**W**hen checking the Python t distribution random generator, np.random.standard_t(), I came upon this manual page, which actually does not explain how the random generator works but spends instead the whole page to recall Gosset’s *t* test, illustrating its use on an energy intake of 11 women, but ending up misleading the readers by interpreting a .009 one-sided p-value as meaning “the null hypothesis [on the hypothesised mean] has a probability of about 99% of being true”! Actually, Python’s standard deviation estimator x.std() further returns by default a non-standard standard deviation, dividing by n rather than n-1…

## Archive for Python

## a null hypothesis with a 99% probability to be true…

Posted in Books, R, Statistics, University life with tags cross validated, hypothesis testing, np.random.standard_t, null hypothesis, numpy, p-value, pseudo-random generator, Python, R, t distribution, W. Gosset, x.std on March 28, 2018 by xi'an## ABCπ

Posted in Books, pictures, Statistics, Travel, University life with tags ABC, ABCpy, Monty Python, Python, statistical software on May 17, 2017 by xi'an**R**itabrata Dutta, Marcel Schöengens, Jukka-Pekka Onnela, and Antonietta Mira recently put a new ABC software on-line, called ABCpy for ABC with Python. The software aims at an automated parallelisation of ABC runs, requiring only code to generate from the (generative) model and the choice of summary statistics and of associated distance. Alternatively an approximate likelihood (as in synthetic likelihood) can be used. The tolerance ε is chosen as a percentile of the prior predictive distribution on the distance. The versions of ABC found in ABCpy are

- Population Monte Carlo for ABC (PMCABC);
- sequential Monte Carlo ABC (ABC-SMC);
- replenishment Sequential Monte Carlo ABC (RSMC-ABC);
- adaptive Population Monte Carlo ABC (APMCABC);
- ABC with subset simulation (ABCsubsim); and
- simulated annealing ABC (SABC)

Anto mentioned ABCpy to me while in Harvard last week and I have not tested the program (my only brush with Python being the occasional call to latex2wp for SeriesB’log). And obviously, writing a blog about Monte (Carlo and) Python makes a link to the Monty Pythons irresistible:

## Think Bayes: Bayesian Statistics Made Simple

Posted in Books, Kids, R, Statistics, University life with tags ABC, Bayesian Analysis, book review, cross validated, Green Tea Press, MCMC, Python, The Bayesian Choice, Think Bayes on October 27, 2015 by xi'an**B**y some piece of luck, I came upon the book *Think Bayes: Bayesian Statistics Made Simple*, written by Allen B. Downey and published by Green Tea Press [which I could relate to No Starch Press, focussing on coffee!, which published *Statistics Done Wrong* that I reviewed a while ago] which usually publishes programming books with fun covers. The book is available on-line for free in pdf and html formats, and I went through it during a particularly exciting administrative meeting…

“Most books on Bayesian statistics use mathematical notation and present ideas in terms of mathematical concepts like calculus. This book uses Python code instead of math, and discrete approximations instead of continuousmathematics. As a result, what would be an integral in a math book becomes a summation, and most operations on probability distributions are simple loops.”

The book is most appropriately published in this collection as most of it concentrates on Python programming, with hardly any maths formula. In some sense similar to Jim Albert’s R book. Obviously, coming from maths, and having never programmed in Python, I find the approach puzzling, But just as obviously, I am aware—both from the comments on my books and from my experience on **X** validated—that a large group (majority?) of newcomers to the Bayesian realm find the mathematical approach to the topic a major hindrance. Hence I am quite open to this editorial choice as it is bound to include more people to think Bayes, or to think they can think Bayes.

“…in fewer than 200 pages we have made it from the basics of probability to the research frontier. I’m very happy about that.”

