
Bayes's Theorem: What's the Big Deal? - NN88
http://blogs.scientificamerican.com/cross-check/bayes-s-theorem-what-s-the-big-deal/
======
hyperpape
Interesting that they mention the medical case, when there's some
psychological work around the idea that we should present these cases in terms
of natural frequencies instead of Bayes' theorem.

The natural frequencies approach is to say "if 10000 people take the test, 100
will have cancer. Of them, 99 will get an accurate positive test, and 1 will
have a false negative test. Of the other 9900, 99 will receive a false
positive, and 9801 will receive a correct negative. What are the odds that
someone who has a positive test has cancer?"

It turns out that doctors and other professionals whose core professional
competency doesn't concern probability do terribly when presented with
percentages and Bayes theorem, but can handle natural frequencies quite well
(here's one quick summary:
[http://opinionator.blogs.nytimes.com/2010/04/25/chances-
are/...](http://opinionator.blogs.nytimes.com/2010/04/25/chances-are/?_r=0)).

As is obvious, this isn't an argument that Bayes' theorem is wrong--it's a
theorem after all. It's an argument about which types of reasoning people can
be easily taught.

~~~
Anderkent
It's true that when the question is formed in frequentist terms, the answer is
much more intuitive. But is that how the problem occurs in real life? The
doctor doesn't see ten thousand people take a test; they see a person take a
test, and get either a positive or negative result. The traditional way of
forming the problem seems closer to actual experience: 'your patient tested
positive. you know how accurate the test is, and how common the disease is;
how likely is it that the result is a false positive?'

~~~
hyperpape
I'm not quite sure what you're saying. Doctors don't observe probabilities or
enormous frequencies. Either way, there are good odds that this is information
that someone is communicating to them, not the result of their personal
experience.

~~~
Anderkent
Doctors observe a result of the test, and know the basic probabilities (in the
example, 99% test accuracy, 1% of population have the disease). The problem is
that they [often] draw incorrect conclusions from those observations (99% test
accuracy and you tested positive? well then you likely - 99% - have the
disease, right?).

The question formed as 'your one patient tested positively' is more
immediately relevant, I'd think. The correspondence with actual practice is
obvious. The question formed as 'out of 10000 ...' could be remembered as a
quirk of statistics, but not actually recalled when someone tests positively
for cancer.

~~~
Jabbles
Of course, doctors do not randomly assign tests to patients. Their prior that
a patient has a disease is a lot higher than the background frequency of it
occurring.

Getting them to estimate their prior would be interesting.

~~~
URSpider94
Except when they do. For example, when 100% of men above a certain age are
screened for prostate cancer, or 100% of women above a certain age are
screened for breast cancer. Both cases spawned major public health campaigns
to encourage screening, followed years later by recommendations AGAINST 100%
screening, based on the high degree of false positives and unnecessary
treatment.

Other cases that come to mind: \-- doctors who offer "full body scans" as a
part of an executive physical; you're pretty much guaranteed to turn up
something that is 2 sigma away from the population norm, somewhere in the
body, on such a scan

\-- spinal x-rays for back pain. Doctors almost always find something
abnormal, and use that to justify the back pain and treat aggressively. But,
we don't really have a good prior; if you x-rayed 1000 people off the street,
would we find similar abnormalities frequently?

------
Laaw
I've been saying this for _years_ , and this is a large reason why I find the
LessWrong folks to be almost entirely full of it. Their inability to come up
with accurate priors is completely lost on many of the folks who follow this
kind of thinking.

A couple of comments are saying, "no duh" to this article, but those folks
likely don't realize quite how many other people are falling into this trap.
"Garbage in, garbage out" is only good advice when the person you're saying it
to realizes they're putting garbage in.

~~~
IanCal
Do priors just start you off closer to the truth? That is to say, if you start
with _any_ prior, will enough additional pieces of evidence _always_ let you
converge on the truth?

Does anyone commonly set their priors to be a distribution? Perhaps a range or
actually a normal distribution to represent a prior with uncertainty?

~~~
Fomite
In my field (Epidemiology), when doing Bayesian analysis, it is _very_ common
to set one's priors to be a distribution. Sometimes the point estimate and
spread of a previously conducted study or meta-analysis, sometimes merely a
uniform distribution with upper and lower bounds ("It is extremely unlikely
that the relative risk of disease for this exposure is below 0.01 or above
100...")

It's been argued that frequentist analysis is essentially a Bayesian analysis
with a prior distribution centered on zero with bounds from positive to
negative infinity.

~~~
skybrian
How does that work? It doesn't sound like a well-defined distribution since
the area under the curve needs to be 1.

~~~
bmh100
It has to do with calculus. If the probability of a given result approaches
zero as the result itself approaches positive or negative infinity, then the
area under the curve approaches 1.

Imagine 1/2 + 1/4 + 1/8 ... to infinity. The sum approaches 1 as the
denominator approaches infinity. With calculus, we can determine that with
mathematical methods.

~~~
gipp
I think he was referring specifically to an unbounded _uniform_ distribution,
which is indeed not well-defined.

------
njohnson41
Good article.

I'm only a bit disappointed that the author seems not to realize that Bayes'
theorem is just a simple consequence of probability theory, and should be
attractive not because "maybe the brain is Bayesian", but because it is based
on sound set-theoretic and analytic principles. If Bayes' theorem is false, so
is probability theory, and so is nearly everything we know about probability.

Edit: Here is a good explanation of the theorem that makes it visually clear
how only set theory is involved in deriving it:
[https://oscarbonilla.com/2009/05/visualizing-bayes-
theorem/](https://oscarbonilla.com/2009/05/visualizing-bayes-theorem/)

~~~
gaur
I guess a hard-line frequentist (if such a person exists) would counter that
you can't assign probabilities to hypotheses or fixed parameters. Then Bayes's
theorem (and every other statement about probability) is true only when
applied to statements about how often a certain event will occur.

But of course, most people _do_ assign probabilities to hypotheses and fixed
parameters, even if only informally. Bayesian probability theory is an attempt
to formalize that kind of intuitive reasoning.

