To what degree does everyone here literally calculate numerical outcomes and make decisions based on those outcomes for everyday decisions using Bayesian probability? Sometimes I can’t tell if when people say they are ‘updating priors’ they are literally doing a calculation and literally have a new number stored somewhere in their head that they keep track of constantly.
If anyone does this could you elaborate more on how you do this? Do you have a book/spreadsheet full of different beliefs with different probabilities? Can you just keep track of it all in your mind? Or calculating probabilities like this only something people do for bigger life problems?
Can you give me a tip for how to start? Is there a set of core beliefs everyone should come up with priors for to start? I was going to apologize if this was a stupid question, but I suppose it should by definition be one if it is in this thread.
Nope, not for everyday decisions. For me “remember to update” is more of a mantra to remember to change your mind at all—especially based on several pieces of weak evidence, which normal procedure would be to individually disregard and thus never change your mind.
I suspect very little, but this does remind me of Warren Buffett speaking on Discounted Cash Flow calculations.
For quick background, an investment is a purchase of a future cash flow. Cash in the future is worth less to you than cash right now, and it is worth less and less as you go further into the future. Most treatments pretend that the proper way to discount the value of cash in the future is to have a discount rate (like 5% or 10% per year) and apply it as an exponential function to future cash.
Warren Buffett, a plausible candidate for the most effective investor ever (or at least so far), speaks highly of DCF (discounted cash flow) as the way to choose between investments. However, he also says he never actually does one other than roughly in his head. Given his excellent abilities at calculating in his head, I think it would translate to something like he never does a DCF calculation that would take up more than about 20 lines in an excel spreadsheet.
There are a broad range of policies that I have that are based on math: not gambling in Las Vegas because it’s expectation value is negative (although mostly I trust the casinos to have set the odds so payouts are negative, I don’t check their math). Not driving too far for small discounts (expense of getting discount should not exceed value of discount). Not ignoring a few thousand dollar difference in a multi-hundred thousand dollar transaction because “it is a fraction of a percent.”
I do often in considering hiring a personal service compare paying for it to how long it would take me to do the job vs how long I would need to work at my current job to hire the other person. I am pretty well paid so this does generally lead to me hiring a lot of things done. A similar calcuation does lead me to systematically ignore costs below about $100 for a lot of things which still “feels” wrong, but which I have not yet been able to do a calculation that shows me it is wrong.
I am actually discouraging my wife and children from pushing my children towards elite colleges and universities on the basis that they are over-priced for what they deliver. I am very unconfident in this one as rich people that I respect continue to just bleed money into their children’s educations. SO I am afraid to go independent of them even as I can’t figure out a calculation that shows what they are doing makes economic sense.
I do look at, or caculate, the price per ounce in making buying decisions, I guess that is an example of a common bayesian calculation.
It depends on what your kids want to do. Elite colleges are not selling education, except to the extent that they have to maintain standards to keep their position. They are selling networking cachet. Which is of very high value to people who want to be one of the masters of the universe, and take their chances with the inbound guillotine.
If your kids want to be doctors. engineers or archaeologists.. no, not worth the price tag. In fact, the true optium move is likely to ship them to Sweden with a note telling them to find a nice girl, naturalize via marriage and take the free ride through stockholm university. ;)
Elite colleges are not selling education, except to the extent that they have to maintain standards to keep their position. They are selling networking cachet.
I attended Swarthmore College and got a totally bitching education. I would recommend Swarthomre to anybody with better than about 740′s on her SATs. For a regular smart kid, Swarthmore educationally is probably a lot of work, and may be valuable but it is not the value proposition I got or that I understand. For me, the incredible quality of the student body and highly motivated and intelligent professors produced an education I do not think you could get no matter how good the profs are if the students were more regular.
My grad-school mate at Caltech, another place with incredible educational results that are not available at lesser institutions, attended Harvard undergrad. His education appeared to be similarly outstanding to the one I got at Swarthmore.
So elite universities may be selling networking cachet, and that may be what some of their customers intend to be buying. But for really smart kids, an elite school is a serious educational opportunity that non-elite schools cannot match.
I certainly do agree that getting a free ride through a good university is a great deal!
I am actually discouraging my wife and children from pushing my children towards elite colleges and universities on the basis that they are over-priced for what they deliver. I am very unconfident in this one as rich people that I respect continue to just bleed money into their children’s educations. SO I am afraid to go independent of them even as I can’t figure out a calculation that shows what they are doing makes economic sense.
