Archive for Bayesian data analysis

freedom prior

Posted in Books, Kids, Statistics with tags , , , , , on December 9, 2020 by xi'an

Another X validated question on which I spent more time than expected. Because of the somewhat unusual parameterisation used in BDA.for the inverse χ² distribution. The interest behind the question is in the induced distribution on the parameter associated with the degrees of freedom ν of the t-distribution (question that coincided with my last modifications of my undergraduate mathematical statistics exam, involving a t sample). Whichever the prior chosen on ν, the posterior involves a nasty term

\pi(\nu)\frac{(\nu)^{n\nu/2}}{\Gamma(\nu/2)^n}{\,(v_1\cdots v_n)^{-\nu/2-1}\exp\Big\{-\nu\sigma^2}\sum_{i=1}^n1\big/2v_i\Big\}

as the Gamma function there is quickly explosive (as can be checked Stirling’s formula). Unless the prior π(ν) cancels this term, which is rather fishy as the prior would then depend on the sample size n. Even though the whole posterior is well-defined (and hence non-explosive). Rather than seeking a special prior π(ν) for computation purposes, I would thus favour a modelling restricted to integer valued ν’s as there is not much motivation in inferring about non-integer degrees of freedom.

souvenirs de Luminy

Posted in Books, Kids, pictures, Statistics, Travel, University life with tags , , , , , , , , , , , , , on July 6, 2020 by xi'an

five postdoc positions in top UK universities & Bayesian health data science

Posted in Statistics with tags , , , , , , , , , , , , , on March 30, 2018 by xi'an

The EPSRC programme New Approaches to Bayesian Data Science: Tackling Challenges from the Health Sciences, directed by Paul Fearnhead, is offering five 3 or 4 year PDRA positions at the Universities of Bristol, Cambridge, Lancaster, Oxford, and Warwick. Here is the complete call:

Salary:   £29,799 to £38,833
Closing Date:   Thursday 26 April 2018
Interview Date:   Friday 11 May 2018

We invite applications for Post-Doctoral Research Associates to join the New Approaches to Bayesian Data Science: Tackling Challenges from the Health Sciences programme. This is an exciting, cross-disciplinary research project that will develop new methods for Bayesian statistics that are fit-for-purpose to tackle contemporary Health Science challenges: such as real-time inference and prediction for large scale epidemics; or synthesizing information from distinct data sources for large scale studies such as the UK Biobank. Methodological challenges will be around making Bayesian methods scalable to big-data and robust to (unavoidable) model errors.

This £3M programme is funded by EPSRC, and brings together research groups from the Universities of Lancaster, Bristol, Cambridge, Oxford and Warwick. There is either a 4 or a 3 year position available at each of these five partner institutions.

You should have, or be close to completing, a PhD in Statistics or a related discipline. You will be experienced in one or more of the following areas: Bayesian statistics, computational statistics, statistical machine learning, statistical genetics, inference for epidemics. You will have demonstrated the ability to develop new statistical methodology. We are particularly keen to encourage applicants with strong computational skills, and are looking to put together a team of researchers with skills that cover theoretical, methodological and applied statistics. A demonstrable ability to produce academic writing of the highest publishable quality is essential.

Applicants must apply through Lancaster University’s website for the Lancaster, Oxford, Bristol and Warwick posts.  Please ensure you state clearly which position or positions you wish to be considered for when applying. For applications to the MRC Biostatistics Unit, University of Cambridge vacancy please go to their website.

Candidates who are considering making an application are strongly encouraged to contact Professor Paul Fearnhead (p.fearnhead@lancaster.ac.uk), Sylvia Richardson (sylvia.richardson@mrc-bsu.cam.ac.uk), Christophe Andrieu (c.andrieu@bristol.ac.uk), Chris Holmes (c.holmes@stats.ox.ac.uk) or Gareth Roberts (Gareth.O.Roberts@warwick.ac.uk) to discuss the programme in greater detail.

We welcome applications from people in all diversity groups.

 

latest issue of Significance

Posted in Statistics with tags , , , , on March 20, 2017 by xi'an

The latest issue of Significance is bursting with exciting articles and it is a shame I do not receive it any longer (not that I stopped subscribing to the RSS or the ASA, but it simply does not get delivered to my address!). For instance, a tribune by Tom Nicolls (from whom I borrowed this issue for the weekend!) on his recent assessment of false positive in brain imaging [I covered in a blog entry a few months ago] when checking the cluster inference and the returned p-values. And the British equivalent of Gelman et al. book cover on the seasonality of births in England and Wales, albeit witout a processing of the raw data and without mention being made of the Gelmanesque analysis: the only major gap in the frequency is around Christmas and New Year, while there is a big jump around September (also there in the New York data).

birdfeedA neat graph on the visits to four feeders by five species of birds. A strange figure in Perils of Perception that [which?!] French people believe 31% of the population is Muslim and that they are lacking behind many other countries in terms of statistical literacy. And a rather shallow call to Popper to running decision-making in business statistics.

Statistical rethinking [book review]

Posted in Books, Kids, R, Statistics, University life with tags , , , , , , , , , , , , , , , , , , , , , on April 6, 2016 by xi'an

Statistical Rethinking: A Bayesian Course with Examples in R and Stan is a new book by Richard McElreath that CRC Press sent me for review in CHANCE. While the book was already discussed on Andrew’s blog three months ago, and [rightly so!] enthusiastically recommended by Rasmus Bååth on Amazon, here are the reasons why I am quite impressed by Statistical Rethinking!

“Make no mistake: you will wreck Prague eventually.” (p.10)

While the book has a lot in common with Bayesian Data Analysis, from being in the same CRC series to adopting a pragmatic and weakly informative approach to Bayesian analysis, to supporting the use of STAN, it also nicely develops its own ecosystem and idiosyncrasies, with a noticeable Jaynesian bent. To start with, I like the highly personal style with clear attempts to make the concepts memorable for students by resorting to external concepts. The best example is the call to the myth of the golem in the first chapter, which McElreath uses as an warning for the use of statistical models (which almost are anagrams to golems!). Golems and models [and robots, another concept invented in Prague!] are man-made devices that strive to accomplish the goal set to them without heeding the consequences of their actions. This first chapter of Statistical Rethinking is setting the ground for the rest of the book and gets quite philosophical (albeit in a readable way!) as a result. In particular, there is a most coherent call against hypothesis testing, which by itself justifies the title of the book. Continue reading