~~~
lottin
I think it's strange this sudden comeback of a theory that was dismissed more
than 70 years ago by Fisher and many others, but no one, as far as I know,
cares to explain why Fisher was wrong and why the theory is right. It makes me
very suspicious, to be honest.

~~~
dragandj
Actually, many Bayesian textbooks cover that. Try Jaynes - Probability Theory:
The Logic of Science.

------
PaulHoule
So can frequentism.

Many investigators in parapsychology who were sincere and intelligent appear
to have based their career on the incorrect use of frequentist statistics.

And it's not just them. Ernerst Rutherford, who discovered the atomic nucleus,
"If your experiment needs statistics, you ought to do a better experiment." In
the 1990s I was a physics grad student and I think none of the professors had
ever heard of the idea of a parameter estimator so we had a bunch of ad-hoc
ways to fit power law coefficients that gave different answers and no way to
judge goodness of fit that was thought out at all.

One postdoc in my lab suffered through a difficult job market before finally,
after a decade of anxiety and uncertainty, got a tenure track position and
eventually wrote a paper on how to fit power law curves... in a statistics
journal.

And this was in a good department with people in which I was proud of both the
teaching and research going on.

~~~
3pt14159
I'm a little confused. Are you saying that a tenure track prof wrote a paper
on how to evauluate fitted power law curves? Was it something else besides
least squares? Because I can't possibly see this getting accepted to a
statistics journal.

~~~
jwmerrill
Fitting distributions is a little bit different than the usual model fitting
scenario where least squares is appropriate. Sometimes people do things like
construct a histogram and then do a least squares fit to the bin heights, but
that procedure doesn't satisfy the usual assumptions that justify least
squares (observations with independent, equal variance, Gaussian errors).

Cosma Shalizi has written some interesting posts on this subject, and also
published papers in statistics journals:

[http://bactra.org/weblog/491.html](http://bactra.org/weblog/491.html)

------
darawk
> If you get tested again, you can reduce your uncertainty

I've always been bothered by statements like this about medical tests. This
assumes that false positives are statistically independent. But isn't it more
likely in general that false positives would be highly correlated in
individuals, test administrators, or labs? E.g. If the same person takes the
same test from the same doctor and sends it to the same lab, it seems
extremely unlikely that the results will be independent. And to me at least,
it seems highly likely that a false positive will correlate with some aspect
of the individual's biological (e.g. some similar substance in the blood to
what's being tested), and as such even using a different doctor/lab would not
be all that likely to ameliorate this issue.

~~~
ucha
That's a nitpick on a correct statement. Unless two tests are always
_perfectly correlated_ , you will reduce your uncertainty. They don't need to
be independent.

~~~
darawk
Sorry, I should have provided a more complete quote:

> If you get tested again, you can reduce your uncertainty enormously, because
> your probability of having cancer, P(B), is now 50 percent rather than one
> percent. If your second test also comes up positive, Bayes’ theorem tells
> you that your probability of having cancer is now 99 percent, or .99.

This statement is incorrect if the results are correlated at all.

------
tzs
Referring to an appearance of Bayes' theorem on Sheldon's whiteboard:

> Bayes’ theorem has become so popular that it even made a guest appearance on
> the hit CBS show Big Bang Theory

That's not a sign that it has become popular, any more than the appearance of
the standard human pedigree notation used by genetic counselors on the same
whiteboard indicates that standard human pedigree notation has become popular
among the general public. It's simply a sign that BBT takes care to make the
whiteboards generally scientifically sensible.

They have a UCLA physicist [1] consultant who works with the producers,
writers, prop people, set decorators and others to try to make things
scientifically accurate.

In this particular episode, both Bayes' theorem and the genetic information
are there because Sheldon was trying to figure out his chances of surviving
until technology reaches the point that he can transfer his mind to an AI and
what he would have to do to improve those chances. So both those things were
on the whiteboard because they are things that would be perfectly reasonable
to find on the whiteboard of someone doing that.

They consulting physicist had a blog [2] where he covered most episodes and
talked about the whiteboards and other scientific content. Here is the entry
for the aforementioned episode [3].

[1]
[http://bigbangtheory.wikia.com/wiki/David_Saltzberg](http://bigbangtheory.wikia.com/wiki/David_Saltzberg)

[2]
[https://thebigblogtheory.wordpress.com](https://thebigblogtheory.wordpress.com)

[3]
[https://thebigblogtheory.wordpress.com/2010/09/30/s04e02-the...](https://thebigblogtheory.wordpress.com/2010/09/30/s04e02-the-
cruciferous-vegetable-amplification/)

~~~
n4r9
P(popular | appeared on BBT) < 1

------
cwyers
> In many cases, estimating the prior is just guesswork, allowing subjective
> factors to creep into your calculations. You might be guessing the
> probability of something that--unlike cancer—does not even exist, such as
> strings, multiverses, inflation or God. You might then cite dubious evidence
> to support your dubious belief. In this way, Bayes’ theorem can promote
> pseudoscience and superstition as well as reason.

Oh please. You can do plenty of psuedoscience and superstition with good old
frequentist statistics. And of all the people you could pick to represent
Bayesian statistics, instead of I don't know, Andrew Gelman or someone, the
author picks... Eliezer Yudkowsky? If nothing else, this provides inspiration
for me to quit procrastinating on my "ASK ME ABOUT ROKO'S BASILISK" novelty
t-shirt idea.

~~~
entrode
I suspect Eliezer is targeted specifically due to his tongue-in-cheek
presentation of understanding Bayesian statistics as being initiation into a
cult. Also due to the author's familiarity with the topic likely specifically
as a result of Eliezer's efforts to popularize the subject and his association
to him resultantly.

~~~
eli_gottlieb
Sure, but who cares? There's an entire field of statistics called "Bayesian
statistics", who do actual math and statistics and don't give a damn about
novelty T-shirts.

