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likelihood-free posterior density learning at OWABI [30 April, 1pm GMT+1, 2pm CEST, 8am EST]

Posted in pictures, Running, Statistics, Travel, University life with tags , , , , , , , , , , , , , , , , on April 17, 2026 by xi'an

The next OWABI webinar will take place on 30 April, at 1pm Coventry time (2pm in Paris, 8am in Columbus, Ohio) and will feature

Oksana A. Chkrebtii (Ohio State University)

Likelihood-free Posterior Density Learning for Uncertainty Quantification in Inference Problems
Generative models and those with computationally intractable likelihoods are widely used to describe complex systems in the natural sciences, social sciences, and engineering. Fitting these models to data requires likelihood-free inference methods that explore the parameter space without explicit likelihood evaluations, relying instead on sequential simulation, which comes at the cost of computational efficiency and extensive tuning. We develop an alternative framework called kernel-adaptive synthetic posterior estimation (KASPE) that uses deep learning to directly reconstruct the mapping between the observed data and a finite-dimensional parametric representation of the posterior distribution, trained on a large number of simulated datasets. We provide theoretical justification for KASPE and a formal connection to the likelihood-based approach of expectation propagation. Simulation experiments demonstrate KASPE’s flexibility and performance relative to existing likelihood-free methods including approximate Bayesian computation in challenging inferential settings involving posteriors with heavy tails, multiple local modes, and over the parameters of a nonlinear dynamical system.

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Bob’s talk at PariSanté

Posted in Books, Statistics, University life with tags , , , , , , , , , , , , , , , on March 25, 2026 by xi'an

We had a wonderful time (and an unusually large audience) at the mostly Monte Carlo seminar last week as Pierre del Moral and Bob Carpenter both presented on exciting recent developments of theirs! Pierre talked about Kantorovich contraction of Markov semigroups, which sounds rather daunting!, but actually covers fairly general and generic convergence results, using tools like potentials and Lyapunov contractions, reminding me of the early days of MCMC and the papers of Gareth Roberts (University of Warwick), Jeff Rosenthal, Richard Tweedie and others.

Bob then spoke about the latest version of NUTS, the within-orbit adaptive NUTS (WALNUTS) sampler, which adapts the step size at every leapfrog step in order to conserve the Hamiltonian and keep the path stable enough. The adaptation is facilitated by incorporating this step size as an extra parameter with an attached distribution, that the authors call Gibbs self tuning (GIST), for coupling tuning parameters and conditionally Gibbs-sampling them per iteration in Hamiltonian Monte Carlo. This has been done in the past, incl. in some of my papers (e.g., Andrieu & Robert, 2004), but I could not cite a particular reference during the seminar.

Further light reflections that came to mind during Bob’s talk:

  • with NUTS, if cycling is feasible in a finite time, we could wait for a second passage at the starting point and then get back halfway (with the difficulty of detecting this second passage)
  • changing the kinetic matrix at each leapfrog jump is actually Riemannian HMC (and with cubic cost!)
  • the doubling mechanism in both the original NUTS and in biased progressive NUTS is simulation wasting
  • but so is (surprise, surprise!) finding adaptive mass matrices for WALNUTS at reasonable costs

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escaping the dark side of the Moon

Posted in Books, pictures, Statistics, University life with tags , , , , , , , , , , , on March 18, 2026 by xi'an

Sub-Cauchy Sampling: Escaping the Dark Side of the Moon was recently posted on arXiv by Sebastiano Grazzi (Warwick), Sifan Liu, Gareth O. Roberts (Warwick), and Jun Yang. With an hommage to Pink Floyd’s 1973 album both Gareth and I listened to at the time. (This was for sure my first Pink Floyd album!)

