Archive for Duke University

off to Durham

Posted in Kids, pictures, Statistics, Travel, University life with tags , , , , , , , , , , , , , , , on August 31, 2026 by xi'an

John J Deely (1933-2025)

Posted in University life with tags , , , , , , , , , , , on February 13, 2025 by xi'an

I just learned that my friend John Deely died last month in West Lafayette. I had come to know him in 1988, when we were both visiting Purdue and sharing an office. He was funny and witty, with a unique and unforgetable laugh, and I remember several evenings with him and Ann. After leaving Purdue, I met John at Bayesian conferences (incl. the Valencia meetings). He had left Christchurch when I visited the University of Canterbury and I never got back to Purdue where he finished his carreer. Our last meeting took place in 2013, for the O’Bayes 2013 conference in Duke. Sadly impacted by the passing away of Dennis Lindley. Farewell, John, for this long trip on the Bayes bus!

[Here the obituary posted on the Purdue Statistics Department Website]

Dr. John Joseph Deely, 92, retired Continuing Lecturer in the Department of Statistics, passed away on January 17, 2025, at his home in West Lafayette, Indiana. Over his decades-long career, John shaped the field of statistics through his teaching, research, and mentoring, leaving an indelible impact on his students, colleagues, and the broader academic community. He will be deeply missed.

John was born in Cleveland, Ohio, on January 13, 1933. He earned an Electrical Engineering degree from Georgia Tech before pursuing his passion for mathematics and statistics at Purdue University, where he completed his M.S. in Mathematics in 1958 and a Ph.D. in Statistics in 1965 under the supervision of Professor Shanti S. Gupta. John’s career took him from Sandia Corporation in Albuquerque, where he worked on cutting-edge research in the space age, to the University of Canterbury in New Zealand, where he spent 28 years growing the statistics program and mentoring generations of students. Under his leadership, the program expanded from a single course with 100 students to a thriving department with eight courses and hundreds of students. In recognition of his contributions, he was promoted rapidly, ultimately serving as Chair of Statistics.

In 1997, John returned to Purdue, where he became a beloved Continuing Lecturer, primarily teaching STAT 113: Statistics and Society. With his sharp wit and engaging teaching style, he introduced thousands of students to the power of statistical reasoning. In his words, “They hate numbers. They hate data. The challenge is can you somehow give such students a little appreciation in statistical reasoning in spite of their hatred of numbers. Can you make it interesting enough? I’m always looking for funny ways, ways in which people abuse statistics.” He was known for his humor, real-world examples, and ability to make statistics both accessible and compelling. Beyond the classroom, he remained an active researcher, collaborating with colleagues worldwide on Bayesian methods, empirical Bayes, and statistical decision theory. His presence at Bayesian meetings often meant that there would be some form of entertainment that involved his ability to make people laugh, as in the presentation of the Delly Awards with Ed George. He retired at the remarkable age of 85.

John is survived by his dear wife of 35 years, Elizabeth “Ann” Young Ann, his six children and their spouses from his first marriage to Anola, eight grandchildren, two great-grandchildren, two stepchildren, and two step-grandchildren. He treasured his family and the life he built with Ann, finding joy in their years together. At this time, no service will be held. May John’s memory bring comfort to all who knew him and inspire future generations in the pursuit of knowledge.

Hamiltonian MC on discrete spaces [a reply from the authors]

Posted in Books, pictures, Statistics, University life with tags , , , , , on July 8, 2017 by xi'an

Q. Why not embed discrete parameters so that the resulting surrogate density function is smooth?

A. This is only possible in very special settings. Let’s say we have a target distribution π(θ, n), where θ is continuous and ‘n’ is discrete. To construct a surrogate smooth density, we would need to somehow smoothly interpolate a collection of functions fn(θ) = π(θ, n) for n = 1, 2, …. It is not clear to us how we can achieve this in a general and tractable way.

Q. How to generalize the algorithm to a more complex parameter space?

A. We provide a clear solution to dealing with a discontinuous target density defined on a continuous parameter space. We agree, however, that there remains the question of whether and how a more complex parameter space can be embedded into a continuous space. This certainly deserves a further investigation. For example, a binary tree can be embedded in to an interval [0,1] through a dyadic expansion of a real number.

Q. Physical intuition of discontinuous Hamiltonian dynamics is not clear from a theory of differential measure-valued equation and selection principle.

A. Hamiltonian dynamics with a discontinuous potential energy has long been used by physicists as a natural model for some physical phenomena (also known as “impulsive systems”). The main difference from a smooth system is that a gradient become a “delta function” at the discontinuity, causing an instantaneous “push” toward the direction of lower potential energy. A theory of differential measure-valued equation / inclusion and selection principle is only a mathematical formalization of such physical systems.

Q. (A special case of) DHMC looks like taking multiple Gibbs steps?

A. The crucial difference from Metropolis-within-Gibbs is the presence of momentum in DHMC, which helps guide a Markov chain toward a high density region.

The effect of momentum is evident in the Jolly-Seber example of Section 5.1, where DHMC shows 60-fold efficiency improvement over a sampler “NUTS-Gibbs” based on conditional updates. Also, a direct comparison of DHMC and Metropolis-within-Gibbs can be found in Section S4.1 where DHMC, thanks to the momentum, is about 7 times more efficient than Metropolis-within-Gibbs (with optimal proposal variances).