------
stuartaxelowen
Read through most of the article just for "people can abuse priors"? Come on.
Anything, used wrongly, can promote superstition and pseudoscience.

~~~
astine
I think you're missing the broader argument, which is using 'mathy' concepts
to dress up poor reasoning. Obviously priors matter, but what matters most of
all is how good/complete your evidence is. Using a mathematical formula to
lend credence to weak evidence (through liberal use of assumptions) is a
hallmark of pseudoscience. The same could be said of many of the abuses of
statistics and Bayes theorem is merely one good example of this.

~~~
Anderkent
Is using mathy concepts to dress up poor reasoning worse than not using
anything to back up your reasoning? At least you can point out exactly what's
wrong with the mathy reasoning.

A colleague of mine says 'Sometimes pulling numbers out of your arse and using
them to make a decision is better than pulling a decision out of your arse'

~~~
astine
"Is using mathy concepts to dress up poor reasoning worse than not using
anything to back up your reasoning?"

I believe so. If your belief is baseless, or based on flimsy evidence or
simple bias, it's best if that's obvious. Dressing up weak reasoning to seem
stronger is a form of lying. It's what we call sophistry. A big part of the
problem is that for a lot of people don't understand the math well enough to
point out what's wrong with it or have a bias towards explanations that seem
complex or sophisticated but really aren't.

It's true that sometimes we have to make a decision based on poor or no
evidence but it should be clear that that is the case when that is the case.
Dressing up the argument only obfuscates that.

~~~
TeMPOraL
Honesty is an ultimate issue here. If my reasoning is shoddy, but I plug it
into some math apparatus, then it'll likely make my problems obviously wrong.
If my reasoning is very inaccurate and the data uncertain, being precise about
it can at least make the results salvageable. Scott Alexander argues for this
position quite well in [0].

Humans can lie with statistics well. But they can lie with plain language even
better.

[0] - [http://slatestarcodex.com/2013/05/02/if-its-worth-doing-
its-...](http://slatestarcodex.com/2013/05/02/if-its-worth-doing-its-worth-
doing-with-made-up-statistics/)

~~~
astine
"If my reasoning is shoddy, but I plug it into some math apparatus, then it'll
likely make my problems obviously wrong."

That's pretty clearly untrue. I remember reading a study recently where the p
value was less than .01 or something like that but where the experimental
design was clearly flawed. The correlation wasn't the correlation they thought
they had. But because the math looked good and it was easier than actually
reviewing the experiment, it was tempting to take the study on face value.

I've read Scott's essay before and I understand his argument, but I don't
think it works. While, you might be able to avoid some bad reasoning simply by
being more systematic, you can also strengthen bad arguments with a faulty
application of statistics. What Scott doesn't do is provide an analysis of how
often each of these things happens. I'd argue that for each time a quick
application of statistics save someone from a bad intuitive judgment, a
misapplication of statistics is used to encourage a bad judgment at least one
time if not more.

Understand that my argument here is not that one should never use statistics
or even Bayes theorem, but that a naive or lazy application can be worse than
no application.

~~~
TeMPOraL
I see your point and I agree.

For myself, I try to limit myself to the mathematical apparatus I feel
comfortable with. I know that if I were to open a statistics textbook, I could
find something to plug in my estimates and reach a conclusion, and I'm pretty
sure the conclusion would be bullshit. I learned it the hard way in high
school - I remember the poor results of trying to solve math and physics
homework assignments on topics I didn't understand yet. The mistakes were
often subtle, but devastating.

------
RogerL
I prefer to think of it in terms of the statistical inversion problem. That
is, we have an event(s) that occur, which we may imperfectly understand. We
take noisy measurements of that event. Clearly, the causal relationship is the
events cause the measurements - a bad measurement does not cause the event to
move.

But, in practice all we have are measurements, and from that we want to find
an optimal (or good) estimate for what the events were. Hence, inversion.

Bayes formula expresses P(x|y) in terms of P(Y|x), so you can perform the
inversion using bayes.

In many fields establishing the prior is difficult, hence frequentist methods
are popular.

There are many techniques for the statistical inversion problem. Trying to
track a ballistic object in a vacuum? Fit the measurements to a second order
polynomial (parabola) and you are done (well, you have to decide least squares
vs robust methods, but it is not such a hard problem in the scheme of things).
Trying to track a manuevering jet, stock prices, or disease incidence rates.
Now your model of the problem is much less clear.

We model lack of information as random variables. It isn't "random" in the
deterministic sense, just in the sense that we don't know. Establish a good
probabilistic description of that lack of knowledge in your prior, and you are
probably going to get good result: this jet fighter is probabilisticly either
moving straight, performing a coordinated turn, or performing an uncoordinated
turn. Use a Markov chain to model those likelihoods (e.g.), and you may end up
with good results. But if your modeling of the prior is poor, well, good luck
to you, your output is probably nonsense.

~~~
jsprogrammer
Most measurements _do_ affect the event.

~~~
jamiek88
ALL measurements at a quantum level at least!

~~~
cbd1984
Believe it or not, the Heisenberg Uncertainty Principle has nothing to do with
measurement.

