**T**oday, provided the Air France strike let me fly to Birmingham airport!, I am back at Gregynog Hall, Wales, for the weekend conference organised there every year by some Welsh and English statistics departments, including Warwick. Looking forward to the relaxed gathering in the glorious Welsh countryside (and hoping that my knee will have sufficiently recovered for some trail running around Gregynog Hall…!) Here are the slides of the talk I will present tomorrow:

## Archive for University of Warwick

## spacings on a torus

Posted in Books, Kids, R, Statistics, University life with tags coupling from the past, cross validated, Dirichlet distribution, perfect sampling, ranking and selection, spacings, torus, University of Warwick, Wilfrid Kendall on March 22, 2018 by xi'an**W**hile in Brussels last week I noticed an interesting question on X validated that I considered in the train back home and then more over the weekend. This is a question about spacings, namely how long on average does it take to cover an interval of length L when drawing unit intervals at random (with a torus handling of the endpoints)? Which immediately reminded me of Wilfrid Kendall (Warwick) famous gif animation of coupling from the past via leaves covering a square region, from the top (forward) and from the bottom (backward)…

The problem is rather easily expressed in terms of uniform spacings, more specifically on the maximum spacing being less than 1 (or 1/L depending on the parameterisation). Except for the additional constraint at the boundary, which is not independent of the other spacings. Replacing this extra event with an independent spacing, there exists a direct formula for the expected stopping time, which can be checked rather easily by simulation. But the exact case appears to be add a few more steps to the draws, 3/2 apparently. The following graph displays the regression of the Monte Carlo number of steps over 10⁴ replicas against the exact values:

## summer school on computational statistics [deadline]

Posted in Books, pictures, Statistics, Travel, University life with tags Amazon, Art Owen, BAYSM 2018, computational statistics, CRiSM, Google, ISBA, ISBA 2018, London Mathematical Society, MCqMC 2018, registration, summer s, University of Warwick on February 23, 2018 by xi'an**R**eminding ‘Og’s readers and others that the early bird registration deadline for our LMS/CRiSM summer school on computational statistics at the University of Warwick, 9-13 July, 2018 is next Thursday, March 01, 2018. This also applies for bursary applications, so do not dally and apply now!

## infinite mixtures are likely to take a while to simulate

Posted in Books, Statistics with tags Amsterdam, cross validated, infinite mixture, Luc Devroye, mixtures, Monte Carlo algorithm, series representation, simulation, University of Warwick on February 22, 2018 by xi'an**A**nother question on X validated got me highly interested for a while, as I had considered myself the problem in the past, until I realised while discussing with Murray Pollock in Warwick that there was no general answer: *when a density f is represented as an infinite series decomposition into weighted densities, some weights being negative, is there an efficient way to generate from such a density?* One natural approach to the question is to look at the mixture with positive weights, *f⁺*, since it gives an upper bound on the target density. Simulating from this upper bound *f⁺* and accepting the outcome x with probability equal to the negative part over the sum of the positive and negative parts *f⁻(x)*/*f(x)* is a valid solution. Except that it is not implementable if

- the positive and negative parts both involve infinite sums with no exploitable feature that can turn them into finite sums or closed form functions,
- the sum of the positive weights is infinite, which is the case when the series of the weights is not absolutely converging.

Even when the method is implementable it may be arbitrarily inefficient in the sense that the probability of acceptance is equal to to the inverse of the sum of the positive weights and that simulating from the bounding mixture in the regular way uses the original weights which may be unrelated in size with the actual importance of the corresponding components in the actual target. Hence, when expressed in this general form, the problem cannot allow for a generic solution.

Obviously, if more is known about the components of the mixture, as for instance the sequence of weights being alternated, there exist specialised methods, as detailed in the section of series representations in Devroye’s (1985) simulation bible. For instance, in the case when positive and negative weight densities can be paired, in the sense that their weighted difference is positive, a latent index variable can be included. But I cannot think of a generic method where the initial positive and negative components are used for simulation, as it may on the opposite be the case that no finite sum difference is everywhere positive.

## annual visit to Oxford

Posted in Kids, pictures, Statistics, Travel, University life with tags Avalon, Bayesian statistics, course, Oxford, OxWaSP, Roxy Music, segregation, St. Hugh's College, University of Oxford, University of Warwick on February 1, 2018 by xi'an**A**s in every year since 2014, I am spending a few days in Oxford to teach a module on Bayesian Statistics to our Oxford-Warwick PhD students. This time I was a wee bit under the weather due to a mild case of food poisoning and I can only hope that my more than sedate delivery did not turn definitely the students away from Bayesian pursuits!

The above picture is at St. Hugh’s College, where I was staying. Or should it be Saint Hughes, since this 12th century bishop was a pre-Brexit European worker from Avalon, France… (This college was created in 1886 for young women of poorer background. And only opened to male students a century later. The 1924 rules posted in one corridor show how these women were considered to be so “dangerous” by the institution that they had to be kept segregated from men, except their brothers!, at all times…)