Q. Unlike HMC, DHMC does not seem to use structural information about the parameter space and local information about the target density?

A. It does. After all, other than the use of Laplace momentum and discontinuity in the target density, DHMC is based on the same principle as HMC — simulating Hamiltonian dynamics to generate a proposal.

The confusion is perhaps due to the fact that the coordinate-wise integrator of DHMC does not require gradients. The gradient of the log density — which may be a “delta” function at discontinuities — plays a clear role if you look at Hamilton’s equations Eq (10) corresponding to a Laplace momentum. It’s just that, thanks to a property of a Laplace momentum and conservation of energy principle, we can approximate the exact dynamics without ever computing the gradient. This is in fact a remarkable property of a Laplace momentum and our coordinate-wise integrator.

Alan Gelfand in Paris

Posted in pictures, Statistics, Travel, University life with tags , , , , , , , on May 11, 2017 by xi'an

Alan Gelfand (Duke University) will be in Paris on the week of May 15 and give several seminars, including one at AgroParisTech on May 16:

Modèles hiérarchiques

and on at CREST (BiPS)  on May 18, 2pm:

Scalable Gaussian processes for analyzing space and space-time datasets

[more] parallel MCMC

Posted in Books, Mountains with tags , , , , , , , , , , on April 3, 2014 by xi'an

Scott Schmidler and his Ph.D. student Douglas VanDerwerken have arXived a paper on parallel MCMC the very day I left for Chamonix, prior to MCMSki IV, so it is no wonder I missed it at the time. This work is somewhat in the spirit of the parallel papers Scott et al.’s consensus Bayes,  Neiswanger et al.’s embarrassingly parallel MCMC, Wang and Dunson’s Weierstrassed MCMC (and even White et al.’s parallel ABC), namely that the computation of the likelihood can be broken into batches and MCMC run over those batches independently. In their short survey of previous works on parallelization, VanDerwerken and Schmidler overlooked our neat (!) JCGS Rao-Blackwellisation with Pierre Jacob and Murray Smith, maybe because it sounds more like post-processing than genuine parallelization (in that it does not speed up the convergence of the chain but rather improves the Monte Carlo usages one can make of this chain), maybe because they did not know of it.

“This approach has two shortcomings: first, it requires a number of independent simulations, and thus processors, equal to the size of the partition; this may grow exponentially in dim(Θ). Second, the rejection often needed for the restriction doesn’t permit easy evaluation of transition kernel densities, required below. In addition, estimating the relative weights wi with which they should be combined requires care.” (p.3)

The idea of the authors is to replace an exploration of the whole space operated via a single Markov chain (or by parallel chains acting independently which all have to “converge”) with parallel and independent explorations of parts of the space by separate Markov chains. “Small is beautiful”: it takes a shorter while to explore each set of the partition, hence to converge, and, more importantly, each chain can work in parallel to the others. More specifically, given a partition of the space, into sets Ai with posterior weights wi, parallel chains are associated with targets equal to the original target restricted to those Ai‘s. This is therefore an MCMC version of partitioned sampling. With regard to the shortcomings listed in the quote above, the authors consider that there does not need to be a bijection between the partition sets and the chains, in that a chain can move across partitions and thus contribute to several integral evaluations simultaneously. I am a bit worried about this argument since it amounts to getting a random number of simulations within each partition set Ai. In my (maybe biased) perception of partitioned sampling, this sounds somewhat counter-productive, as it increases the variance of the overall estimator. (Of course, not restricting a chain to a given partition set Ai has the incentive of avoiding a possibly massive amount of rejection steps. It is however unclear (a) whether or not it impacts ergodicity (it all depends on the way the chain is constructed, i.e. against which target(s)…) as it could lead to an over-representation of some boundaries and (b) whether or not it improves the overall convergence properties of the chain(s).)

“The approach presented here represents a solution to this problem which can completely remove the waiting times for crossing between modes, leaving only the relatively short within-mode equilibration times.” (p.4)

A more delicate issue with the partitioned MCMC approach (in my opinion!) stands with the partitioning. Indeed, in a complex and high-dimension model, the construction of the appropriate partition is a challenge in itself as we often have no prior idea where the modal areas are. Waiting for a correct exploration of the modes is indeed faster than waiting for crossing between modes, provided all modes are represented and the chain for each partition set Ai has enough energy to explore this set. It actually sounds (slightly?) unlikely that a target with huge gaps between modes will see a considerable improvement from the partioned version when the partition sets Ai are selected on the go, because some of the boundaries between the partition sets may be hard to reach with a off-the-shelf proposal. (Obviously, the second part of the method on the adaptive construction of partitions is yet in the writing and I am looking forward its aXival!)

Furthermore, as noted by Pierre Jacob (of Statisfaction fame!), the adaptive construction of the partition has a lot in common with Wang-Landau schemes. Which goal is to produce a flat histogram proposal from the current exploration of the state space. Connections with Atchadé’s and Liu’s (2010, Statistical Sinica) extension of the original Wang-Landau algorithm could have been spelled out. Esp. as the Voronoï tessellation construct seems quite innovative in this respect.