In terms of return on investment, elite colleges seem to be worthwhile. Read this; more coverage on OB and the places linked from there. It’s a bit controversial but my impression was that you’d probably be better off going someplace prestigious. Credit to John_Maxwell_IV for giving me those links, which was most of the reason I’m going to a prestigious college instead of an average one. I’m extremely doubtful about the educational value of education for smart people, but the prestige still seems to make it worth it.
These obviously become a really good deal if you can get financial aid, and many prestigious places do need-blind admissions, i.e. they will give you free money if you can convince them you’re smart. Also look at the ROIs of places you’re considering. Value of information is enormous here.
I am actually discouraging my wife and children from pushing my children towards elite colleges and universities on the basis that they are over-priced for what they deliver.
It’s quite hard to do a full estimate of the benefits you get from going to an elite college. There are a lot of intangibles and a lot of uncertainty—consider e.g. networking potential or the acquisition of good work habits (smart students at mediocre places rapidly become lazy).
Even if you restrict yourself to the analysis of properly discounted future earning potential (and that’s a very limited approach), the uncertainties are huge and your error bars will be very very wide.
I generally go by the “get into the best school you can and figure out money later” guideline :-)
I agree with much of what you’re saying. I make similar back of the envelope calculations.
One small point of clarity is that “money is worth less in the future” is not a general rule but a function of inflation which is affected strongly by national monetary policy. While it likely won’t change in the USA in the near future, it COULD, so I think it’s important to recognize that and be able to change behavior if necessary.
Lots of people attend an elite college because of signalling, not because it’s an investment. Keep questioning the value of such an education!
One small point of clarity is that “money is worth less in the future” is not a general rule but a function of inflation which is affected strongly by national monetary policy. While it likely won’t change in the USA in the near future, it COULD, so I think it’s important to recognize that and be able to change behavior if necessary.
I’m sorry I didn’t explain that well enough. WHat I meant is money you are going to get in the future is not worth as much as money you are going to get now. Even if we work with inflationless dollars, this is true. It happens because the sooner you have a dollar, the more options you have as to what to do with it. So if I know I am going to get a 2013 dollar in 2023, that is worth something to me because there are things I will want to do in the future. But would I pay a dollar know to get a 2013 dollar in 2023? Definitely not, I would just keep my dollar. Would I pay 80 cents? 50 cents? I would certainly pay 25 cents, and might pay 50 cents. If I paid 50 cents, I would be estimating that the things I might do with 50 cents between 2013 and 2023 are about equal in value to me, right now, with the current value I would place on the things I might do with a $1 in 2023 or later. The implicit discount then for 10 years is 50% if I am willing to pay 50 cents now for a 2013 $1 in 2023. The discount rate, assuming exponential change in time as all interest rate calculations do, is about 7%. Note this is a discount in real terms, as it is a 2013 $1 value I will receive in 2023. In principle, if inflation had accumulated 400% by 2023, I would actually be receiving $5 2023 dollars for a 26%/year nominal return on my initial investment, even though I have only a 7%/year real return and 21%/year inflation.
“money is worth less in the future” is not a general rule but a function of inflation
That is only partially true. The time value of money is a function not only of inflation, but of other things as well, notably the value of time (e.g. human lives are finite) and opportunity costs.
In fact, one of the approaches to figuring out the proper discounting rate for future cash flows is to estimate your opportunity costs and use that.
I’d be alarmed if anyone claimed to accurately numerically update their priors. Non-parametric Bayesian statistics is HARD and not the kind of thing I can do in my head.
I had the same worry/question when I first found LW. After meeting with all the “important” people (Anna, Luke, Eliezer...) in person, I can confidently say: no, nobody is carrying around a sheet of paper and doing actual Bayesian updating. However, most people in these circles notice when they are surprised/confused, act on that feeling, and if they were wrong, then they update their believes, followed soon by their actions. This could happen from one big surprise or many small ones. So there is a very intuitive sort of Bayesian updating going on.
Your brain does most of this at lightning speed unconsciously. Often, trying to make the process unto a deliberative, conscious one slows it down so much that the results are of little practical use.
I only literally do an expected outcome calculation when I care more about having numbers than I do about their validity, or when I have unusually good data and need rigor. Most of the time the uncertainties in your problem formulation will dominate any advantage you might get from doing actual Bayesian updates.