~~~
jsprogrammer
Is someone claiming otherwise?

~~~
cbd1984
Lots and lots of people, especially people who don't know about conjugate
pairs or the Fourier transform.

------
haberman
I am only just learning about this stuff, but there are several things in this
article that seem incorrectly explained. Conceptual clarity is paramount to
me, so it drove me a little crazy!

> Bayes’ theorem is a method for calculating the validity of beliefs
> (hypotheses, claims, propositions) based on the best available evidence
> (observations, data, information).

Bayes theorem is a statement about probability, not "validity." This
description makes it sound like Bayes theorem is a function BT(belief,
evidence) = validity of belief. But it's not like that at all.

Probability is a way of measuring uncertainty. Things are uncertain for two
main reasons: either we can't observe them directly ("do I have this disease
or not?") or they haven't happened yet ("what side will this coin flip land
on?"). (If you believe in a deterministic universe, the second is just a
special case of the first.)

The "beliefs" (aka priors/posteriors) in Bayes theorem are statements of
probability. To use the article's example, if it is claimed that 1% of the
population has a certain disease, your "belief" or "prior" is that P(I have
the disease) = 0.01. The article seems to get confused and think that the
"belief" here is "I have the disease." Bayes theorem doesn't tell you about
"the probability that a belief is true" like the article says, the belief _is_
a probability. It also doesn't tell you if your belief is "valid."

Bayes theorem takes your existing belief about the probability of something
and gives you a new probability that incorporates some evidence you observed.

------
cronjobber
Here's a proposal: Bayesian scientists shouldn't select their own prior.
Instead publish how your results would update any prior, including the one
picked by me, the reader.

I certainly haven't thought this through, but maybe this would make science
more modular: combine the updates from M studies and calculate the new,
combined update. Statisticians, does this work?

~~~
arcanus
This does happen. I've had paper reviewers request results with an
appropriately selected uninformative prior:
[https://en.wikipedia.org/wiki/Jeffreys_prior](https://en.wikipedia.org/wiki/Jeffreys_prior)

Typically, if you are practitioner in the field, it is not too difficult to
identify instances where the result is highly dependent on the choice of
prior.

------
sago
The current fashion for BT really bugs me.

BT inverts conditional probabilities. If you can estimate P(E), P(H) and
P(E|H) better than P(H|E) it will give you a better result. It is one of many
probability identities. But someone it has become 'the one', as if, say P(H|E)
= P(H&E)/P(E) isn't much use, but put two of those together: world changing.

I've seen so much crap come out of this fad. My particular favourite is in
theology. William Lane Craig has demonstrated that Jesus raised from the dead,
to a high probability. Richard Carrier has shown that there was no historical
Jesus. Funny how few people ever run BT and find it _contradicts_ their views.

I think part of the problem comes from a lack of understanding of the
difference between frequentist and bayesian interpretations of probability.
I've yet to see these folks show BT working in anything but frequentist data.
And then they'll switch and use it to demonstrate why their Bayesian situation
is correct.

~~~
logfromblammo
Bayes does more than just invert the conditional. Of P(x), P(y), P(x|y), and
P(y|x), if you know any three, then Bayes will give you the fourth.

It's just an equation. Garbage inputs will yield garbage outputs. In the realm
of theology, it is of no more use than Pascal's Wager as an expected value
calculation. All the input values are made up, so the output value is equally
fabricated.

If you're using it on real, verifiable statistics, such as verified spam in an
e-mail corpus, you can use Bayes to make a classifier to automatically
identify spam to a high degree of accuracy. But if you are estimating for any
of the three numbers you need to know, the fourth that you calculate will also
be suspect.

------
lqdc13
I just love how some guy, who by his own admission read a little Wikipedia on
the topic, is critiquing a statistical method.

It would make for a much stronger argument if he actually showed some numbers
where people are getting the priors wrong. That is, how often people get the
priors wrong and the probability of mistake if they used a different strategy
more commonly used in the field.

------
theseatoms
> The potential for Bayes abuse begins with P(B), your initial estimate of the
> probability of your belief, often called the “prior.”

tldr; priors matter

~~~
lordCarbonFiber
That was my thought as well. Garbage in = garbage out, that's pretty standard
in most fields. I really didn't like how the author treated the theorem as if
it's some sort of magic, aside from something everyone that's taken a college
prob/stat class has derived from first principles.

~~~
sago
The problem is that advocates do treat it as a magical thing. They extrapolate
from the fact it is proven to the claim that all knowledge is Bayesian, to the
implication that all Bayesian reasoning is knowledge.

This fashion is why, for example, BT has been used to both prove the
resurrection of Jesus, and to prove that Jesus didn't exist: both to a very
high probability.

~~~
lordCarbonFiber
I'm almost sad I've never met one of these people in the wild. I'd really like
to sit down and watch someone, with a straight face, try to say they both have
a set probability for their belief on Jesus AND the probability that some
vague ~evidence~ would exist given that belief.

------
GavinB
This headline does not reflect the article and is needlessly inflammatory.
This article is an explanation of Bayes theorem and overall very positive of
it. The "used wrongly" quote is just stating that it's not immune to biases
and error. Pretty much any tool "used wrongly" can cause errors.

