On the certainty that God exists and why Bayesians should go π

Up to this day I defined my theological position as Agnostic, which is not saying much given the different interpretations and philosophical flavors we have to position ourselves when it comes to God. This is why sometimes I instead simply reply to The Question with something like “Both alternatives are equally crazy, so I don’t know. But, can we use statistics to better describe our position in these kind of philosophical matters, or even dictate how should we live our lives? Yes, we can.

WARNING: Beware agnostics!!! I will show mathematical arguments that might turn you into a full blown Believer or a hardcore Atheist… So if you keep reading don’t say I did not warn you.

Marx
These are my principles…    But if you don’t like them I have others.

If we envision probability as a measure linked to a random process then questions like “What is the probability that God exists?” imply a sort of Supra-God that creates universes with Gods with a frequency p. But then some might argue that this Supra-God is actually God so, at the end, these kind of philosophical questions make no statistical sense for such frequentist interpretation of probability.

Then we have those that interpret probability as a degree of belief on matters subject to uncertainty, this interpretation is the one hold by Bayesian Statistics.

So if I wear a Bayesian hat and I am asked The Question then, instead replying “I don’t know” to describe my ignorance I should reply with “50%” or “p=1/2“. This is so because when Bayesians (The Objective Kind) have no information on a problem they use a plethora of principles in a Groucho style fashion to figure out a prior distribution to kick off Bayes’ Theorem machinery.

But there are an infinite number of prior distributions with an expected value of 1/2 so, which among this infinite number describe better my agnosticism? Is there such thing as a unique agnostic prior to rule them all? Well, it seems this Holy Grail does not exist since we can read in highly commendable Bayesian books like Bernardo & Smith thing like:

In general we feel that it is sensible to choose a non-informative prior which expresses ignorance relative to information which can be supplied by a particular experiment. If the experiment is changed, then the expression of relative ignorance can be expected to change correspondingly. (Box and Tiao, 1973 p.46).

Wait, what? We change the experiment and our prior ignorance changes too? In fact not all Bayesians agree with their existence; (Howson 2002; O’Hagan 2006; Press 2003) they regard any Bayesian Objective “non-informative” priors simply as well formed beliefs… So I’ll pick on the Subjective kind interpretation and in this post I am going to well form my belief in God.

Plus, in the process of cooking my Agnostic prior I’ll discuss why Bayesians should measure their beliefs from 0 to π instead from 0 to 1; This later measure is too frequentist for them and π makes more mathematical sense since trigonometrical functions are going to naturally pop up everywhere in our prior belief endeavor. Continue reading

Are human minds statistical machines?

Human minds are the mother of all interesting things since anything that we might consider interesting is so because our minds make us believe so. Seems then reasonable that all kind of philosophical issues and scientific problems cannot be properly addressed unless we correctly understand how our minds work, but what we know about how they work?

sexynun
            I’m a sinner, I’m a saint…

Cognitive Science offers many theories on how any mind might work, but when it comes to our minds there seem to be evidences put forward by psychologists that, whatever the way they work,  human minds do not abide to the laws of probabilities.

Several attempts have been made to explain these results, and one of the latest comes from the hand of Quantum Mechanics… No kidding.

So when I saw this valiant attempt from theoretical physicists to explain how the human mind works by using their all mighty and powerful Quantum Hammer, I thought it was a good moment to explain an alternative solution that I myself worked out long, long ago, after being exposed to this problem by philosopher Paul Thagard in his excellent book MIND.

Also, Sister Hot is my assistant and I need her to prove my point which is that our minds might abide to probability laws more than we think after all. If you want to know how she is going to assist me you need to keep reading; probability can be sexy 😉 Continue reading

15 to 42 percent of medical research are false positives (Yet Another Calculation)

A while ago I found a very interesting paper from Leah R. Jager and Jeffrey T. Leek  via a post in the Simply Statistics blog arguing that most published medical research is true with a rate of false positives among reported results of 14% ± 1%.  Their paper came as a response to an essay from John P. A. Ioannidis and several others authors claiming that most published research findings are false.

After dealing with some criticisms Mr. Leek made a good point in his post:

“I also hope that by introducing a new estimator of the science-wise fdr we inspire more methodological development and that philosophical criticisms won’t prevent people from looking at the data in new ways.”

