Are p-values an objective measure? Bayesian Statistics are not as objective as Frequentist statistics for the simple reason that they need more assumptions, that is, a prior. This is why to even talk about Objective Bayesian Statistics is an oxymoron and yet seems to be the most popular Bayesian school out there. But anyhow, how about p-values then, can they be subjective? Is there such thing as Objectivity in statistics?
For a time I thought p-values were an objective measure but then a couple of blows put to rest my dream on having an objective procedure to deal with uncertainty. This is the story of the Subjectivity one-two combo that knocked out flat my Objectivity dreams…
I wanted to be a scientist ever since I read a comic where scientist Bruce Banner turns into The Incredible Hulk. I did not know what a scientist was or what kind of scientist I wanted to be, yet, I thought that the scientific career sounded like lots of fun if it can turn you up into a huge green monster.
I guess that for children of my age back in those days Marvel comics were the closest thing to Harry Potter for children nowadays (Let’s get ready for a massive turn up of sorcerers and witches in the coming years by the way).
So there I am after a few years since I read the comic and for reasons beyond this post but that can easily be described like a billiard break(ing bad) I end up with a couple of degrees; Computer Science and Statistics, and a Master in Operation Research (more of the same stuff).
Yet, I never considered myself (nor did anyone else) as a scientist or a researcher since, well… when programming I don’t feel much like doing science no matter how big the word science is in my Computer Science degree, and the degree in Statistics does not make me feel like an scientist either nor the Master like a researcher.
There was a time when some of the work I was doing could be named as Data Mining and this seemed to push me further and further away from my childhood dream since now I could be considered a Miner instead of a Scientist… Don’t get me wrong, Miner is no a bad profession if you want to start a revolution but all the glamour of the word science was gone and so my dream to be a scientist darkened with soot.
But then… Data Sciencecame along, wait, what? That’s right! Data Science is what you get when we consider every procedure that brings us knowledge stripped of any field background, the intersection of every science known to men, the Mixed Martial Arts of knowledge. Data Science… if you think about it, can there be any other kind of science?
Not surprisingly when meeting with fellow Data Scientists we’ll find out they come from all sort of venues and that data science teams are usually Macedonian salads of scientific backgrounds which include Physicists (of course) and Musicians (you heard me).
So turns out that after so many years my dream came true and I became exactly what I wished back in those days: a Scientist with no particular field… but data, and since everything is data, now everything is my field. So I can finally proudly say “Scientist at last, Scientist at last, thanks God almighty I’m a Scientist at last!”.
And now if you excuse me I have to go back to my scientific project codenamed Green. Thank you very much.
I find the use of statistics in the justice system a thrilling subject, specially so when you find out that some persons like Lucia de Berk have been handed life sentences based solely on flaw statistics coming from experts like Mr. Henk Elffers. So I’ll talk in this post about what he did wrong and how to avoid this kind of huge boo-boo in our statistical lives.
The use of statistics in the justice system has actually a long history, the amazing mathematician / engineer / physicist / philosopher of science Henri Poincaré already had to correct the misuse of statistics in the infamous Dreyfus trial.
But it was in the Lucia de Berk trial where combining p-values wrongly handed her a life sentence. I won’t go into the details of the trial, for that there are many other places like Mr. Richard D. Gillweb page account of the trial and a video worth to have a look to. Instead I will focus on how to appropriately deal with a bunch of p-values to make sense of our data. Continue reading →
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.
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 →
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?
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 →
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.
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 →
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.
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:
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.