(In case it's changed, the headline currently reads "Bayes theorem used
wrongly, can promote superstition and pseudoscience")

~~~
mfoy_
I think the title isn't quite so off. The article is trying to point out that
people should be wary of using it wrongly.

Like other commentators have pointed out, the saying "garbage in garbage out"
only helps when you stop to think whether or not you're putting garbage in.

------
logfromblammo
They were doing great until they got up to the re-test, claiming that the
second positive gives you 99% certainty you have cancer. That only works if
the second test is completely independent from the first. If you repeat the
first test a second time, only for those who get a positive result on the
first, the same condition that caused a false positive on the first can cause
a false positive on the second.

In reality, a cheap blood or urine test is likely to be followed by a more
expensive test on a second portion of the same sample, then by an even more
expensive tissue biopsy. Redoing an identical test only reduces random errors.
It does not address the diagnostic bias of the test itself.

For instance, a pregnancy test detects hCG, from the placenta of a developing
fetus. A man with various types of cancer or liver disease may also produce
hCG, and can therefore produce a false positive for every test of that type,
no matter how many repetitions. This does not give him greater confidence that
he is pregnant!

Understanding Bayes also requires an understanding of event independence! For
truly independent events, P(x|y) = P(x) and P(y|x) = P(y).

------
pdkl95
> Bayesians claim that their methods can help scientists overcome confirmation
> bias

The claim isn't that Bayesianism somehow prevents biases. Using a Bayesian
approach is important in science because frequentism _answers the wrong
question_ [1].

    
    
        Many scientists operate as if the confidence interval is a Bayesian
        credible region, but it demonstrably is not ...
    
        I think the reason this mistake is so common is that in many simple
        cases ... the confidence interval and the credible region happen
        to coincide. Frequentism, in this case, correctly answers the question
        you ask, but only because of the happy accident that Bayesianism gives
        the same result for that problem.
    

[1] [http://jakevdp.github.io/blog/2014/06/12/frequentism-and-
bay...](http://jakevdp.github.io/blog/2014/06/12/frequentism-and-
bayesianism-3-confidence-credibility/)

(I'm referencing part 3 for the discussion of why frequentism is inappropriate
in science, but I recommend reading the series from the beginning)

------
philh
I feel like there are multiple questions getting conflated:

* Does Bayes help honest enquirers to find the truth? (Relative to what? At what skill level?)

* Does Bayes help bullshitters to hide the truth? (Relative to what? At what skill level of bullshitter and mark?)

Re the second, I think it's difficult to use Bayes to bullshit someone who
understands Bayes as well as you do.

------
yzmtf2008
To me, the single most easy to understand form of Bayes' Theorem is:

    
    
        P(A|B) * P(B) = P(A∩B) = P(B|A) * P(A)
    

An intuitive explanation to the equation:

The (possibility of events A and B both happening) equals the (possibility of
A happening when B is happening) * the (possibility of B happening), which
equals to the (possibility of B happening when A is happening) * the
(possibility of A happening).

Combining that with a Venn diagram:

    
    
        {A (A}∩{B) B}
    

Since P(B|A) means the chance of event B happening when A is happening, in
this case which indicates that __both A and B are happening __, it 's really
just the area of (A∩B) divided by (A), which can be translated to (P(A|B) *
P(B)) / P(A).

------
smcg
Kind of a clickbait title considering the article is a bit more nuanced than
that.

------
astine
I've had people seriously claim to me that using Bayes theorem to evaluate
beliefs that one deals with in ones everyday life using evidence that one
comes across in everyday life was likely a good idea and would reduce bias. I
wish I'd had the presence of mind to point out that that did nothing to
eliminate the selection bias of one's own experience. No mathematical formula
can draw meaning out of weak or flawed evidence.

Trying to do so is like trying to 'enhance' a blurry photo so that you can see
details in the photo that didn't exist.

~~~
Anderkent
Even if you only get weak of flawed evidence, then you do what you can to make
the best decisions given that evidence. No one tries to suggest you do actual
bayesian calculations on everything you know, for the simplest reason that
it's not computationally viable.

But if your beliefs directly contradict bayes then you're doing something
wrong - there's an inconsistency that's likely worth investigating, unless the
matter is really minor. It's a sanity check for your decision making, not a
constructive algorithm for the best decision.

------
jedberg
> Cognitive scientists conjecture that our brains incorporate Bayesian
> algorithms as they perceive, deliberate, decide.

As a Cognitive scientist myself, this amused me. The reason being because in
the 1950s, Cognitive scientists thought that the brain worked like telephone
switching equipment.

Basically, we fit our current model of cognition to the most popular model of
computing at the time. Looks like the trend hasn't stopped (although to be
fair we we were talking about the Baysian model of cognition 20 years ago, so
at least that one lasted a while).

------
SandroG
Bayes in action: The author of this article had a set of prior beliefs about
the Bayes's Theorem, which evolved after he reviewed more evidence.

------
exelius
Bayesian probability is catching on because the technology has finally caught
up to the point where it's feasible. Thanks to the web and the proliferation
of big data, we now have enough observations that Bayesian models can be
trained (this was always the hard part). This doesn't mean we don't need smart
people figuring out what things the model should and shouldn't look at; but
it's at least possible to do today.

It also doesn't hurt that the Bayes theorem is at its heart a map-reduce
problem. Where once Bayes' theorem was considered a cumbersome artifact for
"brute forcing" probability, it's now likely faster than competing methods of
statistical analysis.

