## Cancún, ISBA 2014 [day #3]

Posted in pictures, Statistics, Travel, University life with tags , , , , , on July 23, 2014 by xi'an

…already Thursday, our [early] departure day!, with an nth (!) non-parametric session that saw [the newly elected ISBA Fellow!] Judith Rousseau present an ongoing work with Chris Holmes on the convergence or non-convergence conditions for a Bayes factor of a non-parametric hypothesis against another non-parametric. I wondered at the applicability of this test as the selection criterion in ABC settings, even though having an iid sample to start with is a rather strong requirement.

Switching between a scalable computation session with Alex Beskos, who talked about adaptive Langevin algorithms for differential equations, and a non-local prior session, with David Rossell presenting a smoother way to handle point masses in order to accommodate frequentist coverage. Something we definitely need to discuss the next time I am in Warwick! Although this made me alas miss both the first talk of the non-local session by Shane Jensen  the final talk of the scalable session by Doug Vandewrken where I happened to be quoted (!) for my warning about discretising Markov chains into non-Markov processes. In the 1998 JASA paper with Chantal Guihenneuc.

After a farewell meal of ceviche with friends in the sweltering humidity of a local restaurant, I attended [the newly elected ISBA Fellow!] Maria Vanucci’s talk on her deeply involved modelling of fMRI. The last talk before the airport shuttle was François Caron’s description of a joint work with Emily Fox on a sparser modelling of networks, along with an auxiliary variable approach that allowed for parallelisation of a Gibbs sampler. François mentioned an earlier alternative found in machine learning where all components of a vector are updated simultaneously conditional on the previous avatar of the other components, e.g. simulating (x’,y’) from π(x’|y) π(y’|x) which does not produce a convergent Markov chain. At least not convergent to the right stationary. However, running a quick [in-flight] check on a 2-d normal target did not show any divergent feature, when compared with the regular Gibbs sampler. I thus wonder at what can be said about the resulting target or which conditions are need for divergence. A few scribbles later, I realised that the 2-d case was the exception, namely that the stationary distribution of the chain is the product of the marginal. However, running a 3-d example with an auto-exponential distribution in the taxi back home, I still could not spot a difference in the outcome.

## impressions, soleil couchant (#2)

Posted in pictures, Travel with tags , , , , , , , on July 12, 2014 by xi'an

## ABC [almost] in the front news

Posted in pictures, Statistics, University life with tags , , , , , , , , , , , , , , on July 7, 2014 by xi'an

My friend and Warwick colleague Gareth Roberts just published a paper in Nature with Ellen Brooks-Pollock and Matt Keeling from the University of Warwick on the modelling of bovine tuberculosis dynamics in Britain and on the impact of control measures. The data comes from the Cattle Tracing System and the VetNet national testing database. The mathematical model is based on a stochastic process and its six parameters are estimated by sequential ABC (SMC-ABC). The summary statistics chosen in the model are the number of infected farms per county per year and the number of reactors (cattle failing a test) per county per year.

“Therefore, we predict that control of local badger populations and hence control of environmental transmission will have a relatively limited effect on all measures of bovine TB incidence.”

This advanced modelling of a comprehensive dataset on TB in Britain quickly got into a high profile as it addresses the highly controversial (not to say plain stupid) culling of badgers (who also carry TB) advocated by the government. The study concludes that “only generic measures such as more national testing, whole herd culling or vaccination that affect all routes of transmission are effective at controlling the spread of bovine TB.” While the elimination of badgers from the English countryside would have a limited effect.  Good news for badgers! And the Badger Trust. Unsurprisingly, the study was immediately rejected by the UK farming minister! Not only does he object to the herd culling solution for economic reasons, but he “cannot accept the paper’s findings”. Maybe he does not like ABC… More seriously, the media oversimplified the findings of the study, “as usual”, with e.g. The Guardian headline of “tuberculosis threat requires mass cull of cattle”.

## sunrise over Warwickshire (#2)

Posted in pictures, Running, Travel, University life with tags , , , , , on July 4, 2014 by xi'an

## back in Warwick

Posted in pictures, Running, Travel, University life with tags , , , on July 2, 2014 by xi'an

## thermodynamic Monte Carlo

Posted in Books, Statistics, University life with tags , , , , on June 27, 2014 by xi'an

Michael Betancourt, my colleague from Warwick, arXived a month ago a paper about a differential geometry approach to relaxation. (In the Monte Carlo rather than the siesta sense of the term relaxation!) He is considering the best way to link a simple base measure ϖ to a measure of interest π by the sequence

$\pi_\beta(x) = \dfrac{e^{-\beta\Delta V(x)}\varpi(x)}{Z(\beta)}$

where Z(β) is the normalising constant (or partition function in the  thermodynamic translation). Most methods are highly dependent on how the sequence of β’s is chosen. A first nice result (for me) is that the Kullback-Leibler distance and the partition function are strongly related in that

$K(\pi_\beta,\pi_\eta) \approx (\eta-\beta) \dfrac{\text{d}Z}{\text{d}\beta}$

which means that the variation in the normalising constant is driving the variation in the Kullback-Leibler distance. The next section goes into differential geometry and the remains from my Master course in differential geometry alas are much too scattered for me to even remember some notions like that of a bundle… So, like Andrew, I have trouble making sense of the resulting algorithm, which updates the temperature β along with the position and speed. (It sounds like an extra and corresponding energy term is added to the original Hamiltonian function.) Even the Beta-Binomial

$k|p\sim\mathrm{B}(n,p)\,,\ p\sim\mathrm{Be}(a,b)$

example is somewhat too involved for me.  So I tried to write down the algorithm step by step in this special case. Which led to

1. update β into β-εδp’²
2. update p into p-εδp’
3. update p’ into p’+ε{(1-a)/p+(b-1)/(1-p)}
4. compute the average log-likelihood, λ* under the tempered version of the target (at temperature β)
5. update p’ into p’+2εβ{(1-a)/p+(b-1)/(1-p)}-ε[λ-λ*]p’
6. update p’ into p’+ε{(1-a)/p+(b-1)/(1-p)}
7. update β into β-εδp’²
8. update p into p-εδp’

where p’ denotes the momentum auxiliary variable associated with the kinetic energy. And λ is the current log-likelihood. (The parameter ε was equal to 0.005 and I could not find the value of δ.) The only costly step in the above list is the approximation of the log-likelihood average λ*. The above details make the algorithm quite clear but I am still missing the intuition behind…

## bluebells

Posted in pictures, Travel with tags , , , on May 24, 2014 by xi'an