In this post, I’ll explain the new smoother introduced in our paper Coupling of Particle Filters with Fredrik Lindsten and Thomas B. Schön from Uppsala University. Smoothing refers to the task of estimating a latent process of length , given noisy measurements of it, ; the smoothing distribution refers to . The setting is state-space models (what else?!), with a fixed parameter assumed to have been previously estimated.
In this post, I’ll write about coupling particle filters, as proposed in our recent paper with Fredrik Lindsten and Thomas B. Schön from Uppsala University, available on arXiv; and also in this paper by colleagues at NUS. The paper is about a methodology with multiple direct consequences. In this first post, I’ll focus on correlated likelihood estimators; in a later post, I’ll describe a new smoothing algorithm. Both are described in detail in the article. We’ve been blessed to have been advertised by xi’an’s og, so glory is just around the corner.
My last post dates back to May 2015… thanks to JB and Julyan for keeping the place busy! I’m not (quite) dead and intend to go back to posting stuff every now and then. And by the way, congrats to both for their new jobs!
Last July, I’ve also started a new job, as an assistant professor in the Department of Statistics at Harvard University, after having spent two years in Oxford. At some point, I might post something on the cultural difference between the
European English and American communities of statisticians.
In the coming weeks, I’ll tell you all about a new paper entitled Coupling of Particle Filters, co-written with Fredrik Lindsten and Thomas B. Schön from Uppsala University in Sweden. We are excited about this coupling idea because it’s simple and yet brings massive gains in many important aspects of inference for state space models (including both parameter inference and smoothing). I’ll be talking about it at the World Congress in Probability and Statistics in Toronto next week and at JSM in Chicago, early in August.
I’ll also try to write about another exciting project, joint work with Christian Robert, Chris Holmes and Lawrence Murray, on modularization, cutting feedback, the infamous cut function of BUGS and all that funny stuff. I’ve talked about it in ISBA 2016, and intend to put the associated tech report on arXiv over the summer.
In Bayesian nonparametrics, many models address the problem of density regression, including covariate dependent processes. These were settled by the pioneering works by [current ISBA president] MacEachern (1999) who introduced the general class of dependent Dirichlet processes. The literature on dependent processes was developed in numerous models, such as nonparametric regression, time series data, meta-analysis, to cite but a few, and applied to a wealth of fields such as, e.g., epidemiology, bioassay problems, genomics, finance. For references, see for instance the chapter by David Dunson in the Bayesian nonparametrics textbook (edited in 2010 by Nils Lid Hjort, Chris Holmes, Peter Müller and Stephen G. Walker). With Kerrie Mengersen and Judith Rousseau, we have proposed a dependent model in the same vein for modeling the influence of fuel spills on species diversity (arxiv).
In our ecological example, the model provides a series of densities on the Y axis (in our case, posterior density of species diversity), indexed by some covariate X (a pollutant). See file density_plot.txt. The following Plotly R code
library(plotly) mydata = read.csv("density_plot.txt") df = as.data.frame(mydata) plot_ly(df, x = Y, y = X, z = Z, group = X, type = "scatter3d", mode = "lines")
provides a graph as below. For the interactive version, see the RPubs page here.
“For about two centuries, Bayesian demography remained largely dormant. Only in recent decades has there been a revival of demographers’ interest in Bayesian methods, following the methodological and computational developments of Bayesian statistics. The area is currently growing fast, especially with the United Nations (UN) population projections becoming probabilistic—and Bayesian.” Bijak and Bryant (2016)
It is interesting to see that Bayesian statistics have been infiltrating demography in the recent years. The review paper Bayesian demography 250 years after Bayes by Bijak and Bryant (Population Studies, 2016) stresses that promising areas of application include demographic forecasts, problems with limited data, and highly structured and complex models. As an indication of this growing interest, ISBA meeting to be held next June will showcase a course and a session devoted to the field (given and organized by Adrian Raftery).
With Vianney Costemalle from INSEE, we recently modestly contributed to the field by proposing a Bayesian model (paper in French) which helps reconciling apparently inconsistent population datasets. The aim is to estimate annual migration flows to France (note that the work covers the period 2004-2011 (long publication process) and as a consequence does not take into account recent migration events). We follow the United Nations (UN) definition of a long-term migrant, who is someone who settles in a foreign country for at least one year. At least two datasets can be used to this aim: 1) the population census , annual since 2004, and 2) data from residence permits . (more…)
On February 19 took place at Collegio Carlo Alberto the second Statalks, a series of Italian workshops aimed at Master students, PhD students, post-docs and young researchers. This edition was dedicated to Bayesian Nonparametrics. The first two presentations were introductory tutorials while the last four focused on theory and applications. All six were clearly biased according to the scientific interests of our group. Below are the program and the slides.