We almost seem to be getting to the point in ad targeting where demographics
are expressed in terms of a set of bayesian properties. You don't even care
what the properties are; just that they're potentially more willing than
average to use your product.

~~~
GFK_of_xmaspast
> It also doesn't hurt that the Bayes theorem is at its heart a map-reduce
> problem.

??? I'm not following. You could say that (numerical) integration is a map-
reduce problem but that's pretty trivial.

------
ssanders82
Since we're on the subject, can anyone point me in the direction of how to
account for correlated inputs? Without adjusting them, it can possibly give
nonsensical probabilities (>1) but my math isn't good enough to decipher the
few academic texts I've seen regarding this situation.

A (very simple) example: I trade stocks. My starting point is that I think a
stock has a 50% chance of rising next year. Then I want to do a Bayesian
iteration with the stock's P/E ratio based on historical data for stocks with
similar P/E ratios. Then I want to also incorporate the P/E ratio of the
industry the stock is in. Obviously these two inputs are correlated and if you
have enough correlated variables, the whole thing breaks down because the
simple theorem only works if all the inputs are independent of each other.

------
tonybeltramelli
Same topic but differently presented by Quanta Magazine
[https://www.quantamagazine.org/20151216-physicists-and-
philo...](https://www.quantamagazine.org/20151216-physicists-and-philosophers-
debate-the-boundaries-of-science/)

------
Houshalter
The fundamental insight of bayesian reasoning is that prior probabilities can
matter a lot in some situations, even when the evidence seems fairly strong.

Look at scientific papers. Usually there is something called a p-value
attached to it, which is usually around 0.05. This means there is only a 5%
chance that the same result could have been produced by random chance.

How strong is that evidence, really? What if you started with a prior
probability of 1 in 1,000 that it's actually true. That is, before you saw the
paper, you would estimate there's only a 0.001% chance it's true. Out of 1,000
similar studies, 49 will be false and yet return a <0.05 p value. Only 1 will
publish actually true results.

------
vezzy-fnord
If you have some time to spare, here's a great paper on a similar topic: the
(mis)use of mathematics and in particular equilibrium methods in economics
after Samuelson and Hicks ("What Went Wrong with Economics?", Peter J.
Boettke, 1997): [http://www.the-dissident.com/Boettke_CR.pdf](http://www.the-
dissident.com/Boettke_CR.pdf)

Pretty much every debate on economic policy between the left and right is full
of fallacies emanating from this episode in history.

------
sixdimensional
I find Bayesian subjective probability even more interesting. It has been
successfully applied in unique situations, such as during the cold war, by a
panel of "experts" in the US, to locate Russian test fired rockets in the
ocean.

------
auvrw
modal logic is an equally valid way to get at a lot of the quandaries
associated with bayesian ideas.

bayes' thm by itself is totally _not_ a "big deal." the idea that every
probability has an associated prior, even if it's not explicitly written in
the notation (so think "prior of prior") is an interesting attempt to cope
with uncertainty in a rigorous way.

i do agree that in some places in the sciences, while "the numbers don't lie,"
the stats can be misleading. still, i can understand why it's useful to make
some statements with statistics in order to quickly arrive at some first-order
approximations.

------
mjgeddes
Bayesianism is a 'grand unified theory of reasoning' that all of science be
should be based on assigning (and updating) probabilities for a list of
possible outcomes; the probabilities are supposed to indicate your subjective
degree of confidence that a given outcome will occur.

Yudkowsky's 'Less Wrong' group of 'rationality' followers, aimed to try to
force-fit all of science into the Bayesian framework. And of course it doesn't
work at all.

I think Andrew Gelman's criticisms are right on the mark.

Probability theory was designed for reasoning about external observations -
sensory data. (for example, "a coin has a 50% chance of coming up heads"). In
terms of predicting things in the external world, it works very well.

Where it breaks down is when you try to apply it to reasoning about your own
internal thought processes. It was never intended to do this. As Gelman
correctly points out, it is simply invalid to try to assign probabilities to
mathematical statements or theories, for instance.

You see 'Less Wrong' followers wasting years of their lives engaging in the
most unbelievable and ludicrous intellectual contortions to try to force-fit
all of science into Bayesianism.

Go to the 'Less Wrong' blog and you can read reams and reams of these
massively complicated and contorted ideas, including such hilarious nonsense
as 'Updateless decision theory' and 'Timeless decision theory'.

\---

David Deutsch in his superb books, 'The Fabric Of Theory' and 'The Beginning
Of Infinity', argued for a different theory of reasoning than Bayesianism.
Deutsch (correctly in my view) pointed out that real science is not based on
probabilistic predictions, but on explanations. So real science is better
thought of as the growth or integration of knowledge, rather than probability
calculations.

In terms of dealing with internal models or hypothesis, I think the correct
solution is not to assign probabilities, but rather to assign a 'conceptual
coherence' value, so for instance rather than say 'outcome x has probability
y' (where x is a hypothesis) you should say 'concept x has conceptual
coherence value y'

Conceptual coherence is the degree with which a hypothesis is integrated with
the rest of your world-model, and I think it accurately captures in
mathematical terms the ideas that Deutsch was trying express.

Probabilities should be viewed as just special cases of conceptual coherence
(in the cases of outcomes where you are dealing with external observations or
sensory data, Bayesianism is perfectly valid).

Then all of the problems with probability go away, and none of the massively
complicated theories expounded on 'Less Wrong' are necessary ;)

------
RodericDay
I think Stephen Bond did some excellent takedowns of the identity politics
that has arisen around Bayes' Theorem back in the day. I wonder where he's at
these days.

The Cult of Bayes' Theorem

[http://laurencetennant.com/bonds/cultofbayes.html](http://laurencetennant.com/bonds/cultofbayes.html)

> _One of Yudkowsky 's constant refrains, appropriating language from Frank
> Herbert's Dune, is "Politics is the Mind-killer". Under this rallying cry,
> Lesswrong insiders attempt to purge discussions of any political opinions
> they disagree with. They strive to convince themselves and their followers
> that they are dealing in questions of pure, refined "rationality" with no
> political content. However, the version of "rationality" they preach is
> expressly politicised._

~~~
TeMPOraL
I've seen this type of writing before. It's a kind of twisted pseudo-criticism
you write against a group you dislike. You can compose stuff like this against
_any_ group. It sounds believable from the outside, especially if you start
sceptical to begin with. But take a closer look - it's actually full of ad-
hominems, cherry-picking facts and presenting them in worst light possible.
I've been a part of several groups that were targeted by such prose - first
the religious group I grew up in, that is a minority in my country; then the
school I went to. My university year used (a very lite version of) such
criticism against another, so I've seen it from the other side as well. Hell,
people write shit like this about HN!

It's hard to defend against such criticism. You'll get boggled down in
refuting specific accusations, but this is something you can never win. The
only winning move is to ignore it completely. Personally, I shun and shame
people who write such stuff, regardless of whether I agree or disagree with
their victims. Dishonesty is a poison that destroys societies.

TL;DR: this text is harmful, malicious bullshit. If it at least offended
people _with style_ , there would be something to save it.

~~~
RodericDay
I know you're a huge advocate for Lesswrong, but not "everybody" or "anyone"
has quotes ripe for picking like Yudkowsky. Stephen Bond is not just throwing
some opinion out there, he's backing it up with first-hand sources:

Yudkowsky on his simplified views of why race gets brought up:

> "Race adds extra controversy to everything; in that sense, it's obvious what
> difference skin colour makes politically".

> "Group injustice has no existence apart from injustice to individuals. It's
> individuals who have brains to experience suffering. It's individuals who
> deserve, and often don't get, a fair chance at life. [...] Skin colour has
> nothing to do with it, nothing at all."

Yudkowsky on our current societal structure, adulating the people who give him
funding:

> One of the major surprises I received when I moved out of childhood into the
> real world, was the degree to which the world is stratified by genuine
> competence.

Yudkowsky writing short stories about a society where rape is legal, leaving
himself ample room for plausible deniability, but putting it up "for debate":

>> "No, us. The ones who remembered the ancient world. Back then we still had
our hands on a large share of the capital and tremendous influence in the
grant committees. When our children legalized rape, we thought that the Future
had gone wrong."

>> Akon's mouth hung open. "You were that prude?"

([https://web.archive.org/web/20131206200429/http://lesswrong....](https://web.archive.org/web/20131206200429/http://lesswrong.com/lw/y8/interlude_with_the_confessor_48/))

I think some well-meaning LessWrongers get caught in the crossfire, but I
think the essay makes a very well grounded case for the blindspots
"rationalists" have towards politics that suit the identity of people like
Yudkowski.