The choice made of operating almost exclusively through motivating examples is rather traditional in US textbooks. See e.g. Albert’s book. While it goes against my French inclination to start from theory and concepts and end up with illustrations, I can see how it operates in a programming book. But as always I fear it makes generalisations uncertain and understanding more shaky… The examples are per force simple and far from realistic statistics issues. Hence illustrates more the use of Bayesian thinking for decision making than for data analysis. To wit, those examples are about the Monty Hall problem and other TV games, some urn, dice, and coin models, blood testing, sport predictions, subway waiting times, height variability between men and women, SAT scores, cancer causality, a Geiger counter hierarchical model inspired by Jaynes, …, the exception being the final Belly Button Biodiversity dataset in the final chapter, dealing with the (exciting) unseen species problem in an equally exciting way. This may explain why the book does not cover MCMC algorithms. And why ABC is covered through a rather artificial normal example. Which also hides some of the maths computations under the carpet.

“The underlying idea of ABC is that two datasets are alike if they yield the same summary statistics. But in some cases, like the example in this chapter, it is not obvious which summary statistics to choose.¨

In conclusion, this is a very original introduction to Bayesian analysis, which I welcome for the reasons above. Of course, it is *only* an introduction, which should be followed by a deeper entry into the topic, and with [more] maths. In order to handle more realistic models and datasets.

## ABC and cosmology

Posted in Books, pictures, Statistics, University life with tags ABC, ABC-PMC, abcpmc, astronomy, astrostatistics, cosmoabc, cosmology, likelihood-free methods, Mahalanobis distance, Python, semi-automatic ABC on May 4, 2015 by xi'an**T**wo papers appeared on arXiv in the past two days with the similar theme of applying ABC-PMC [one version of which we developed with Mark Beaumont, Jean-Marie Cornuet, and Jean-Michel Marin in 2009] to cosmological problems. (As a further coincidence, I had just started refereeing yet another paper on ABC-PMC in another astronomy problem!) The first paper cosmoabc: Likelihood-free inference via Population Monte Carlo Approximate Bayesian Computation by Ishida et al. [“et al” including Ewan Cameron] proposes a Python ABC-PMC sampler with applications to galaxy clusters catalogues. The paper is primarily a description of the cosmoabc package, including code snapshots. Earlier occurrences of ABC in cosmology are found for instance in this earlier workshop, as well as in Cameron and Pettitt earlier paper. The package offers a way to evaluate the impact of a specific distance, with a 2D-graph demonstrating that the minimum [if not the range] of the simulated distances increases with the parameters getting away from the best parameter values.

“We emphasis[sic]that the choice of the distance function is a crucial step in the design of the ABC algorithm and the reader must check its properties carefully before any ABC implementation is attempted.”E.E.O. Ishida et al.

The second [by one day] paper Approximate Bayesian computation for forward modelling in cosmology by Akeret et al. also proposes a Python ABC-PMC sampler, abcpmc. With fairly similar explanations: maybe both samplers should be compared on a reference dataset. While I first thought the description of the algorithm was rather close to our version, including the choice of the empirical covariance matrix with the factor 2, it appears it is adapted from a tutorial in the Journal of Mathematical Psychology by Turner and van Zandt. One out of many tutorials and surveys on the ABC method, of which I was unaware, but which summarises the pre-2012 developments rather nicely. Except for missing Paul Fearnhead’s and Dennis Prangle’s semi-automatic Read Paper. In the abcpmc paper, the update of the covariance matrix is the one proposed by Sarah Filippi and co-authors, which includes an extra bias term for faraway particles.

“For complex data, it can be difficult or computationally expensive to calculate the distance ρ(x; y) using all the information available in x and y.”Akeret et al.

In both papers, the role of the distance is stressed as being quite important. However, the cosmoabc paper uses an L1 distance [see (2) therein] in a toy example without normalising between mean and variance, while the abcpmc paper suggests using a Mahalanobis distance that turns the d-dimensional problem into a comparison of one-dimensional projections.