- A gentle introduction to Bayesian Nonparametrics I (Antonio Canale)
- A gentle introduction to Bayesian Nonparametrics II (Julyan Arbel)
- Dependent processes in Bayesian Nonparametrics (Matteo Ruggiero)
- Asymptotics for discrete random measures (Pierpaolo De Blasi)
- Applications to Ecology and Marketing (Antonio Canale)
- Species sampling models (Julyan Arbel)
[This is a guest post by my friend and colleague Bernardo Nipoti from Collegio Carlo Alberto,
The matches of the group stage of the UEFA Champions league have just finished and next Monday, the 14th of December 2015, in Nyon, there will be a round of draws for deciding the eight matches that will compose the first round of the knockout phase.
As explained on the UEFA website, rules are simple:
- two seeding pots have been formed: one consisting of group winners and the other of runners-up;
- no team can play a club from their group or any side from their own association;
- due to a decision by the UEFA Executive Committee, teams from Russia and Ukraine cannot meet.
The two pots are:
Group winners: Real Madrid (ESP), Wolfsburg (GER), Atlético Madrid (ESP), Manchester City (ENG), Barcelona (ESP, holders), Bayern München (GER), Chelsea (ENG), Zenit (RUS);
Group runners-up: Paris Saint-Germain (FRA), PSV Eindhoven (NED), Benfica (POR), Juventus (ITA), Roma (ITA), Arsenal (ENG), Dynamo Kyiv (UKR), Gent (BEL).
Giving these few constraints, are there some matches that are more likely to be drawn than others? For example, supporters of Barcelona might wonder whether the seven possible teams (PSG, PSV, Benfica, Juventus, Arsenal, Dynamo Kyiv and Gent) are all equally likely to be the next opponent of their favorite team. (more…)
I have been recently invited to referee a paper for a journal I had never heard of before: the International Journal of Biological Instrumentation, published by VIBGYOR Online Publishers. This publisher happens to be on the blacklist of predatory publishers by Jeffrey Beall which inventory:
Potential, possible, or probable predatory scholarly open-access publishers.
I have kindly declined the invitation. Thanks Igor for the link.
Some time ago, Cédric Villani came to Turin for delivering two talks. One intended for youngsters (high school level say), another one for a wider audience, as a recipient of the Peano Prize. He commented on live, in Italian per favore:
“Grazie mille! Un grande piacere e un grande onore per me!”
I attended both. The reason why I attended the first being that I am acting as a research advisor for Math en Jeans groups. Villani spoke about his book, Birth of a Theorem, or Théorème Vivant. He also shared a list of se7en thoughts/tips about doing research, with illustrations. I find them quite inspiring, here they are.
Illustrating this by showing Faà di Bruno’s formula Wikipedia page. I like this quote, since the formula enters moment computation for objects I’m using everyday. And also because Faà di Bruno lived in Italian Piedmont, precisely in Turin.
“The most important and the most mysterious.”
- Favorable environment
Showing pictures of several places where he worked, including Institut Henri Poincaré. Not sure that this one is the most favorable environment for scientific productivity (as a Director I mean).
Meaning between scientists, not trade. Explaining briefly about polymath projects. And displaying a snapshot of Gowers’s Weblog as an illustration of how diverse exchanges he means. I also believe that blogs are a great information medium🙂
With snapshots of Musica Ricercata sheet music. And a paragraph of La disparition, a novel without the letter e by Georges Perec. Writing this makes me realize how foolish such an enterprise would look like in mathematics.
- Work & Intuition
Interesting to see these two at the same level.
- Perseverance & Luck
Same comment as for point 6.
El Capitan is a very nice mountain. It’s also the latest OS X version which messes things up with . Be aware of this before you update. I wasn’t!
I quote from a fix explained here:
Under OS X 10.11, El Capitan, writing to “/usr” is no longer allowed, even with Administrator privileges. The usual symbolic link to the active Distribution, “/usr/texbin”, is therefore removed (if it was there from a previous OS version) and cannot be installed. Many GUI applications have the path to those binaries set to “/usr/texbin” by default and will no longer find the binaries there.
I had to reinstall MacTex, then to update my GUI application (texmaker) for and finally to replace every “/usr/texbin” by “/Library/TeX/texbin”, as shown below.