The advantage of the Bayesian mindset is that it gives you a rough idea of how evidence should affect your subjective probability estimate for a scenario, and how pieces of evidence of different strengths interact with each other. You do need to work through a reasonable number of examples to get a feel for how that works, but once you have that intuition you rarely need to do the math.
To what degree does everyone here literally calculate numerical outcomes and make decisions based on those outcomes for everyday decisions using Bayesian probability? Sometimes I can’t tell if when people say they are ‘updating priors’ they are literally doing a calculation and literally have a new number stored somewhere in their head that they keep track of constantly.
If anyone does this could you elaborate more on how you do this? Do you have a book/spreadsheet full of different beliefs with different probabilities? Can you just keep track of it all in your mind? Or calculating probabilities like this only something people do for bigger life problems?
Can you give me a tip for how to start? Is there a set of core beliefs everyone should come up with priors for to start? I was going to apologize if this was a stupid question, but I suppose it should by definition be one if it is in this thread.
Nope, not for everyday decisions. For me “remember to update” is more of a mantra to remember to change your mind at all—especially based on several pieces of weak evidence, which normal procedure would be to individually disregard and thus never change your mind.
I never do this. See this essay by gwern for an example of someone doing this.
I suspect very little, but this does remind me of Warren Buffett speaking on Discounted Cash Flow calculations.
For quick background, an investment is a purchase of a future cash flow. Cash in the future is worth less to you than cash right now, and it is worth less and less as you go further into the future. Most treatments pretend that the proper way to discount the value of cash in the future is to have a discount rate (like 5% or 10% per year) and apply it as an exponential function to future cash.
Warren Buffett, a plausible candidate for the most effective investor ever (or at least so far), speaks highly of DCF (discounted cash flow) as the way to choose between investments. However, he also says he never actually does one other than roughly in his head. Given his excellent abilities at calculating in his head, I think it would translate to something like he never does a DCF calculation that would take up more than about 20 lines in an excel spreadsheet.
There are a broad range of policies that I have that are based on math: not gambling in Las Vegas because it’s expectation value is negative (although mostly I trust the casinos to have set the odds so payouts are negative, I don’t check their math). Not driving too far for small discounts (expense of getting discount should not exceed value of discount). Not ignoring a few thousand dollar difference in a multi-hundred thousand dollar transaction because “it is a fraction of a percent.”
I do often in considering hiring a personal service compare paying for it to how long it would take me to do the job vs how long I would need to work at my current job to hire the other person. I am pretty well paid so this does generally lead to me hiring a lot of things done. A similar calcuation does lead me to systematically ignore costs below about $100 for a lot of things which still “feels” wrong, but which I have not yet been able to do a calculation that shows me it is wrong.
I am actually discouraging my wife and children from pushing my children towards elite colleges and universities on the basis that they are over-priced for what they deliver. I am very unconfident in this one as rich people that I respect continue to just bleed money into their children’s educations. SO I am afraid to go independent of them even as I can’t figure out a calculation that shows what they are doing makes economic sense.
I do look at, or caculate, the price per ounce in making buying decisions, I guess that is an example of a common bayesian calculation.
It depends on what your kids want to do. Elite colleges are not selling education, except to the extent that they have to maintain standards to keep their position. They are selling networking cachet. Which is of very high value to people who want to be one of the masters of the universe, and take their chances with the inbound guillotine. If your kids want to be doctors. engineers or archaeologists.. no, not worth the price tag. In fact, the true optium move is likely to ship them to Sweden with a note telling them to find a nice girl, naturalize via marriage and take the free ride through stockholm university. ;)
I attended Swarthmore College and got a totally bitching education. I would recommend Swarthomre to anybody with better than about 740′s on her SATs. For a regular smart kid, Swarthmore educationally is probably a lot of work, and may be valuable but it is not the value proposition I got or that I understand. For me, the incredible quality of the student body and highly motivated and intelligent professors produced an education I do not think you could get no matter how good the profs are if the students were more regular.
My grad-school mate at Caltech, another place with incredible educational results that are not available at lesser institutions, attended Harvard undergrad. His education appeared to be similarly outstanding to the one I got at Swarthmore.
