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How Bayes’ Rule Emerged Triumphant from Two Centuries of Controversy

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Re: How Bayes’ Rule Emerged Triumphant from Two Centuries of Controversy

#11

Post by mikekchar »

amasad wrote: post #7
arcanus wrote: post #2

Bayesian here. 'The theory that would not die' is a wonderful read, and notes how many scientists used Bayesian techniques (subjective probability) in a variety of contexts while the field was still unpopular (arguably, heretical) in the mainstream statistical community. Bayes was nevertheless used to inform ballistics calculations, help crack the enigma code, or inform search patterns for lost nuclear weapons. I don…

As someone new to Bayesianism I'd be interested in hearing your experience applying it in day-to-day life. How useful do you think it is to the ordinary Joe? From my brief experience, after learning Bayes, my intuition about things involving probabilities grew very different than the people around me. For example, my friends were planning a skydiving trip and I googled the name of the skydiving business and found tha…

The one place I've used Bayes (hopefully properly!) is in a spaced repetition flash card program. Usually spaced repetition algorithms wait a certain amount of time based on how many times you have seen and remembered a card. The more times you have remembered it, the longer you wait. It then creates a schedule for each day. You review the cards that have "expired" their wait time.

I wanted to turn this upside down. Instead I sorted the cards by how likely you would be to remember them (a function of the number of times you have already remembered it and the amount of time that has passed since you last saw it). I put the least likely to be remembered cards first and the most likely to be remembered cards last.

As you reviewed the cards you would either remember them or not remember them. I supposed that cards grouped together had a similar probability of being remembered (only valid if my sort algorithm was correct, but I had some confidence on that since I based it on somebody else's research ;-) ). I then used Bayes to estimate the probability of getting the card correct.

So instead of scheduling the cards, I simply had the user keep reviewing until I had a certain confidence that there was a 90% or more of getting the cards correct. At which point I left the rest for another day (the probability goes down over time). Interestingly as the test is binary (remembered/not remembered) Bayes could be simplified down to getting it right a certain number of times in a row. This was simpler for the user to understand without significantly reducing the accuracy of the estimate.

Gratifyingly the system worked incredibly well. I added an option to continue drilling the cards after you hit the 90% mark and I very rarely got into a situation where the estimate was wrong.

Re: How Bayes’ Rule Emerged Triumphant from Two Centuries of Controversy

#12

Post by kybernetikos »

amasad wrote: post #7
arcanus wrote: post #2

Bayesian here. 'The theory that would not die' is a wonderful read, and notes how many scientists used Bayesian techniques (subjective probability) in a variety of contexts while the field was still unpopular (arguably, heretical) in the mainstream statistical community. Bayes was nevertheless used to inform ballistics calculations, help crack the enigma code, or inform search patterns for lost nuclear weapons. I don…

As someone new to Bayesianism I'd be interested in hearing your experience applying it in day-to-day life. How useful do you think it is to the ordinary Joe? From my brief experience, after learning Bayes, my intuition about things involving probabilities grew very different than the people around me. For example, my friends were planning a skydiving trip and I googled the name of the skydiving business and found tha…

Did you find out the base statistics for fatalities in skydiving? That that particular business had fatalities may just indicate that they do a lot more volume or more advanced types of skydiving than other companies (in which case they may actually be safer than the norm). For me, one of the big differences Bayes rule makes is spotting that information nearly always needs context to understand it correctly. You don't have the whole story unless you have a sensible prior.

Re: How Bayes’ Rule Emerged Triumphant from Two Centuries of Controversy

#13

Post by kybernetikos »

mikekchar wrote: post #11
amasad wrote: post #7

Earlier quoted context omitted.

As someone new to Bayesianism I'd be interested in hearing your experience applying it in day-to-day life. How useful do you think it is to the ordinary Joe? From my brief experience, after learning Bayes, my intuition about things involving probabilities grew very different than the people around me. For example, my friends were planning a skydiving trip and I googled the name of the skydiving business and found tha…

The one place I've used Bayes (hopefully properly!) is in a spaced repetition flash card program. Usually spaced repetition algorithms wait a certain amount of time based on how many times you have seen and remembered a card. The more times you have remembered it, the longer you wait. It then creates a schedule for each day. You review the cards that have "expired" their wait time. I wanted to turn this upside down.…

That sounds very interesting. Is your program available anywhere?

Re: How Bayes’ Rule Emerged Triumphant from Two Centuries of Controversy

#14

Post by mtrimpe »

mikekchar wrote: post #11
amasad wrote: post #7

Earlier quoted context omitted.

As someone new to Bayesianism I'd be interested in hearing your experience applying it in day-to-day life. How useful do you think it is to the ordinary Joe? From my brief experience, after learning Bayes, my intuition about things involving probabilities grew very different than the people around me. For example, my friends were planning a skydiving trip and I googled the name of the skydiving business and found tha…

The one place I've used Bayes (hopefully properly!) is in a spaced repetition flash card program. Usually spaced repetition algorithms wait a certain amount of time based on how many times you have seen and remembered a card. The more times you have remembered it, the longer you wait. It then creates a schedule for each day. You review the cards that have "expired" their wait time. I wanted to turn this upside down.…

That sounds fascinating. Is there anywhere you could look at the result (or code ;) of this work?

Re: How Bayes’ Rule Emerged Triumphant from Two Centuries of Controversy

#15

Post by amasad »

kybernetikos wrote: post #12
amasad wrote: post #7

Earlier quoted context omitted.

