Archive for Black Death

Sequentially Constrained Monte Carlo

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

This newly arXived paper by S. Golchi and D. Campbell from Vancouver (hence the above picture) considers the (quite) interesting problem of simulating from a target distribution defined by a constraint. This is a question that have bothered me for a long while as I could not come up with a satisfactory solution all those years… Namely, when considering a hard constraint on a density, how can we find a sequence of targets that end up with the restricted density? This is of course connected with the zero measure case posted a few months ago. For instance, how do we efficiently simulate a sample from a Student’s t distribution with a fixed sample mean and a fixed sample variance?

“The key component of SMC is the filtering sequence of distributions through which the particles evolve towards the target distribution.” (p.3)

This is indeed the main issue! The paper considers using a sequence of intermediate targets hardening progressively the constraint(s), along with an SMC sampler, but this recommendation remains rather vague and hence I am at loss as to how to make it work when the exact constraint implies a change of measure. The first example is monotone regression where y has mean f(x) and f is monotone. (Everything is unidimensional here.) The sequence is then defined by adding a multiplicative term that is a function of ∂f/∂x, for instance

Φ(τ∂f/∂x),

with τ growing to infinity to make the constraint moving from soft to hard. An interesting introduction, even though the hard constraint does not imply a change of parameter space or of measure. The second example is about estimating the parameters of an ODE, with the constraint being the ODE being satisfied exactly. Again, not exactly what I was looking for. But with an exotic application to deaths from the 1666 Black (Death) plague.

And then the third example is about ABC and the choice of summary statistics! The sequence of constraints is designed to keep observed and simulated summary statistics close enough when the dimension of those summaries increases, which means they are considered simultaneously rather than jointly. (In the sense of Ratmann et al., 2009. That is, with a multidimensional distance.) The model used for the application of the SMC is the dynamic model of Wood (2010, Nature). The outcome of this specific implementation is not that clear compared with alternatives… And again sadly does not deal with the/my zero measure issue.

The Devil’s Disciples

Posted in Books with tags , , , , , on May 8, 2010 by xi'an

`Magic?’ echoed Bartholomew warily. `Do you really believe in this sort of things?’

I have finished my fourteenth chronicle of Matthew Bartholomew, The Devil’s Disciples, and this one seems to be the most disappointing of all! Maybe it is getting harder and harder for the author, Susanna Gregory, to find good plots and to sustain a realistic and exciting pace for her novels within the same environment of 14th Century Cambridge and with the same characters from the fictional college Michaelhouse. This novel mostly suffers from a poor plot, as most of the action is unbelievable and anachronistic, while the final resolution is anticlimactic and disappointing. I have found that the recent chronicles have become less credible from a historical viewpoint and some of the exchanges in The Devil’s Disciples are anachronistic. From a global perspective, the book deals (once again) with witchcraft and the fight between Church and the followers of Satanic rites. While I accept the core idea that the Black Death of 1347 has had a strong psychological impact on the beliefs of the survivors and that this could have driven people away from the Church into anti-Christian sects, the openness of their move is not plausible. At that time, witchery was both an heresy and a major crime (because people also believed in charms and curses), the Church inquisition had already been instituted by the Pope, and thus the idea of someone declaring his or her support of a sorcerer/witch or openly attending a sorcery meeting does not make sense to me. The relativity of beliefs expressed in the quote below does not belong to the 14th Century! (The same comment applies to the handling of a book of curses by half the characters in the novel.)

`It is a battle between two belief systems, each with its own merits and failings. The Sorcerer will not see himself as wicked but as one who offers a viable alternative to the Church.’

At the individual level, I find the main characters fairly shallow, Bartholomew spending most of the book running from one point of Cambridge to another one and not doing much else for being so exhausted by the Marathonian training! The changes in a well-established character like Father William are difficult to believe and the final uncovering of the two main culprits is both predictable and implausible to the extreme! Both Brother Michael and Matthew Bartholomew are missing the obvious clues and it takes the providential return of Clippesby to uncover the Sorcerer’s plot (whose point remains obscure to me).So both parts that constitute the appeal of a historical whodunnit are mostly lost in The Devil’s Disciples. I hope the next chronicle, A Vein of Deceit, succeeds better! (Even though early reviews are not promising…)