## data scientist position

Posted in R, Statistics, University life with tags ABC, advanced Monte Carlo methods, École Polytechnique, CREST, Economie et gestion des nouveles données, ENSAE, job offer, machine learning, Matlab, Python, Université Paris Dauphine on April 8, 2014 by xi'an**O**ur newly created Chaire “Economie et gestion des nouvelles données” in Paris-Dauphine, ENS Ulm, École Polytechnique and ENSAE is recruiting a data scientist starting as early as May 1, the call remaining open till the position is filled. The location is in one of the above labs in Paris, the duration for at least one year, salary is varying, based on the applicant’s profile, and the contacts are Stephane Gaiffas (stephane.gaiffas AT cmap DOT polytechnique.fr), Robin Ryder (ryder AT ceremade DOT dauphine.fr). and Gabriel Peyré (peyre AT ceremade DOT dauphine.fr). Here are more details:

**Job description**

The chaire “Economie et gestion des nouvelles données” is recruiting a talented young engineer specialized in large scale computing and data processing. The targeted applications include machine learning, imaging sciences and finance. This is a unique opportunity to join a newly created research group between the best Parisian labs in applied mathematics and computer science (ParisDauphine, ENS Ulm, Ecole Polytechnique and ENSAE) working hand in hand with major industrial companies (Havas, BNP Paribas, Warner Bros.). The proposed position consists in helping researchers of the group to develop and implement large scale data processing methods, and applying these methods on real life problems in collaboration with the industrial partners.

A non exhaustive list of methods that are currently investigated by researchers of the group, and that will play a key role in the computational framework developed by the recruited engineer, includes :

● Large scale non smooth optimization methods (proximal schemes, interior points, optimization on manifolds).

● Machine learning problems (kernelized methods, Lasso, collaborative filtering, deep learning, learning for graphs, learning for timedependent systems), with a particular focus on large scale problems and stochastic methods.

● Imaging problems (compressed sensing, superresolution).

● Approximate Bayesian Computation (ABC) methods.

● Particle and Sequential Monte Carlo methods

Candidate profileThe candidate should have a very good background in computer science with various programming environments (e.g. Matlab, Python, C++) and knowledge of high performance computing methods (e.g. GPU, parallelization, cloud computing). He/she should adhere to the open source philosophy and possibly be able to interact with the relevant communities (e.g. scikitlearn initiative). Typical curriculum includes engineering school or Master studies in computer science / applied maths / physics, and possibly a PhD (not required).

Working environmentThe recruited engineer will work within one of the labs of the chaire. He/she will benefit from a very stimulating working environment and all required computing resources. He/she will work in close interaction with the 4 research labs of the chaire, and will also have regular meetings with the industrial partners. More information about the chaire can be found online at http://www.di.ens.fr/~aspremon/chaire/

## Bayesian programming [book review]

Posted in Books, Kids, pictures, Statistics, University life with tags artificial intelligence, Bayesian inference, Bayesian programming, CHANCE, conjugate priors, E.T. Jaynes, graphical models, maximum entropy, Python, robots on March 3, 2014 by xi'an

“We now think the Bayesian Programming methodology and tools are reaching maturity. The goal of this book is to present them so that anyone is able to use them. We will, of course, continue to improve tools and develop new models. However, pursuing the idea that probability is an alternative to Boolean logic, we now have a new important research objective, which is to design specific hsrdware, inspired from biology, to build a Bayesian computer.”(p.xviii)

**O**n the plane to and from Montpellier, I took an extended look at Bayesian Programming a CRC Press book recently written by Pierre Bessière, Emmanuel Mazer, Juan-Manuel Ahuactzin, and Kamel Mekhnacha. *(Very nice picture of a fishing net on the cover, by the way!)* Despite the initial excitement at seeing a book which final goal was to achieve a Bayesian computer, as demonstrated by the above quote, I however soon found the book too arid to read due to its highly formalised presentation… The contents are clear indications that the approach is useful as they illustrate the use of Bayesian programming in different decision-making settings, including a collection of Python codes, so it brings an answer to the *what* but it somehow misses the *how* in that the construction of the priors and the derivation of the posteriors is not explained in a way one could replicate.

