Archive for time series
Venice time series workshop
Posted in pictures, Statistics, Travel, University life with tags asymptotics, Ca' Foscari University, distribution-free inference, econometrics, ERC, instrumental variables, Italia, stationarity, time series, unit roots, Università Ca' Foscari Venezia, Venice, workshop on May 25, 2026 by xi'an
sample-efficient inference for simulators: complex noise models and time-series [One World ABC seminar]
Posted in Statistics with tags Gaussian processes, likelihood-free inference, One World ABC Seminar, simulator, simulator model, time series, webinar on February 18, 2023 by xi'anThe next One World ABC seminar will take place next Thursday, 23 Feb, at 9:30 UK time, with a talk by Alexander Aushev, on the above, based on a paper with Tran, Pesonen, Howes, and Kaski:
Simulators are becoming more complex, with their parameter inference requiring as few simulations as possible. This talk will go over two likelihood-free inference (LFI) challenges for computationally intensive simulators. The first challenge is modeling complex simulator noise, which is frequently oversimplified by existing methods or needs far too many simulations. I will discuss how LFI can handle multimodal, non-stationary, and heteroscedastic noise distributions in Bayesian Optimization by using deep Gaussian processes as surrogate models. The second challenge involves simulators in time-series settings, in which the observed time-series data is generated by an unknown stochastic process of simulator parameters. Modern LFI methods, in such cases, either require an accurate model of parameter transition dynamics (e.g. available for sampling) or assume it to be linear. In the last part of the talk, I will discuss the challenges and solutions for performing LFI in such time-series settings, which involve learning the unknown transition dynamics of simulator parameters.
ABC forecasts
Posted in Books, pictures, Statistics with tags ABC, ABC consistency, Australia, forecasting, MCMC convergence, Monash University, prediction, state space model, time series on January 9, 2018 by xi'an
My friends and co-authors David Frazier, Gael Martin, Brendan McCabe, and Worapree Maneesoonthorn arXived a paper on ABC forecasting at the turn of the year. ABC prediction is a natural extension of ABC inference in that, provided the full conditional of a future observation given past data and parameters is available but the posterior is not, ABC simulations of the parameters induce an approximation of the predictive. The paper thus considers the impact of this extension on the precision of the predictions. And argues that it is possible that this approximation is preferable to running MCMC in some settings. A first interesting result is that using ABC and hence conditioning on an insufficient summary statistic has no asymptotic impact on the resulting prediction, provided Bayesian concentration of the corresponding posterior takes place as in our convergence paper under revision.
“…conditioning inference about θ on η(y) rather than y makes no difference to the probabilistic statements made about [future observations]”
The above result holds both in terms of convergence in total variation and for proper scoring rules. Even though there is always a loss in accuracy in using ABC. Now, one may think this is a direct consequence of our (and others) earlier convergence results, but numerical experiments on standard time series show the distinct feature that, while the [MCMC] posterior and ABC posterior distributions on the parameters clearly differ, the predictives are more or less identical! With a potential speed gain in using ABC, although comparing parallel ABC versus non-parallel MCMC is rather delicate. For instance, a preliminary parallel ABC could be run as a burnin’ step for parallel MCMC, since all chains would then be roughly in the stationary regime. Another interesting outcome of these experiments is a case when the summary statistics produces a non-consistent ABC posterior, but still leads to a very similar predictive, as shown on this graph.
This unexpected accuracy in prediction may further be exploited in state space models, towards producing particle algorithms that are greatly accelerated. Of course, an easy objection to this acceleration is that the impact of the approximation is unknown and un-assessed. However, such an acceleration leaves room for multiple implementations, possibly with different sets of summaries, to check for consistency over replicates.
Bayesian Essentials with R [book review]
Posted in Books, R, Statistics, University life with tags Bayesian Core, Bayesian Essentials with R, book review, Jean-Michel Marin, Kent State University, R, Technometrics, time series on July 28, 2016 by xi'an[A review of Bayesian Essentials that appeared in Technometrics two weeks ago, with the first author being rechristened Jean-Michael!]
“Overall this book is a very helpful and useful introduction to Bayesian methods of data analysis. I found the use of R, the code in the book, and the companion R package, bayess, to be helpful to those who want to begin using Bayesian methods in data analysis. One topic that I would like to see added is the use of Bayesian methods in change point problems, a topic that we found useful in a recent article and which could be added to the time series chapter. Overall this is a solid book and well worth considering by its intended audience.”
David E. BOOTH
Kent State University
Nonlinear Time Series just appeared
Posted in Books, R, Statistics, University life with tags book review, CHANCE, EM algorithm, Eric Moulines, Markov chains, MCMC, Monte Carlo Statistical Methods, nonlinear time series, particle filters, pMCMC, R, Randal Douc, sequential Monte Carlo, simulation, statistical inference, time series on February 26, 2014 by xi'an
My friends Randal Douc and Éric Moulines just published this new time series book with David Stoffer. (David also wrote Time Series Analysis and its Applications with Robert Shumway a year ago.) The books reflects well on the research of Randal and Éric over the past decade, namely convergence results on Markov chains for validating both inference in nonlinear time series and algorithms applied to those objects. The later includes MCMC, pMCMC, sequential Monte Carlo, particle filters, and the EM algorithm. While I am too close to the authors to write a balanced review for CHANCE (the book is under review by another researcher, before you ask!), I think this is an important book that reflects the state of the art in the rigorous study of those models. Obviously, the mathematical rigour advocated by the authors makes Nonlinear Time Series a rather advanced book (despite the authors’ reassuring statement that “nothing excessively deep is used”) more adequate for PhD students and researchers than starting graduates (and definitely not advised for self-study), but the availability of the R code (on the highly personal page of David Stoffer) comes to balance the mathematical bent of the book in the first and third parts. A great reference book!
