#thomas bayes

[lindahall]

John Canton – Scientist of the Day

John Canton, a British mathematician and schoolmaster, was born July 31, 1718, in Stroud, Gloucestershire. 

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[nofatclips]

3blue1brown on probability vs odds and the medical test paradox

[irreflexion]

Inteligencia Teo-artificial

En el cementerio londinense de Bunhill Fields está enterrado el reverendo Thomas Bayes, que murió en 1761, con una lápida en la que sólo se menciona su nombre y el de sus familiares, ajeno a la influencia que su obra está teniendo en el mundo 250 años después. Escribió sólo un par de libros durante su vida, uno teológico sobre la “Divina Providencia y la felicidad de sus criaturas“, y otro sobre…

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[tagitables]

This has nothing to do with Lakatos but I’m gonna think otherwise when it comes to Bayesianism for real.

[thephilosophyofwho]

Updating Our Experience with The Doctor

The past two posts have been on things we shouldn't necessarily believe:  magic and miracles.  We looked at the stage magic tricks in the Fourth Doctor's serial The Talons Weng-Chiang, in which a stage magician by the name of Li H'sen Chang.  Chang uses his show to kidnap individuals to feed his master and keep him alive until he can be returned to his proper time in the future.  We examined the miracle of the Centurion Rory and his resurrection after he disappeared into a crack in the Universe.  The Doctor struggled to come up with an explanation at first that was consistent with the laws of nature (i.e. people who are dead do not return to life). Eventually he found a scientific explanation, but he was doubtful for a second.  He was strongly disinclined to believe that miracles could occur and Scottish philosopher, David Hume, would argue rightly so.

Hume argued that any testimony has to pass two tests.  In the direct test, the testimony has to come from a credible witness or witnesses.  In the reverse test, the event that the testimony discussed had to be likely.  If it didn't pass both these tests then it wasn't likely that the event occurred. But Hume's argument was slightly more complex.  He argued that every event has a probability of occurring.  There is a very small probability of a dead individual being brought back and another small probability of a magician willfully killing his assistant with swords in a box.  Upon hearing testimony of (or witnessing) these events we may consider the testimony and the probability that it is false.  If the probability that the event did not occur is greater than the probability of the testimony being false, we doubt that the event occurred. For miracles, which have an infinitesimally small probability of being true, we find that we need to have a very large body of testimony to believe.  Hume believed the only option was to have testimony from everyone in the world corroborate the occurrence of the miracle in order to believe it actually happened.

Hume probably didn't know it at the time, but his two tests on how to evaluate the evidence of miracles mimicked worked being done by Reverend Thomas Bayes.  Bayes was even working at about the same time as Hume, but none of his work on this was published during Bayes life.  Importantly Bayesian thinking didn’t really take off until the 20th century, when probability was formally codified.  Most epistemology looks at statements being true or false, either 0% or 100% true.  Bayesian epistemology, instead looks at probabilistic statements about our degree of belief in a claim.  A probabilistic statement about a degree of belief in a claim may look like this:  “I believe there is a 50% chance that the next flip of this fair coin will land on heads.”  “The weather forecaster assigned a 30% chance of rain tomorrow.”  or “The economist believes there is a 73% chance that there will be a stock market crash within the next 3 years.”

Bayesian epistemology is given by the principle of conditionalization.  An event or claim (it will rain tomorrow) is conditional on another event or claim (it rained today) if the probability of it raining tomorrow is different based on whether it rained today or not.  Formally, the principle of conditionalization says that if I have an initial probability that of a claim, and I acquire new evidence about a claim where there is some degree of dependency between the two claims then I am logically compelled to change my initial probabilities and develop different final probabilities. It rains 1 out of every 5 days where I live (or the probability of rain on any given day is 20%).  If it rains today, the probability of rain tomorrow is 60%. It’s logical for me to believe that in 1 out of every 5 days, it will rain tomorrow.  But if I observe that it is raining today, then I should believe that in 3 out of every 5 days that follow a rainy day, it will rain tomorrow.

Bayesian epistemology has implications for the evaluation of testimony in the social context.  Let’s say I hear a claim that someone has been brought back to life as a Roman centurion.  I may have a naïve probability that the claim of a miracle is very, very low.  When I evaluate the probability that the report is accurate, I may also rate that probability as very, very low.  But in doing so, I am also evaluating that the person providing my testimony has a very low reliability.  If on the other hand I have a witness who testifies that they have seen a stage magician perform an illusion and I believe the testimony, I am also evaluating that the witness is a reliable and credible individual.

Magic and miracles are incredible things.  Magic forces us to confront what we perceive to be reality as we try to explain new observations that are inconsistent with previous beliefs.  Miracles also challenge well-established natural laws, but unlike magic we don’t believe miracles to be true because the testimony we have in support of them is often insufficient.  Both David Hume and the Rev. Thomas Bayes argued that we should take the quality of the evidence into account when we evaluate claim.  But while Hume explicitly argued for it in the case of miracles, Bayes (and the rest of the Bayesians) would probably want us to apply it to all of our experiences and testimony we find ourselves evaluating.    

[academicatheism]

How Bayes’ Rule Can Make You A Better Thinker

Having a strong opinion about an issue can make it hard to take in new information about it, or to consider other options when they're presented. Thankfully, there’s an old rule that can help us avoid this problem — and even help us make good decisions when we’re uncertain. Here’s how Bayesian Reasoning works, and why it can make you a better thinker.

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[lolstats-blog]

[jordanneinnyc]

...We must think differently about our ideas -- and how to test them. We must become more comfortable with probability and uncertainty.

Nate Silver in an this month's Vanity Fair about Thomas Bayes' theory

Silver discusses his predictions of the upcoming Presidential election (you all should vote by the way) and how we must not put so much faith in them in his interview with John Heilpern. Regardless his predictions and the outcome of November 6th, it applies to all parts of my life.

I competed my Bachelor of Arts in Psychology and Sociology at the University of California, Santa Barbara. From my experience, every prediction I've made about my research projects in both of these topics was wrong. The projects on self-expansion and employee relations yielded different results that I would have never imagined predicting.

I took a huge gamble applying for NYU for a Masters in Publishing. Call it God's grace or luck, I got in. I have to now figure out which decisions will lead me to a career in magazine publishing. I can predict that I will do really well in my editorial classes that will help me get an editorial internship and maybe become the fashion editor of Vanity Fair -- I aim high. But, right now I'm doing a lot better in finance. Perhaps I should consider that track.

As someone who used to have tunnel vision, I'm realizing the positivity of keeping my options open. I've become a stronger, level-headed, more flexible person than I was two years ago because I've accepted that uncertainty exists. So, thank you Nate Silver for reminding me about this. I hope you are right about the election though.