Archive for climate modelling

March(es) for Science

Posted in Statistics with tags , , , , , , , on April 22, 2017 by xi'an

Today there are around 500 marches for Science organised around the World (incl. on in Kangerlussuaq, Qeqqata, Greenland!). Primarily to protest the unprecedented attacks of trumpism on science, scientific values, and scientists, and not only through budget cuts, agency closures, public data erasures, but also denegation of scientific expertise and data to advance financial and partisan interests against climate, water preservation, minorities rights, women equality, and international relations. Being now at a remote retreat in Northern Wales, I will walk virtually at the Cardiff March for Science.

early rejection MCMC

Posted in Books, Statistics, University life with tags , , , , , , , , on June 16, 2014 by xi'an

In a (relatively) recent Bayesian Analysis paper on efficient MCMC algorithms for climate models, Antti Solonen, Pirkka Ollinaho, Marko Laine, Heikki Haario, Johanna Tamminen and Heikki Järvinen propose an early rejection scheme to speed up Metropolis-Hastings algorithms. The idea is to consider a posterior distribution (proportional to)

\pi(\theta|y)= \prod_{k=1}^nL_i(\theta|y)

such that all terms in the product are less than one and to compare the uniform u in the acceptance step of the Metropolis-Hastings algorithm to


then, if u is smaller than the ratio, to


and so on, until the new value has been rejected or all terms have been evaluated. The scheme obviously stops earlier than the regular Metropolis-Hastings algorithm, at no significant extra cost when the product above does not factor through a sufficient statistic. Solonen et al.  suggest ordering the terms so that the computationally simpler ones are computed first. The upper bound assumption requires and is equivalent to finding the maximum on each term of the product, though, which may be costly in its own for non-standard distributions. With my students Marco Banterle and Clara Grazian, we actually came upon this paper when preparing our delayed acceptance paper as (a) it belongs to the same category of accelerated MCMC methods (delayed acceptance and early rejection are somehow synonymous!) and (b) it mentions the early prefetching papers of Brockwell (2005) and Strid (2009).

“The acceptance probability in ABC is commonly very low, and many proposals are rejected, and ER can potentially help to detect the rejections sooner.”

In the conclusion, Solonen et al. point out a possible link with ABC but, apart from the general idea of rejecting earlier by looking at a subsample or at a proxy simulation of a summary statistics, which is also the idea at the core of Dennis Prangle’s lazy ABC, there is no obvious impact on a likelihood-free method like ABC.

simulating Nature

Posted in Books, Statistics with tags , , , , , , , , , , , , , , , on July 25, 2012 by xi'an

This book, Simulating Nature: A Philosophical Study of Computer-Simulation Uncertainties and Their Role in Climate Science and Policy Advice, by Arthur C. Petersen, was sent to me twice by the publisher for reviewing it for CHANCE. As I could not find a nearby “victim” to review the book, I took it with me to Australia and read it by bits and pieces along the trip.

“Models are never perfectly reliable, and we are always faced with ontic uncertainty and epistemic uncertainty, including epistemic uncertainty about ontic uncertainty.” (page 53)

The author, Arthur C. Petersen, was a member of the United Nations’ Intergovernmental Panel on Climate Change (IPCC) and works as chief scientist at the PBL Netherlands Environmental Assessment Agency. He mentions that the first edition of this book, Simulating Nature, has achieved some kind of cult status, while being now out of print,  which is why he wrote this second edition. The book centres on the notion of uncertainty connected with computer simulations in the first part (pages 1-94) and on the same analysis applied to the simulation of climate change, based on the experience of the author, in the second part (pages 95-178). I must warn the reader that, as the second part got too focussed and acronym-filled for my own taste, I did not read it in depth, even though the issues of climate change and of the human role in this change are definitely of interest to me. (Readers of CHANCE must also realise that there is very little connection with Statistics in this book or my review of it!) Note that the final chapter is actually more of a neat summary of the book than a true conclusion, so a reader eager to get an idea about the contents of the book can grasp them through the eight pages of the eighth chapter.

“An example of the latter situation is a zero-dimensional (sic) model that aggregates all surface temperatures into a single zero-dimensional (re-sic) variable of globally averaged surface temperature.” (page 41)

The philosophical questions of interest therein are that a computer simulation of reality is not reproducing reality and that the uncertainty(ies) pertaining to this simulation cannot be assessed in its (their) entirety. (This the inherent meaning of the first quote, epistemic uncertainty relating to our lack of knowledge about the genuine model reproducing Nature or reality…) The author also covers the more practical issue of the interface between scientific reporting and policy making, which reminded me of Christl Donnelly’s talk at the ASC 2012 meeting (about cattle epidemics in England). The book naturally does not bring answers to any of those questions, naturally because a philosophical perspective should consider different sides of the problem, but I find it more interested in typologies and classifications (of types of uncertainties, in crossing those uncertainties with panel attitudes, &tc.) than in the fundamentals of simulation. I am obviously incompetent in the matter, however, as a naïve bystander, it does not seem to me that the book makes any significant progress towards setting epistemological and philosophical foundations for simulation. The part connected with the author’s implication in the IPCC shed more light on the difficulties to operate in committees and panels made of members with heavy political agendas than on the possible assessments of uncertainties within the models adopted by climate scientists…With the same provision as above, the philosophical aspects do not seem very deep: the (obligatory?!) reference to Karl Popper does not bring much to the debate, because what is falsification to simulation? Similarly, Lakatos’ prohibition of “direct[ing] the modus tollens at [the] hard core” (page 40) does not turn into a methodological assessment of simulation praxis.

