At Sylvia Richardson’s career celebration last Friday, I gave a talk on How many components in a mixture? which was most relevant given Sylvia’s contributions to mixture inference over the years, including her highly influential 1997 Read Paper with Peter Green. The other talks highlighted the many facets of Sylvia to the field and the profession, including obviously her MRC Unit directorship but also her RSS Presidency when she drove along with Chris Holmes the remarkable society’s response to the COVID pandemic. The day ended up with a diner in Emmanuel College (in the Dining Hall rather than the larger, noisier, and more formal Hall where I was once invited for the Midsummer Dinner by Sylvia). It was also a great opportunity to reconnect with friends I had not seen for ages.
Archive for Cam river
Festschift for Sylvia
Posted in Books, pictures, Statistics, Travel, University life with tags Cam river, Cambridge colleges, Dirichlet process Gaussian mixture, distributed computing, Emmanuel College, Festschrift, finite mixtures, Midsummer, MRC Biostatistics Unit, RJMCMC, statistical evidence, Sylvia Richardson on May 17, 2023 by xi'annested sampling when prior and likelihood clash
Posted in Books, Statistics with tags Cam river, Cambridge, conflicting prior, efficiency measures, efficient importance sampling, intractable constant, marginal likelihood, nested sampling, statistical evidence, tempering on April 3, 2018 by xi'an
A recent arXival by Chen, Hobson, Das, and Gelderblom makes the proposal of a new nested sampling implementation when prior and likelihood disagree, making simulations from the prior inefficient. The paper holds the position that a single given prior is used over and over all datasets that come along:
“…in applications where one wishes to perform analyses on many thousands (or even millions) of different datasets, since those (typically few) datasets for which the prior is unrepresentative can absorb a large fraction of the computational resources.” Chen et al., 2018
My reaction to this situation, provided (a) I want to implement nested sampling and (b) I realise there is a discrepancy, would be to resort to an importance sampling resolution, as we proposed in our Biometrika paper with Nicolas. Since one objection [from the authors] is that identifying outlier datasets is complicated (it should not be when the likelihood function can be computed) and time-consuming, sequential importance sampling could be implemented.
“The posterior repartitioning (PR) method takes advantage of the fact that nested sampling makes use of the likelihood L(θ) and prior π(θ) separately in its exploration of the parameter space, in contrast to Markov chain Monte Carlo (MCMC) sampling methods or genetic algorithms which typically deal solely in terms of the product.” Chen et al., 2018
The above salesman line does not ring a particularly convincing chime in that nested sampling is about as myopic as MCMC since based on the similar notion of a local proposal move, starting from the lowest likelihood argument (the minimum likelihood estimator!) in the nested sample.
“The advantage of this extension is that one can choose (π’,L’) so that simulating from π’ under the constraint L'(θ) > l is easier than simulating from π under the constraint L(θ) > l. For instance, one may choose an instrumental prior π’ such that Markov chain Monte Carlo steps adapted to the instrumental constrained prior are easier to implement than with respect to the actual constrained prior. In a similar vein, nested importance sampling facilitates contemplating several priors at once, as one may compute the evidence for each prior by producing the same nested sequence, based on the same pair (π’,L’), and by simply modifying the weight function.” Chopin & Robert, 2010
Since the authors propose to switch to a product (π’,L’) such that π’.L’=π.L, the solution appears like a special case of importance sampling, with the added drwaback that when π’ is not normalised, its normalised constant must be estimated as well. (With an extra nested sampling implementation?) Furthermore, the advocated solution is to use tempering, which is not so obvious as it seems in small dimensions. As the mass does not always diffuse to relevant parts of the space. A more “natural” tempering would be to use a subsample in the (sub)likelihood for nested sampling and keep the remainder of the sample for weighting the evaluation of the evidence.
Britain, please stay!
Posted in Books, Kids, pictures, Running, University life with tags Brexit, Britain, Cam river, Cambridge, dawn, Europe, European Union, referendum, UK, United Kingdom on June 7, 2016 by xi'an
A love letter from some Europeans against Brexit that appeared in the Times Literary Supplement a few days ago, and which message I definitely support:
All of us in Europe respect the right of the British people to decide whether they wish to remain with us in the European Union. It is your decision, and we will all accept it. Nevertheless, if it will help the undecided to make up their minds, we would like to express how very much we value having the United Kingdom in the European Union. It is not just treaties that join us to your country, but bonds of admiration and affection. All of us hope that you will vote to renew them. Britain, please stay.
sunrise on the Cam
Posted in pictures, Running, Travel, University life with tags Cam river, Cambridge, rowing on January 28, 2012 by xi'an