~~~
TeMPOraL
I'm not _that_ huge advocate of LW. I used to frequent the site, I read the
Sequences and generally liked what I saw.

RE parts you quoted. Of course they look bad, because they've been ripped out
from context.

Race:

[http://lesswrong.com/lw/kk/why_are_individual_iq_differences...](http://lesswrong.com/lw/kk/why_are_individual_iq_differences_ok/)

This is an article asking, to quote: "But why is it that the rest of the world
seems to think that individual genetic differences are okay, whereas racial
genetic differences in intelligence are not?". Yudkowsky seems to argue that
making big controversies around whether there are, or are not, differences
between "races" is missing the point; it's just one of many variables and we
should focus on fixing intelligence disparities for everyone.

Society:

[http://lesswrong.com/lw/ub/competent_elites/](http://lesswrong.com/lw/ub/competent_elites/)

This blogpost is marked as controversial from the get-go. It covers a quite
interesting theory IMO - that the very common meme, which says that elites are
stupid and evil, is in fact wrong. Eliezer argues towards a more socially
uncomfortable opinion - that elites are, in fact, smarter and better at
organizing things. Given that this is a belief most people are heavily biased
against, it actually may be the "thing you can't say", per PG's essay at
[http://www.paulgraham.com/say.html](http://www.paulgraham.com/say.html).

Story:

Geez. This is a sci-fi story. Moreover, it's _explicitly designed_ to fuck
with reader's moral intuitions. That's its _entire point_. Personally, I find
it fun and insightful, but it is _heavy_. You can read the whole work here:

[http://lesswrong.com/lw/y4/three_worlds_collide_08/](http://lesswrong.com/lw/y4/three_worlds_collide_08/)

\--

And to be clear. I'm not idolizing Eliezer. He's just a man who thought a lot
about some stuff, and wanted to share it. He sometimes gets it wrong (and, as
opposed to many, has at least the courage to admit he was wrong). But I
absolutely hate this kind of bullshit pseudocriticism when it's directed
against _anyone_ \- be it my friend or enemy, be it someone I admire or
despise of. Eliezer is not beyond criticism, but we can do better than that.

~~~
RodericDay
I guess I just disagree with you that they're taken out of context?

1\. Bond posits Yudkowski thinks that racism is mostly due to genetic
difference, and not about the deliberate, mostly political disenfranchisement
of minorities.

You say this is a wrong because his appraisal of the situation as being caused
by genetic disparities is benevolent, and that he wants to work to "fix" it.

These aren't in contradiction- to say that it's unfortunate that society is
racialized, but that it's due to traits rather than politics, is better than
being wantonly racist, but still a well-known form of fallacious racism. Some
would say this latter one is actually worse in terms of perpetuating the
situation.

2\. Of course it's "controversial from the get go". He looks at the
disproportionate representation of certain people in ie: tech, and concludes
that it's because they're "more competent". Nothing here seems to be a
counter, you're just basically saying "it's politically incorrect so it's
probably right".

3\. Clearly it's just a story. This point eludes exactly nobody. The whole
point is that these kind of people find these questions ("is rape really
bad?") really intriguing rather than obvious. It makes you wonder about the
power of Bayesian reasoning- the exact point of the essay.

I think you're too uncharitable to critical writers like Bond (it took me a
while to acquire a taste for this vicious kind of writing), underestimating
their and their audiences' understanding. As a result, you think this context
adds way more than it does.

~~~
edanm
"1\. Bond posits Yudkowski thinks that racism is mostly due to genetic
difference, and not about the deliberate, mostly political disenfranchisement
of minorities."

You don't need to take the author's word for it. Look at the article itself.

The article is _not_ about the question of whether race affects intelligence.
It's saying that that question is much less important than the fact that
individuals have different IQ levels _regardless_ of race. At least in the
context of this article, which is asking whether "God is fair".

To make it crystal clear - Yudkowsky is saying:

1\. Forget race. There are clear, obvious, and gigantic _genetic_ differences
in individuals which cause differences in intelligence.

2\. This is "unjust".

3\. We should be upset about this, and try to fix it.

That's all he's saying in that article - it is not at all racist.

If you think otherwise, please - quote the relevant part of the article and
explain yourself.

~~~
RodericDay
I'm not gonna do a good job at explaining this, because it's far from my
subject area, but the problem is that your demand for "the relevant part" asks
for blunt evidence of a subtle phenomenon.

When we talk about politics, context matters. Someone like Yudkowsky doesn't
believe stupidly racist things, like a KKK member or turn-of-century
politician, or even modern anti-immigration people. Bond's targeting something
much more subtle.

The point is that here you have a man who naively keeps trying to push the
dialogue "beyond race" ("forget race"), in a forum where if you scroll down to
the comment section, you'll see Jeff H. with 5 upvotes defending Watson's
racist remarks, with Epiphany at 0 upvotes talking about the cultural reasons
why IQ tests fail.

It's about the framework, and what it allows, and about what allows the people
championing it to be naive or indifferent about what it allows. Someone
discussing coldly and clinically the pros and cons of rape isn't a rapist, but
there's something else about someone who can have discussion coldly and
clinically. Some people take pride in their level-headedness about tough
topics, others would take it as a signal of their lack of empathy with the
victims, and the signal this sends to people who do feel passionately about
it.

And so Yudkowsky will discuss race in this goofy aloof kind of way- "maybe
black people are intellectually inferior, _let 's talk about it_, does it even
matter in the end?", and some people will believe that this is the right kind
of coolness to produce neat solutions, and others will believe it robs the
steam off of the emotional connection that would engage people in political
action for change.

You have to suss this kind of thing out, and if you plain don't want to
believe me that there's something enabling towards racism and sexism and other
various supremacist ideologies in the LessWrong ecosystem, you don't really
have to.