And thus, following this advice, I didn’t let criticisms prevent me from looking at the data in a new way. So for this problem I have devised a probability distribution for p-values to then fit the data via MLE and infer from there the rate of false positives.

pvalues PDF CDFSo this is my take; 15.33% rate of false positive with a worse case scenario of 41.75% depending on how mischievous researchers are but, in any case, and contrary to what others authors claim, most medical research seems to be true.

Continue reading

Priesthood, Pedophilia & Homosexuality

  • At most 22 percent of catholic priests in the USA are homosexuals.
  • Homosexual men in the USA, as a group, molest children at a rate at least 15 times higher than heterosexual men.

One  asteroid rubs Earth, a meteorite crashes on Russia and, a few days later, Pope Benedict XVI took the cosmic message and resigned. Nonetheless many people question the true reason for his resignation alleging that it has nothing to do with fatigue but rather with homosexuality networks within the Church (CNN guest claiming a 50% of homosexuals among priests) and unresolved pedophilia scandals. So I took a look at this percentage with our best friend when it comes to politically incorrect statistics; Bayes’ Theorem, and I got the results displayed above.

pope_kiss

I know, I know, the numbers are pretty crazy, but they are based on data fetched from official sources and, before going into the details, let me play sociologist. Although homosexuals, as a group, molest children at higher rates than heterosexuals it is very important to realize that this does not necessarily mean homosexuals are more prone towards this behavior, assuming this might constitute an ecological fallacy, in this case it makes more sense that this outcome obeys to the fact that young boys are way less protected by parents than young girls and predators take advantage of this.

The Calculations

To estimate the rate of homosexuals among catholic priests we will first estimate how much more likely are male homosexuals to engage in pederasty compared to male heterosexuals, then we will use this result join with the by gender percentage of children abused by catholic priests (81 percent of the victims were males in the USA) to calculate the final figure.

I'll protect you Continue reading

There is no Theorem but Bayes’ and Laplace is His Prophet

As a student I thought that there was no fanaticism involved in the world of Mathematics. Sure in Science you always have crackpots and competing crazy theories around but I thought such things could not possibly happen with something so aseptic and precise as math. So you can imagine my surprise when I found out about this curious religious group in the field of Statistics who call themselves Bayesians.

there is no theorem but bayes

Bayesianism is a religion which demands its followers to use Bayes’ Theorem for any reasoning involving uncertainty regardless whether the reasoning is deductive or inductive in nature, though they also advice to consider more everyday life questions like Continue reading

Media on “Video Games & Violence”

video.games.study
                                           Click to watch video

This is the numerical result the researchers used to make their “ridiculous” assumptions in their paper:

The ANOVA procedure for repeated measurement designs yield significant results for the

  • dACC (Wilk’s Λ = 0.33, F = 4.59, p <.027, η2 = 0.67)
  • rACC (Wilk’s Λ= 0.19, F = 9.55, p <.003, η2 = 0.81)
  • amygdala (Wilk’s Λ = 0.28, F = 5.75, p<.014, η2 = 0.72)

Tests for linear trends were significant in the three ROIs:

  • dACC: F = 8.28, p < .014;
  • rACC: F = 17.97, p < .001;
  • amygdala: F = 30.02, p < .001

but not for higher order trends

The other study they mention does not involve any experiment and is merely a review of other studies.

Whether the significance in the study is significant for science is up to the researchers but, yeah, we can make assumptions with a sample size of just 13. Interestingly, others would regard “too many” people in a sample size as a manipulation to achieve significance. So I guess that when we don’t like something we can always find reasons to complain about it.

Climategate (3/3): Fear mongering

The last post in this Climategate series is dedicated to the climate of fear mongering we all see every now and then in the media claiming extreme weather patterns linked to global warming in an end-of-the-world tone. I will offer some insights and calculations to show that “extremist” might be wrong.

So let us begin with the Australia Climate Change? New Colors Added To Forecast Maps news that spread like… well.. wildfire not just in Australia but through all over the world.

o-AUSTRALIA-CLIMATE-CHANGE-570

It seems that poor climatologists in Australia had no choice but to reuse the purple color already in use for the negative range (-25, -18) ºC for the positive range (50, 54) ºC. What could possibly have done these people but to mix cold and hot weather colors!? well, here’s an idea:

Not Scary Colors for Australian Temperatures

There it goes a present for climatologists in Australia; 121 not scary-oh-my-gaw-how-hot-it-is different colors for the range (-60,60) ºC, and just in case you need more I have a few spare millions. You’re welcome.

Okay, okay, to be fair Continue reading