions, the appropriate Bayesian adjustment is huge for actions with prima facie effectiveness many standard above the mean but which have substantial error bars.
Humans do not have conscious/explicit access to most of what feeds into their implicit Bayesian prior and so in situations where a naive Fermi calculation yields high expected value and where there’s high uncertainty, evolutionarily & experientially engrained heuristics can be a better guide to assessing the value of the action than attempting to reason explicitly as in the section entitled “Applying Bayesian adjustments to cost-effectiveness estimates for donations, actions, etc.”
The first paraphrasing certainly addresses your first point. Assuming the prior has normal distribution with variance σ0^2 and mean μ0 and you measure μ, assuming that errors are normally distributed with variance σ^2, the updated mean is (μ σ0^2 + μ0 σ0^2)/(σ0^2 + σ0^2). The higher σ, the less the updating moves the estimate. This is standard Bayes.
I can’t parse your second point.
It is indeed possible that evolutionarily engrained heuristics are a better guide than a more formal approach. But is is also possible that they aren’t, especially applied to situations which are rare and so didn’t exert selection pressure during human evolution. Many times I have seen common sense declared superior over formal analysis, but almost never had such declaration been supported by good arguments.
I agree that the Pascalesque arguments that appear on LW now and then, based on Fermi calculations and astronomical figures, such as
are suspicious. But the problem lies already in the outlandish figure—the author should have taken the Fermi calculation, considered its error bars and combine it with his prior; presumably the result would be much lower then. If the HoldenKarnofsky’s post suggests that, I agree. Only I am not sure whether the post doesn’t rather suggest to accept that the expected value is unknowable and we should therefore ignore it, or even that it really may be 10^28, but we should ignore it nevertheless.
Re: #1, okay, it was unclear to me that all of that was packaged into your first paraphrasing.
Re: #2, not sure how else to explain; I had in mind the Pascal Mugging portion of the post.
Re: #3, as I mentioned to benelliott I would advocate a mixed strategy (heuristics together with expected value calculations). Surely our evolutionarily engrained heuristics a better guide than formal reasoning for some matters bearing on the efficacy of a philanthropic action.
All but the final section of the post are arguing precisely along these lines.
Not sure what Holden would say about this; maybe he’ll respond clarifying.
That seems probable, and therefore I haven’t said that I disagree with the post, but that I am confused about what it suggests. But I have some problems with the non-final sections, too, mainly concerning the terminology. For example, the phrases “estimated value” and “expected value”, e.g. in
are used as if it simply meant “result of the Fermi calculation” instead of “mean value of probability distribution updated by the Fermi calculation”. It seems to me that the post nowhere explicitly says that such estimates are incorrect and that it is advocating standard Bayesian reasoning, only done properly. After first reading I rather assumed that it proposes an extension to Bayes, where the agent after proper updating classifies the obtained estimates based on their reliabilities.
Also, I was not sure whether the post discusses a useful everyday technique when formal updating is unfeasible, or whether it proposes an extension to probability theory valid on the fundamental level. See also cousin_it’s comments.
As for #2, i.e.
mostly I am not sure what you refer to by appropriate Bayesian adjustment. On the first reading I interpreted is as “the correct approach, in contrast to EEV”, but then it contradicts your apparent position expressed in the rest of the comment, where you argue that substantial error bars shoul prevent huge updating. The second interpretation may be “the usual Bayes updating”, but then it is not true, as I argued in #1 (and in fact, I only repeat Holden’s calculations).
I’m very sure that in the section to which you refer “estimated value” means “result of a Fermi calcuation” (or something similar) as opposed “mean value of probability distribution updated by the Fermi calculation.” (I personally find this to be clear from the text but may have been influenced by prior correspondence with Holden on this topic.)
The reference to “differences in the reliability and robustness of the estimates” refers to the size of the error bars (whether explicit or implicit) about the initial estimate.
Here too I’m very sure that the post is discussing a useful everyday technique when formal updating is unfeasible rather than an extension to probability theory valid on a fundamental level.
Here we had a simple misunderstanding; I meant “updating from the initial (Fermi calculation-based) estimate to a revised estimate after taking into account one’s Bayesian prior” rather than “updating one’s Bayesian prior to a revised Bayesian prior based on the initial (Fermi calculation-based) estimate.”
I was saying “when there are large error bars about the initial estimate, the initial estimate should be revised heavily”, not “when there are large error bars about the initial estimate, one’s Bayesian prior should be revised heavily.” On the contrary, larger the error bars about the initial estimate, the less one’s Bayesian prior should change based on the estimate.
I imagine that we’re in agreement here. I think that the article is probably pitched at someone with less technical expertise than you have; what seems obvious and standard to you might be genuinely new to many people and this may lead to you to assume that it’s saying more than it is.
Then I suppose that we don’t have disagreement, too.