~~~
yummyfajitas
_You have to suss this kind of thing out, and if you plain don 't want to
believe me that there's something enabling towards racism and sexism and other
various supremacist ideologies in the LessWrong ecosystem, you don't really
have to._

There is definitely something enabling about it. A lot of modern politics
wants you to NOT believe black people are stupid criminals.

Yudkowsky would almost certainly endorse "if black people are stupid criminals
I want to believe black people are stupid criminals, if black people are not
stupid criminals I want to believe they are not stupid criminals". (This is
the litany of tarski, which he endorses, applied to a specific case.) One
could certainly view this as "enabling" supremacist views under the
circumstances that reality supports them.

Is a fair summary of your critique that Yudkowsky is rationally and
unemotionally reasoning about problems which are normally addressed via
appeals to emotion, and this subverts emotional appeals to the masses to take
certain actions?

I've read your post several times, and this is the most charitable takeaway I
can come up with. But this sounds insane so I feel like I must be
misunderstanding something.

~~~
RodericDay
Someone who feels injustice, but hasn't had the time or resources to codify it
into a calm rational treatise is said to be speaking from emotion. Someone who
merely experiences base greed, but is able to justify it to themselves as
righteous and deliberate and socially beneficial with a bunch of babble, is
considered rational.

And so, the idea that the rigid set of discursive boundaries that
LessWrongians impose upon themselves may favor a political outcome (the status
quo) seems ridiculous to you, because you use "rational" as a compliment and
"emotional" as an insult.

~~~
RodericDay
I can't seem to post a reply, so I'll wrap it up here.

I'm criticizing an ecosystem. Yudkowsky-types noodle with weird hypotheticals,
others with elitist views get validation. Fantasizing of fixing our current
issues with futuristic tech, using it as a yard-stick to criticize ie: a
collective black identity from forming a political block, is not explicitly
pro-status quo but ends up being so in practice.

~~~
TeMPOraL
So the only criticism here is that views of various people on LW forum do not
conform to the mainstream social justice outrage narrative, where everything
needs to be politicized and "status quo" must be fought?

That's sort of the entire point of "Politics is the Mind-Killer" statement, a
point which Bond also missed - LW community wants to focus on effective ways
to deal with actual problems, as opposed to doing politics. They're not
criticizing "a collective black identity", speaking against them "forming a
political block". They're not talking about it. It's besides the point of that
article and mostly besides the point of the entire community, which tends to
focus on how to make things better for _everyone_.

Frankly, I find it funny to see accusations of racism aimed at people who are
known to seriously, and not just as a figure of speech, consider humanity as
one great family who are in it together. But then again, everyone of us who is
not outraged is secretly a racist and supports the enemy.

Also consider the core statement of the Mind-Killer article:

"Politics is an extension of war by other means. Arguments are soldiers. Once
you know which side you're on, you must support all arguments of that side,
and attack all arguments that appear to favor the enemy side; otherwise it's
like stabbing your soldiers in the back—providing aid and comfort to the
enemy. People who would be level-headed about evenhandedly weighing all sides
of an issue in their professional life as scientists, can suddenly turn into
slogan-chanting zombies when there's a Blue or Green position on an issue."

It's perfectly OK to avoid that kind of political discussions. I'd say it's
weird to actually partake in them.

~~~
RodericDay
I'd love to reply to you all (ie: siblings) but this discussion is just
sprawling (not a fan of "tree-and-leaf" fanning arguments, I much prefer
linear forums), and I just can't put in the time.

FWIW, you strike me as a good person, as do many LWers. I wish I could
communicate to you the nuance of my issues with statements like "humanity as
one great family", but I'm a newbie at the study of ideology myself, so I
wouldn't do a good job.

À la prochaine!

------
SFjulie1
[http://elis.dvo.ru/~lab_11/bib/hershkowitz-
nadal.pdf](http://elis.dvo.ru/~lab_11/bib/hershkowitz-nadal.pdf) I found a
thesis on the topic.

Seems the upper bound of estimation when using bayesian probability for
estimating parameters with data gets overestimated when the size of the data
grows.

It does not makes sense to me, can someone explain this to me as if I was an
idiot?

PS one of the searcher in his lab used to say: if you try to find to hard a
physical law, you might eventually find it.

(quote from the thesis below)

Most of the results concerning the behavior of the mutual information,
observed for this particular family, are ‘‘universal,’’ in that they will be
qualitatively the same for any problem that can be formulated as either a
parameter estimation task or a neural coding task. .... Besides the asymptotic
regime p large, N arbitrary, we have also considered the case of large N at
any given value of a5p/N. In this regime we have both replica calculations and
exact bounds, in particular, an upper bound for the class information and
explicit upper and lower bounds for the mutual information obtained with the
techniques of [7]. The results suggest that the replica symmetry ansatz give
the correct solution. The lower bound is then quite good whereas the upper
bound overestimate the mutual information by a factor that keeps increasing
with the data size.

------
such_a_casual
So let me get this straight, statistics can be misused? I almost stopped
reading as soon as I saw the image from the big bang theory. (That show
presents nerds the way other people want to see them. Not the way nerds
actually are.) It appears that the author of this article is just a
journalist:

[http://www.johnhorgan.org/](http://www.johnhorgan.org/)

I don't see anything in there about him ever being a scientist, a
statistician, or anyone who would actually use this theorem. In fact, he even
went to school for journalism.

I really don't understand where this author is coming from when he says things
like, "I conveniently decided that Bayes was a passing fad." Why should we
care about his opinion on the matter? Is he reporting to us what Bay Theorem
is and its significance, or is he giving us his uniformed opinion on the
matter?