As someone new to Bayesianism I'd be interested in hearing your experience applying it in day-to-day life. How useful do you think it is to the ordinary Joe? From my brief experience, after learning Bayes, my intuition about things involving probabilities grew very different than the people around me. For example, my friends were planning a skydiving trip and I googled the name of the skydiving business and found tha…

Did you find out the base statistics for fatalities in skydiving? That that particular business had fatalities may just indicate that they do a lot more volume or more advanced types of skydiving than other companies (in which case they may actually be safer than the norm). For me, one of the big differences Bayes rule makes is spotting that information nearly always needs context to understand it correctly. You don'…

Yeah I thought about this and could find a news article that said they did around 5000 jumps a year since they started in 2001 (and they're located in Las Vegas so they I assume most of their customers are first timers). So that is 75000 jumps. In the news I could find two fatalities, and two serious injuries (but let's ignore those for now). Apparently, statisticians use the term "micromorts" which means a death per million activities when talking about risks from things like this. So for this business the track record is 26.7 micromorts. Compared to the base statistics in skydiving--which is 9--this means that this business has 3 times the likely risk. Am I getting this right?

Re: How Bayes’ Rule Emerged Triumphant from Two Centuries of Controversy

#16

Post by function_seven »

amasad wrote: post #15
kybernetikos wrote: post #12

Earlier quoted context omitted.

Did you find out the base statistics for fatalities in skydiving? That that particular business had fatalities may just indicate that they do a lot more volume or more advanced types of skydiving than other companies (in which case they may actually be safer than the norm). For me, one of the big differences Bayes rule makes is spotting that information nearly always needs context to understand it correctly. You don'…

Yeah I thought about this and could find a news article that said they did around 5000 jumps a year since they started in 2001 (and they're located in Las Vegas so they I assume most of their customers are first timers). So that is 75000 jumps. In the news I could find two fatalities, and two serious injuries (but let's ignore those for now). Apparently, statisticians use the term "micromorts" which means a death per…

Sounds like it. But like you said they're almost all probably first-timers, given the location. It's hard to tell if that completely explains the micromort difference or not.

Also, it is possible that due to those fatalities, the business implemented better safety protocols as a response and may actually be safer now than it was then.

It's my Jack in the Box theory. Back in the 90s there were a couple high profile food poisoning cases (salmonella I think) where customers had died after eating at Jack in the Box. It nearly ruined the company. But my feeling is that the safest time to eat there is a month or so after those events. When all the restaurants would be kicking their food-handling practices into high gear.

So now I eat at Chipotle more often than I did before. Shorter lines and probably the cleanest food. I hope. My "theory" may be bullshit.

Re: How Bayes’ Rule Emerged Triumphant from Two Centuries of Controversy

#17

Post by moon_of_moon »

If you are in London you can visit the tombstone of the good Reverend Bayes at the Bunhill Fields burial grounds, a short walk from the Old Street tube station, and pay your respects. There is also a bench facing a spacious lawn that you can sit on and contemplate Bayes in silence. He probably sat there at some point, come to think of it.

Re: How Bayes’ Rule Emerged Triumphant from Two Centuries of Controversy

#18

Post by danbruc »

Is there any (uncontroversial) theory that rigorously defines what a 50 % probability for heads and tails means? It certainly doesn't mean that in the long run you will obtain the same number of heads and tails because there is a (vanishing) chance that you will always get heads even though the coin is actually fair. And just saying that you will obtain the same or at least similar number of heads and tails with high probability is a circular definition at best.

Does Bayesian thinking just deny the existence of intrinsic probabilities or considers them out of scope? Assuming there is such a thing as true randomness, for example in quantum physics (and it is not due to our ignorance of hidden variables like in Bohemian mechanics), could a Bayesian assign probabilities to the outcomes? Would a Bayesian be mislead into assigning something other than 50/50 for spin up and spin down if he, by chance, only observes spin up although he is really confident that this is just a statistical fluke? If he is mislead, does that mean that uncertainty about the truth of his assumptions creeps in in case the system momentarily deviates from the expected behavior?

Re: How Bayes’ Rule Emerged Triumphant from Two Centuries of Controversy

#19

Post by hacker42 »

I could never quite understand the divide between Bayesian statistics and frequentist statistics. Both seem to be ultimately about counting the frequency by which something occurs and normalizing this frequency with respect to the number of all possible outcomes. Bayesian statistics essentially is concerned with the application of the Bayesian updating technique by which one can iteratively improve a distribution over the values a parameter toward the true distribution using Bayes' rule. One can prove that given sufficiently many updates, the initial distribution does not matter as long it is non-zero for all possible values.

What I am not quite seeing is how this has philosophical implications which divide the field into Frequentists and Bayesians. It rather seems that Bayesian statistics is just a frequentist method that is helpful for dealing with noisy measurements as one can always recover from a bad distributions using more updates.

Re: How Bayes’ Rule Emerged Triumphant from Two Centuries of Controversy

#20

Post by paol »

danbruc wrote: post #18

Is there any (uncontroversial) theory that rigorously defines what a 50 % probability for heads and tails means? It certainly doesn't mean that in the long run you will obtain the same number of heads and tails because there is a (vanishing) chance that you will always get heads even though the coin is actually fair. And just saying that you will obtain the same or at least similar number of heads and tails with high…

> doesn't mean that in the long run you will obtain the same number of heads and tails

IANAM, but in my understanding that's exactly what it means, if you express "in the long run" as "the ratio tends to 0.5 as the number of tosses tends toward ∞"

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