“A modeling methodology is not sufficient to run Bayesian programs. We also require an efficient Bayesian inference engine to automate the probabilistic calculus. This assumes we have a collection of inference algorithms adapted and tuned to more or less specific models and a software architecture to combine them in a coherent and unique tool.” (p.9)

**F**or instance, all models therein are described via the curly brace formalism summarised by

which quickly turns into an unpalatable object, as in this example taken from the online PhD thesis of Gabriel Synnaeve (where he applied Bayesian programming principles to a MMORPG called StarCraft and developed an AI (or bot) able to play BroodwarBotQ)

thesis that I found most interesting!

“Consequently, we have 21 × 16 = 336 bell-shaped distributions and we have 2 × 21 × 16 = 772 free parameters: 336 means and 336 standard deviations.¨(p.51)

**N**ow, getting back to the topic of the book, I can see connections with statistical problems and models, and not only via the application of Bayes’ theorem, when the purpose (or *Question*) is to take a decision, for instance in a robotic action. I still remain puzzled by the purpose of the book, since it starts with very low expectations on the reader, but hurries past notions like Kalman filters and Metropolis-Hastings algorithms in a few paragraphs. I do not get some of the details, like this notion of a discretised Gaussian distribution (I eventually found the place where the 772 prior parameters are “learned” in a phase called “identification”.)

“Thanks to conditional independence the curse of dimensionality has been broken! What has been shown to be true here for the required memory space is also true for the complexity of inferences. Conditional independence is the principal tool to keep the calculation tractable. Tractability of Bayesian inference computation is of course a major concern as it has been proved NP-hard (Cooper, 1990).”(p.74)

**T**he final chapters (Chap. 14 on “Bayesian inference algorithms revisited”, Chap. 15 on “Bayesian learning revisited” and Chap. 16 on “Frequently asked questions and frequently argued matters” [!]) are definitely those I found easiest to read and relate to. With mentions made of conjugate priors and of the EM algorithm as a (Bayes) classifier. The final chapter mentions BUGS, Hugin and… Stan! Plus a sequence of 23 PhD theses defended on Bayesian programming for robotics in the past 20 years. And explains the authors’ views on the difference between Bayesian programming and Bayesian networks (“any Bayesian network can be represented in the Bayesian programming formalism, but the opposite is not true”, p.316), between Bayesian programming and probabilistic programming (“we do not search to extend classical languages but rather to replace them by a new programming approach based on probability”, p.319), between Bayesian programming and Bayesian modelling (“Bayesian programming goes one step further”, p.317), with a further (self-)justification of why the book sticks to discrete variables, and further more philosophical sections referring to Jaynes and the principle of maximum entropy.

“The “objectivity” of the subjectivist approach then lies in the fact that two different subjects with same preliminary knowledge and same observations will inevitably reach the same conclusions.”(p.327)

Bayesian Programming thus provides a good snapshot of (or window on) what one can achieve in uncertain environment decision-making with Bayesian techniques. It shows a long-term reflection on those notions by Pierre Bessière, his colleagues and students. The topic is most likely too remote from my own interests for the above review to be complete. Therefore, if anyone is interested in reviewing any further this book for CHANCE, before I send the above to the journal, please contact me. (Usual provisions apply.)

## speed of R, C, &tc.

Posted in R, Running, Statistics, University life with tags Baum-Welch algorithm, C, EM, HMM, Matlab, Octave, Python, R, Scilab, speed on February 3, 2012 by xi'an**M**y Paris colleague (and fellow-runner) Aurélien Garivier has produced an interesting comparison of 4 (or 6 if you consider scilab and octave as different from matlab) computer languages in terms of speed for producing the MLE in a hidden Markov model, using EM and the Baum-Welch algorithms. His conclusions are that

- matlab is a lot faster than R and python, especially when vectorization is important : this is why the difference is spectacular on filtering/smoothing, not so much on the creation of the sample;
- octave is a good matlab emulator, if no special attention is payed to execution speed…;
- scilab appears as a credible, efficient alternative to matlab;
- still, C is
**a lot**faster; the inefficiency of matlab in loops is well-known, and clearly shown in the creation of the sample.

(In this implementation, R is “only” three times slower than matlab, so this is not so damning…) All the codes are available and you are free to make suggestions to improve the speed of of your favourite language!