A few years ago, I was asked by Isabelle Drouet to contribute a chapter to a multi-disciplinary book on the Bayesian paradigm, book that is now soon to appear. In French. It has this rather ugly title of Bayesianism today. Not that I had hear of Bayesianism or bayésianime previously. There are chapters on the Bayesian notion(s) of probability, game theory, statistics, on applications, and on the (potentially) Bayesian structure of human intelligence. Most of it is thus outside statistics, but I will certainly read through it when I receive my copy.
Archive for Philosophy of Science
Le bayésianisme aujourd’hui
Posted in Books, Statistics with tags Bayesianism, book chapter, epistemology, foundations, France, French book, game theory, Philosophy of Science on September 19, 2016 by xi'anon de Finetti’s instrumentalist philosophy of probability
Posted in Books, Statistics, Travel, University life with tags Bayesian foundations, behaviorism, Bruno de Finetti, Paris, philosophy, Philosophy of Science, realism, subjective probability, subjective versus objective Bayes on January 5, 2016 by xi'an
On Wednesday January 6, there is a conference in Paris [10:30, IHPST, 13, rue du Four, Paris 6] by Joseph Berkovitz (University of Toronto) on the philosophy of probability of Bruno de Finetti. Too bad this is during MCMSkv!
De Finetti is one of the founding fathers of the modern theory of subjective probability, where probabilities are coherent degrees of belief. De Finetti held that probabilities are inherently subjective and he argued that none of the objective interpretations of probability makes sense. While his theory has been influential in science and philosophy, it has encountered various objections. In particular, it has been argued that de Finetti’s concept of probability is too permissive, licensing degrees of belief that we would normally call imprudent. Further, de Finetti is commonly conceived as giving an operational, behaviorist definition of degrees of belief and accordingly of probability. Thus, the theory is said to inherit the difficulties embodied in operationalism and behaviorism. We argue that these and some other objections to de Finetti’s theory are unfounded as they overlook various central aspects of de Finetti’s philosophy of probability. We then propose a new interpretation of de Finetti’s theory that highlights these central aspects and explains how they are an integral part of de Finetti’s instrumentalist philosophy of probability. Building on this interpretation of de Finetti’s theory, we draw some lessons for the realist-instrumentalist controversy about the nature of science.
how to build trust in computer simulations: Towards a general epistemology of validation
Posted in Books, pictures, Statistics, Travel, University life with tags epistemology, Germany, Hannover, Philosophy of Science, simulation model on July 8, 2015 by xi'an
I have rarely attended a workshop with such a precise goal, but then I have neither ever attended a philosophy workshop… Tonight, I am flying to Han(n)over, Lower Saxony, for a workshop on the philosophical aspects of simulated models. I was quite surprised to get invited to this workshop, but found it quite a treat to attend a multi-disciplinary meeting about simulations and their connection with the real world! I am less certain I can contribute anything meaningful, but still look forward to it. And will report on the discussions, hopefully. Here is the general motivation of the workshop:
“In the last decades, our capacities to investigate complex systems of various scales have been greatly enhanced by the method of computer simulation. This progress is not without a price though: We can only trust the results of computer simulations if they have been properly validated, i.e., if they have been shown to be reliable. Despite its importance, validation is often still neglected in practice and only poorly understood from a theoretical perspective. The aim of this conference is to discuss methodological and philosophical problems of validation from a multidisciplinary perspective and to take first steps in developing a general framework for thinking about validation. Working scientists from various natural and social sciences and philosophers of science join forces to make progress in understanding the epistemology of validation.”
another view on Jeffreys-Lindley paradox
Posted in Books, Statistics, University life with tags Bayes factor, frequentist inference, Jeffreys-Lindley paradox, Philosophy of Science, Québec, Université Laval on January 15, 2015 by xi'an
I found another paper on the Jeffreys-Lindley paradox. Entitled “A Misleading Intuition and the Bayesian Blind Spot: Revisiting the Jeffreys-Lindley’s Paradox”. Written by Guillaume Rochefort-Maranda, from Université Laval, Québec.