So elite universities may be selling networking cachet, and that may be what some of their customers intend to be buying. But for really smart kids, an elite school is a serious educational opportunity that non-elite schools cannot match.
I certainly do agree that getting a free ride through a good university is a great deal!
In terms of return on investment, elite colleges seem to be worthwhile. Read this; more coverage on OB and the places linked from there. It’s a bit controversial but my impression was that you’d probably be better off going someplace prestigious. Credit to John_Maxwell_IV for giving me those links, which was most of the reason I’m going to a prestigious college instead of an average one. I’m extremely doubtful about the educational value of education for smart people, but the prestige still seems to make it worth it.
These obviously become a really good deal if you can get financial aid, and many prestigious places do need-blind admissions, i.e. they will give you free money if you can convince them you’re smart. Also look at the ROIs of places you’re considering. Value of information is enormous here.
It’s quite hard to do a full estimate of the benefits you get from going to an elite college. There are a lot of intangibles and a lot of uncertainty—consider e.g. networking potential or the acquisition of good work habits (smart students at mediocre places rapidly become lazy).
Even if you restrict yourself to the analysis of properly discounted future earning potential (and that’s a very limited approach), the uncertainties are huge and your error bars will be very very wide.
I generally go by the “get into the best school you can and figure out money later” guideline :-)
I agree with much of what you’re saying. I make similar back of the envelope calculations.
One small point of clarity is that “money is worth less in the future” is not a general rule but a function of inflation which is affected strongly by national monetary policy. While it likely won’t change in the USA in the near future, it COULD, so I think it’s important to recognize that and be able to change behavior if necessary.
Lots of people attend an elite college because of signalling, not because it’s an investment. Keep questioning the value of such an education!
I’m sorry I didn’t explain that well enough. WHat I meant is money you are going to get in the future is not worth as much as money you are going to get now. Even if we work with inflationless dollars, this is true. It happens because the sooner you have a dollar, the more options you have as to what to do with it. So if I know I am going to get a 2013 dollar in 2023, that is worth something to me because there are things I will want to do in the future. But would I pay a dollar know to get a 2013 dollar in 2023? Definitely not, I would just keep my dollar. Would I pay 80 cents? 50 cents? I would certainly pay 25 cents, and might pay 50 cents. If I paid 50 cents, I would be estimating that the things I might do with 50 cents between 2013 and 2023 are about equal in value to me, right now, with the current value I would place on the things I might do with a $1 in 2023 or later. The implicit discount then for 10 years is 50% if I am willing to pay 50 cents now for a 2013 $1 in 2023. The discount rate, assuming exponential change in time as all interest rate calculations do, is about 7%. Note this is a discount in real terms, as it is a 2013 $1 value I will receive in 2023. In principle, if inflation had accumulated 400% by 2023, I would actually be receiving $5 2023 dollars for a 26%/year nominal return on my initial investment, even though I have only a 7%/year real return and 21%/year inflation.
That is only partially true. The time value of money is a function not only of inflation, but of other things as well, notably the value of time (e.g. human lives are finite) and opportunity costs.
In fact, one of the approaches to figuring out the proper discounting rate for future cash flows is to estimate your opportunity costs and use that.
I’d be alarmed if anyone claimed to accurately numerically update their priors. Non-parametric Bayesian statistics is HARD and not the kind of thing I can do in my head.
I had the same worry/question when I first found LW. After meeting with all the “important” people (Anna, Luke, Eliezer...) in person, I can confidently say: no, nobody is carrying around a sheet of paper and doing actual Bayesian updating. However, most people in these circles notice when they are surprised/confused, act on that feeling, and if they were wrong, then they update their believes, followed soon by their actions. This could happen from one big surprise or many small ones. So there is a very intuitive sort of Bayesian updating going on.
Your brain does most of this at lightning speed unconsciously. Often, trying to make the process unto a deliberative, conscious one slows it down so much that the results are of little practical use.
I only literally do an expected outcome calculation when I care more about having numbers than I do about their validity, or when I have unusually good data and need rigor. Most of the time the uncertainties in your problem formulation will dominate any advantage you might get from doing actual Bayesian updates.
The advantage of the Bayesian mindset is that it gives you a rough idea of how evidence should affect your subjective probability estimate for a scenario, and how pieces of evidence of different strengths interact with each other. You do need to work through a reasonable number of examples to get a feel for how that works, but once you have that intuition you rarely need to do the math.