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 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 →
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.
In the previous post I showed how James Hansen at GISS NASA clearly over estimated global warming in the late 80’s due to the modeling choices he made. To make a point on how influential the choice of a model is, in this post I will make modeling choices that will allow us to claim that global warming can be explained as a fluke in a random process.
I like to explain the relationship between data and models saying that data is the shadow reality casts, and models are what we believe is casting the shadow. So once we have a model we can use it to cast shadows (make predictions) like the one James Hansen did and could be read in 1986 newspapers:
Hansen predicted global temperatures should be nearly 2 degrees higher in 20 year. “Which is about the warmest the earth has been in the las 100,000 years.”
Interestingly James Hansen downgraded his prediction in a 1988 paper from the nearly two degrees higher to a one degree higher. Though to be fair I would not be surprised if media misquoted him; I might not trust scientists but I absolutely distrust media.
Anyhow, let’s now compare NASA’s prediction in this 1988 paper (in red) to what actually happened years later (in blue):
Deception is all around us, in every little parcel of our life; from our personal Bart Simpson’s “It wasn’t me” to our local TV news host selling us the latest “You’re not going to believe this” but we eventually do. One might just wish there would exist communities out there with higher standards like, for example, Christians priests but, nope, they cover up pedophile networks in order to preserve The Church’s “good” name. But how about the atheist priests a.k.a scientists? How about their standards?
Well, unfortunately the community of scientists might have more to do with priesthood than one might expect or desire, and a nice example of this would be the Climategate (or the Climatic Research Unit email controversy, as some people had the kindness to rename the Climategate article in the Wikipedia following Fox News’ motto “fair and balanced” )
So in this post I am going to replicate earlier studies on global warming to uncover how over pessimistic were the maths models of the past, but I will also talk about human weakness, and scientists are human… for now.