This paper starts by assuming an unbiased estimator of the parameter of interest θ and under test for the null θ=θ0. (Which makes we wonder at the reason for imposing unbiasedness.) Another highly innovative (or puzzling) aspect is that the Lindley-Jeffreys paradox presented therein is described without any Bayesian input. The paper stands “within a frequentist (classical) framework”: it actually starts with a confidence-interval-on-θ-vs.-test argument to argue that, with a fixed coverage interval that excludes the null value θ0, the estimate of θ may converge to θ0 without ever accepting the null θ=θ0. That is, without the confidence interval ever containing θ0. (Although this is an event whose probability converges to zero.) Bayesian aspects come later in the paper, even though the application to a point null versus a point null test is of little interest since a Bayes factor is then a likelihood ratio.
As I explained several times, including in my Philosophy of Science paper, I see the Lindley-Jeffreys paradox as being primarily a Bayesiano-Bayesian issue. So just the opposite of the perspective taken by the paper. That frequentist solutions differ does not strike me as paradoxical. Now, the construction of a sequence of samples such that all partial samples in the sequence exclude the null θ=θ0 is not a likely event, so I do not see this as a paradox even or especially when putting on my frequentist glasses: if the null θ=θ0 is true, this cannot happen in a consistent manner, even though a single occurrence of a p-value less than .05 is highly likely within such a sequence.
Unsurprisingly, the paper relates to the three most recent papers published by Philosophy of Science, discussing first and foremost Spanos‘ view. When the current author introduces Mayo and Spanos’ severity, i.e. the probability to exceed the observed test statistic under the alternative, he does not define this test statistic d(X), which makes the whole notion incomprehensible to a reader not already familiar with it. (And even for one familiar with it…)
“Hence, the solution I propose (…) avoids one of [Freeman’s] major disadvantages. I suggest that we should decrease the size of tests to the extent where it makes practically no difference to the power of the test in order to improve the likelihood ratio of a significant result.” (p.11)
One interesting if again unsurprising point in the paper is that one reason for the paradox stands in keeping the significance level constant as the sample size increases. While it is possible to decrease the significance level and to increase the power simultaneously. However, the solution proposed above does not sound rigorous hence I fail to understand how low the significance has to be for the method to stop/work. I cannot fathom a corresponding algorithmic derivation of the author’s proposal.
“I argue against the intuitive idea that a significant result given by a very powerful test is less convincing than a significant result given by a less powerful test.”
The criticism on the “blind spot” of the Bayesian approach is supported by an example where the data is issued from a distribution other than either of the two tested distributions. It seems reasonable that the Bayesian answer fails to provide a proper answer in this case. Even though it illustrates the difficulty with the long-term impact of the prior(s) in the Bayes factor and (in my opinion) the need to move away from this solution within the Bayesian paradigm.
the god delusion [statistically speaking]
Posted in Books, Kids, pictures, Statistics, Travel, University life with tags atheism, Bangalore, India, Philosophy of religions, Philosophy of Science, Richard Dawkins on August 22, 2014 by xi'an
While in Bangalore, I spotted Richard Dawkins’ The God delusion in the [fantastic if chaotic] campus bookstore and bought the Indian edition for a nominal amount. I read most of it during my week in Boston. And finished by the lake in Maine. While I agree with most of the points made in Dawkins’ book about the irrationality of religions, and of their overall negative impact on human societies, I found the first part rather boring in that I see little appeal in dissecting so minutely the [infinitely many] incoherences of religious myths and beliefs, as this will likely miss the intended target [i.e., literal believers]. Similarly, the chapter on evolution versus intelligent design made valuable points, albeit I had already seen them before. Nothing wrong with repeating those, in particular that evolution has little to do with chance, but again unlikely to convince the [fundamentalist] masses. Overall, the book mostly focus on the Judeo-Christian-Muslim branch of religions, which may reflect on the author’s own culture and upbringing but also misses the recent attempts of Buddhism to incorporate science into their picture.
“A universe in which we are alone except for other slowly evolved intelligences is a very different universe from one with an original guiding agent whose intelligent design is responsible for its very existence.” (p.85)
What is most interesting in the book (for me) is when Dawkins tries to set the God hypothesis as a scientific hypothesis and to apply scientific methods to validate or invalidate this hypothesis. Even though there is no p-value or quantitative answer at the end. Despite the highly frequent use of “statistical” and “statistically improbable” in the corresponding chapter. What’s even more fascinating is Dawkins’ take at Bayesian arguments! Either because it is associated with a reverent or because it relies on subjective prior assessments, Bayesian statistics does not fit as a proper approach. Funny enough, Dawkins himself relies on subjective prior probabilities when discussing the likelihood of find a planet such as Earth. Now, into the details [with the Devil1] in a rather haphazard order or lack thereof: Continue reading