“I argue that the application of statistical methods is not sufficient for adequately dealing with uncertainty.” (page 18)

“I agree (…) that the theory behind the concepts of random and systematic errors is purely statistical and not related to the locations and other dimensions of uncertainty.” (page 55)

Statistics is mostly absent from the book, apart from the remark that statistical uncertainty (understood as the imprecision induced by a finite amount of data) differs from modelling errors (the model is not reality), which the author considers cannot be handled by statistics (stating that Deborah Mayo‘s theory of statistical error analysis cannot be extended to simulation, see the footnote on page 55). [In other words, this book has no connection with Monte Carlo Statistical Methods! With or without capitals… Except for a mention of `real’ random number generators on—one of many—footnotes on page 35.]  Mention is made of “subjective probabilities” (page 54), presumably meaning a Bayesian perspective. But the distinction between statistical uncertainty and scenario uncertainty which “cannot be adequately described in terms of chances or probabilities” (page 54) misses the Bayesian perspective altogether, as does the following sentence that “specifying a degree of probability or belief [in such uncertainties] is meaningless since the mechanism that leads to the events are not sufficiently known” (page 54).

“Scientists can also give their subjective probability for a claim, representing their estimated chance that the claim is true. Provided that they indicate that their estimate for the probability is subjective, they are then explicitly allowing for the possibility that their probabilistic claim is dependent on expert judgement and may actually turn out to be false.” (page 57)

In conclusion, I fear the book does not bring enough of a conclusion on the philosophical justifications of using a simulation model instead of the actual reality and on the more pragmatic aspects of validating/invalidating a computer model and of correcting its imperfections with regards to data/reality. I am quite conscious that this is an immensely delicate issue and that, were it to be entirely solved, the current level of fight between climate scientists and climatoskeptics would not persist. As illustrated by the “Sound Science debate” (pages 68-70), politicians and policy-makers are very poorly equipped to deal with uncertainty and even less with decision under uncertainty. I however do not buy the (fuzzy and newspeak) concept of “post-normal science” developed in the last part of Chapter 4, where the scientific analysis of a phenomenon is abandoned for decision-making, “not pretend[ing] to be either value-free or ethically neutral” (page 75).

MCMC at ICMS (3)

Posted in pictures, Statistics, Travel, University life with tags , , , , , , , , , , , , , , , on April 26, 2012 by xi'an

The intense pace of the two first days of our workshop on MCMC at ICMS had apparently taken an heavy toll on the participants as a part of the audience was missing this morning! Although not as a consequence of the haggis of the previous night at the conference dinner, nor even as a result of the above pace. In fact, the missing participants had opted ahead of time for leaving the workshop early, which is understandable given everyone’s busy schedule, esp. for those attending both Bristol and Edinburgh workshops, however slightly impacting the atmosphere of the final day. (Except for Mark Girolami who most unfortunately suffered such a teeth infection that he had to seek urgent medical assistance yesterday afternoon. Best wishes to Mark for a prompt recovery, say I with a dental appointment tomorrow…!)

The plenary talk of the day was delivered by Heikki Haario, who provided us with a survey of the (adaptive) MCMC advances he and his collaborators had made in the analysis of complex and immensely high-dimensional weather models. This group of Finnish researchers, who started from inverse problem analysis rather than from MCMC, have had a major impact on the design and validation of adaptive MCMC algorithms, especially in the late 1990’s. (Heikki also was a co-organizer of the Adap’ski workshops, workshops that may be continued, stay tuned!) The next talk, by Marko Laine, was also about adaptive MCMC algorithms, with the difference that the application was climate modelling. It contained interesting directions about early stopping (“early rejection”, as opposed to “delayed rejection”) of diverging proposals (gaining 80% in computing time!) and about parallel adaptation. Still in the same theme, Gersende Fort explained the adaptive version of the equi-energy sampler she and co-authors had recently developed. Although she had briefly presented this paper in Banff a month ago, I found the talk quite informative about the implementation of the method and at the perfect technical level (for me!).

In [what I now perceive as] another recurrent theme of the workshop, namely the recourse to Gaussian structures like Gaussian processes (see, e.g., Ian Murray’s talk yesterday), Andrew Stuart gave us a light introduction to random walk Metropolis-Hastings algorithms on Hilbert spaces. In particular, he related to Ian Murray’s talk of yesterday as to the definition of a “new” random walk (due to Radford Neal)  that makes a proposal

y=\sqrt{1-\beta^2}x_{t-1}+\beta\zeta\quad 0<\beta<1,\zeta\sim\varphi(|\zeta|)

that still preserves the acceptance probability of the original (“old”) random walk proposal. The final talks of the morning were Krys Latuszynski’s and Nick Whiteley’s very pedagogical presentations of the convergence properties of manifold MALA and of particle filters for hidden Markov models.  In both cases, the speakers avoided the overly technical details and provided clear intuition in the presented results, a great feat after those three intense days of talks! (Having attended Nick’s talk in Paris two weeks ago helped of course.)

Unfortunately, due to very limited flight options (after one week of traveling around the UK) and also being slightly worried at the idea of missing my flight!, I had to leave the meeting along with all my French colleagues right after Jean-Michel Marin’s talk on (hidden) Potts driven mixtures, explaining the computational difficulties in deriving marginal likelihoods. I thus missed the final talk of the workshop by Gareth Tribello. And delivering my final remarks at the lunch break.

Overall, when reflecting on those two Monte Carlo workshops, I feel I preferred the pace of the Bristol workshop, because it allowed for more interactions between the participants by scheduling less talks… This being said, the organization at ICMS was superb (as usual!) and the talks were uniformly very good so it also was a very profitable meeting, of a different kind! As written earlier, among other things, it induced (in me) some reflections on a possible new research topic with friends there. Looking forward to visit Scotland again, of course!