**W**hile attending my last session at MCqMC 2018, in Rennes, before taking a train back to Paris, I was confronted by this radical opinion upon our previous work with Matt Moores (Warwick) and other coauthors from QUT, where the speaker, Maksym Byshkin from Lugano, defended a new approach for maximum likelihood estimation using novel MCMC methods. Based on the point fixe equation characterising maximum likelihood estimators for exponential families, when theoretical and empirical moments of the natural statistic are equal. Using a Markov chain with stationary distribution the said exponential family, the fixed point equation can be turned into a zero divergence equation, requiring simulation of pseudo-data from the model, which depends on the unknown parameter. Breaking this circular argument, the authors note that simulating pseudo-data that reproduce the observed value of the sufficient statistic is enough. Which is related with Geyer and Thomson (1992) famous paper about Monte Carlo maximum likelihood estimation. From there I was and remain lost as I cannot see why a derivative of the expected divergence with respect to the parameter θ can be computed when this divergence is found by Monte Carlo rather than exhaustive enumeration. And later used in a stochastic gradient move on the parameter θ… Especially when the null divergence is imposed on the parameter. In any case, the final slide shows an application to a large image and an Ising model, solving the problem (?) in 140 seconds and suggesting indecency, when our much slower approach is intended to produce a complete posterior simulation in this context.

## Archive for image processing

## indecent exposure

Posted in Statistics with tags ABC, Bayesian optimisation, Bretagne, Brittany, exponential families, image analysis, image processing, inference, Lugano, maximum likelihood estimation, MCqMC 2018, pre-processing, Rennes on July 27, 2018 by xi'an## who’s that travelling salesman path?!

Posted in Statistics with tags image processing, puzzle, StippleGen, travelling salesman on July 18, 2017 by xi'an## capture-recapture homeless deaths

Posted in Statistics, Travel, University life with tags Bristol, capture-recapture, covariate, death rate, generalised linear models, homeless, image processing, INED on August 28, 2014 by xi'an**I**n the newspaper I grabbed in the corridor to my plane today (flying to Bristol to attend the SuSTaIn image processing workshop on “High-dimensional Stochastic Simulation and Optimisation in Image Processing” where I was kindly invited and most readily accepted the invitation), I found a two-page entry on estimating the number of homeless deaths using capture-recapture. Besides the sheer concern about the very high mortality rate among homeless persons (expected lifetime, 48 years; around 7000 deaths in France between 2008 and 2010) and the dreadful realisation that there are an increasing number of kids dying in the streets, I was obviously interested in this use of capture-recapture methods as I had briefly interacted with researchers from INED working on estimating the number of (living) homeless persons about 15 years ago. Glancing at the original paper once I had landed, there was alas no methodological innovation in the approach, which was based on the simplest maximum likelihood estimate. I wonder whether or not more advanced models and [Bayesian] methods of inference could [or should] be used on such data. Like introducing covariates in the process. For instance, when conditioning the probability of (cross-)detection on the cause of death.

## Pre-processing for approximate Bayesian computation in image analysis

Posted in R, Statistics, University life with tags ABC, Chamonix, image processing, MCMC, MCMSki IV, Monte Carlo Statistical Methods, path sampling, Potts model, QUT, simulation, SMC-ABC, Statistics and Computing, sufficient statistics, summary statistics on March 21, 2014 by xi'an**W**ith Matt Moores and Kerrie Mengersen, from QUT, we wrote this short paper just in time for the MCMSki IV Special Issue of *Statistics & Computing*. And arXived it, as well. The global idea is to cut down on the cost of running an ABC experiment by removing the simulation of a humongous state-space vector, as in Potts and hidden Potts model, and replacing it by an approximate simulation of the 1-d sufficient (summary) statistics. In that case, we used a division of the 1-d parameter interval to simulate the distribution of the sufficient statistic for each of those parameter values and to compute the expectation and variance of the sufficient statistic. Then the conditional distribution of the sufficient statistic is approximated by a Gaussian with these two parameters. And those Gaussian approximations substitute for the true distributions within an ABC-SMC algorithm à la Del Moral, Doucet and Jasra (2012).

**A**cross 20 125 × 125 pixels simulated images, Matt’s algorithm took an average of 21 minutes per image for between 39 and 70 SMC iterations, while resorting to pseudo-data and deriving the genuine sufficient statistic took an average of 46.5 hours for 44 to 85 SMC iterations. On a realistic Landsat image, with a total of 978,380 pixels, the precomputation of the mapping function took 50 minutes, while the total CPU time on 16 parallel threads was 10 hours 38 minutes. By comparison, it took 97 hours for 10,000 MCMC iterations on this image, with a poor effective sample size of 390 values. Regular SMC-ABC algorithms cannot handle this scale: It takes 89 hours to perform *a single* SMC iteration! (Note that path sampling also operates in this framework, thanks to the same precomputation: in that case it took 2.5 hours for 10⁵ iterations, with an effective sample size of 10⁴…)

**S**ince my student’s paper on Seaman et al (2012) got promptly rejected by *TAS* for quoting too extensively from my post, we decided to include me as an extra author and submitted the paper to this special issue as well.

## from down-under, Lake Menteith upside-down

Posted in Books, R, Statistics with tags Bayesian Core, image processing, Lake of Menteith, Loch Lomond, typos on January 23, 2013 by xi'an**T**he dataset used in *Bayesian Core* for the chapter on image processing is a Landsat picture of Lake of Menteith in Scotland (close to Loch Lomond). (Yes, Lake of Menteith, not Loch Menteith!) Here is the image produced in the book. I just got an email from Matt Moores at QUT that the image is both rotated and flipped:

The image of Lake Mentieth in figure 8.6 ofBayesian Coreis upside-down and back-to-front, so to speak. Also, I recently read a paper by Lionel Cucala & J-M Marin that has the same error.

This is due to the difference between matrix indices and image coordinates: matrices in R are indexed by [row,column] but image coordinates are [x,y]. Also, y=1 is the first row of the matrix, but the bottom row of pixels in an image.

Only a one line change to the R code is required to display the image in the correct orientation:image(1:100,1:100,t(as.matrix(lm3)[100:1,]),col=gray(256:1/256),xlab="",ylab="")

As can be checked on Googlemap, the picture is indeed rotated by a -90⁰ angle and the transpose correction does the job!