## Monte Carlo fusion

Posted in Statistics with tags , , , , , , , , , on January 18, 2019 by xi'an

Hongsheng Dai, Murray Pollock (University of Warwick), and Gareth Roberts (University of Warwick) just arXived a paper we discussed together last year while I was at Warwick. Where fusion means bringing different parts of the target distribution

f(x)∝f¹(x)f²(x)…

together, once simulation from each part has been done. In the same spirit as in Scott et al. (2016) consensus Monte Carlo. Where for instance the components of the target cannot be computed simultaneously, either because of the size of the dataset, or because of privacy issues.The idea in this paper is to target an augmented density with the above marginal, using for each component of f, an auxiliary variable x¹,x²,…, and a target that is the product of the squared component, f¹(x¹)², f²(x²)², … by a transition density keeping f¹(.)²,f²(.)²,… invariant:

$f^c(x^c)^2 p_c(y|x^c) / f_c(y)$

as for instance the transition density of a Langevin diffusion. The marginal of

$\prod_c f^c(x^c)^2 p_c(y|x^c) / f_c(y)$

as a function of y is then the targeted original product. Simulating from this new extended target can be achieved by rejection sampling. (Any impact of the number of auxiliary variables on the convergence?) The practical implementation actually implies using the path-space rejection sampling methods in the Read Paper of Beskos et al. (2006). (An extreme case of the algorithm is actually an (exact) ABC version where the simulations x¹,x²,… from all components have to be identical and equal to y. The opposite extreme is the consensus Monte Carlo Algorithm, which explains why this algorithm is not an efficient solution.) An alternative is based on an Ornstein-Uhlenbeck bridge. While the paper remains at a theoretical level with toy examples, I heard from the same sources that applications to more realistic problems and implementation on parallel processors is under way.

## O’Bayes 2019: speakers, discussants, posters!

Posted in pictures, Statistics, University life with tags , , , , on January 2, 2019 by xi'an

The program for the next O’Bayes conference in Warwick, 28 June-02 July, 2019, is now set. Speakers and discussants have been contacted by the scientific committee and accepted our invitation! As usual, there will be poster sessions on the nights of 29 and 30 June and the call is open for poster submissions, until January 31, to be sent to me as a one page pdf document containing either the poster itself or title, abstract and references. (Using my email address at either Dauphine or Warwick is fine. Or bayesianstatistics on gmail.)

## reading pile for X break

Posted in Books, pictures, Statistics, Travel, University life with tags , , , , , , , , , , , , , , on December 28, 2018 by xi'an

## Le Monde puzzle [#1076]

Posted in Books, Kids, R, Travel with tags , , , , , , , , , on December 27, 2018 by xi'an

A cheezy Le Monde mathematical puzzle : (which took me much longer to find [in the sense of locating] than to solve, as Warwick U does not get a daily delivery of the newspaper [and this is pre-Brexit!]):

Take a round pizza (or a wheel of Gruyère) cut into seven identical slices and turn one slice upside down. If the only possibly moves are to turn three connected slices to their reverse side, how many moves at least are needed to recover the original configuration? What is the starting configuration that requires the largest number of moves?

Since there are ony N=2⁷ possible configurations, a brute force exploration is achievable, starting from the perfect configuration requiring zero move and adding all configurations found by one additional move at a time… Until all configurations have been visited and all associated numbers of steps are stable. Here is my R implementation

```nztr=lengz=rep(-1,N) #length & ancestor
nztr[0+1]=lengz[0+1]=0
fundz=matrix(0,Z,Z) #Z=7
for (i in 1:Z){ #only possible moves
fundz[i,c(i,(i+1)%%Z+Z*(i==(Z-1)),(i+2)%%Z+Z*(i==(Z-2)))]=1
lengz[bit2int(fundz[i,])+1]=1
nztr[bit2int(fundz[i,])+1]=0}
while (min(lengz)==-1){ #second loop omitted
for (j in (1:N)[lengz>-1])
for (k in 1:Z){
m=bit2int((int2bit(j-1)+fundz[k,])%%2)+1
if ((lengz[m]==-1)|(lengz[m]>lengz[j]+1)){
lengz[m]=lengz[j]+1;nztr[m]=j}
}}
```

Which produces a path of length five returning (1,0,0,0,0,0,0) to the original state:

```> nztry(2)
[1] 1 0 0 0 0 0 0
[1] 0 1 1 0 0 0 0
[1] 0 1 0 1 1 0 0
[1] 0 1 0 0 0 1 0
[1] 1 1 0 0 0 0 1
[1] 0 0 0 0 0 0 0
```

and a path of length seven in the worst case:

```> nztry(2^7)
[1] 1 1 1 1 1 1 1
[1] 1 1 1 1 0 0 0
[1] 1 0 0 0 0 0 0
[1] 0 1 1 0 0 0 0
[1] 0 1 0 1 1 0 0
[1] 0 1 0 0 0 1 0
[1] 1 1 0 0 0 0 1
[1] 0 0 0 0 0 0 0
```

Since the R code was written for an arbitrary number Z of slices, I checked that there is no solution for Z being a multiple of 3.

## waiting for the red lights to change

Posted in pictures, Running, Travel with tags , , , , , on December 22, 2018 by xi'an

## Max Ent at Max Plank

Posted in Statistics with tags , , , , , , , , , , on December 21, 2018 by xi'an

## assistant professorships at Warwick Stats

Posted in pictures, Statistics, Travel, University life with tags , , , , , on November 24, 2018 by xi'an

There is an opening for three assistant professor positions in our department at the University of Warwick, starting next Fall. With a new Head of Department. The candidate should be an excellent academic in statistics (to be interpreted in the widest sense and to include both applied and methodological statistics, probability, probabilistic operational research and mathematical finance together with interdisciplinary topics involving one or more of these areas). Deadline is January 2019. (See this link from Warwick U for indications on how to get working rights from abroad. Uncertain Brexity times…)