R corset: Bringing Math models back in shape

So your perfect ideal mathematical model returns values that are impossible; probabilities bigger than one or smaller than zero, negative stock market values, et cetera, and now you feel like quoting George Box… again.

corset-math

Sometimes the mathematical model embeds a solution to keep things real like, for example, logistic regressions. However, very often many popular models like ARIMA offer no possibility to bound its results within business or scientific constrains, and then what? These are a few common options:

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Objectivity is dead, long live Objectivity!

Are p-values an objective measure? Bayesian Statistics is not as objective as Frequentist statistics is 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? death_of_the_justice_by_quadraro-d6sapo4

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 down flat my Objectivity dreams…

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How to combine p-values to avoid a sentence of life in prison

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.

Lucia reads post, photo by Carole Edrich
Lucia reads post, photo by Carole Edrich (Photo credit: Wikipedia)

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. Gill web 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