This highly original work is a sequel to the stereographic projection paper by Yang, Latuszýnski and Roberts (which was itself vaguely connected to our unpublished origami sampler). As in the stereographic projection method, the Euclidean space supporting the target is turned into a spherical cap of a hyper-sphere, referred to as the complement of the dark side of the Moon (or its bright side), and defined with respect to an observer ο who was at the north pole in the original method. The proposed MCMC algorithm, the Sub-Cauchy Projection Sampler (SCS), is a random-walk-type Metropolis algorithm on the bright side and it gets its name from being uniformly ergodic for sub-Cauchy targets. An explanation for this massive achievement is that points at infinity in the Euclidean space are now mapped to the (d − 1)-dimensional boundary of the dark side rather than at the north pole of the hypersphere. Meaning that the push-forward density may remain bounded. (The random walk on the bright side involves projections for proposals ending on the dark side, while keeping the target intact.) There are several calibration parameters to the algorithm that can be tuned by variational arguments (and the goal of getting near a uniform distribution over the bright side), since optimal acceptance rates no longer apply.

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OWABI⁷, 25 March 2026: Robust Simulation Based Inference (10am EST time)

Posted in Books, Statistics, University life with tags , , , , , , , , , , , , , , , on March 9, 2026 by xi'an

Speaker:  Larry Wasserman (Carnegie Mellon University)

Title: Robust Simulation Based Inference
Abstract: Simulation-Based Inference (SBI) is an approach to statistical inference where simulations from an assumed model are used to construct estimators and confidence sets. SBI is often used when the likelihood is intractable and to construct confidence sets that do not rely on asymptotic methods or regularity conditions. Traditional SBI methods assume that the model is correct, but, as always, this can lead to invalid inference when the model is misspecified. This paper introduces robust methods that allow for valid frequentist inference in the presence of model misspecification. We propose a framework where the target of inference is a projection parameter that minimizes a discrepancy between the true distribution and the assumed model. The method guarantees valid inference, even when the model is incorrectly specified and even if the standard regularity conditions fail. Alternatively, we introduce model expansion through exponential tilting as another way to account for model misspecification. We also develop an SBI based goodness-of-fit test to detect model misspecification. Finally, we propose two ideas that are useful in the SBI framework beyond robust inference: an SBI based method to obtain closed form approximations of intractable models and an active learning approach to more efficiently sample the parameter space.
Keywords: Exponential tilting, model misspecification, robust inference, simulation based inference, valid inference.
Reference: Lorenzo Tomaselli, Valérie Ventura, Larry Wasserman. Robust Simulation Based Inference. Preprint at ArXiv:2508.02404

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explicit convergence bounds for Metropolis

Posted in Books, Statistics, University life with tags , , , , , , , , on March 2, 2026 by xi'an

C\,L\, d\,\sigma^{2}\, e^{-2\, L\, d\,\sigma^{2}}\,\frac{m}{L}\,\frac{1}{d}\leqslant\gamma_{P}\leqslant\min\left\{ \frac{1}{2}\, L\,\sigma^{2},\left(1+m\,\sigma^{2}\right)^{-d/2}\right\}

Last week, our MCMC reading group in PariSanté started reading Explicit convergence bounds for Metropolis Markov chains by my friends Christophe Andrieu, Anthony Lee, Sam Power, and Andi Wang (University of Warwick), recently published in the Annals of Applied Probability. The paper is centred on the bound above. Which may sound cryptic but gives a non-asymptotic explicit bound on the spectral gap γ, when the potential of the target is L-smooth, m-strongly convex and twice continuously differentiable, in dimension d, with a proposal being the Gaussian random walk with scale σ.  With C = 1.972 10⁻⁴. if “possibly a few orders of magnitude larger”. This characterisation of the spectral gap leads to a sharper identification of d⁻¹ as the proper rate for σ². Other consequences are finding the order of the number of simulations to reach a χ² distance of ε,

e^{2\,\varsigma}\,\varsigma\,\kappa\, d\,\left\{ \log d+\log\kappa-\log\varepsilon\right\}

when κ is the condition number L/m and

\sigma^2=\varsigma\, L^{-1}\, d^{-1}

And a bound on the ergodic averages

{\rm var} (Pf )\leqslant10141\,\varsigma\,e^{2\,\varsigma}\,\kappa\, d\,\left\Vert f\right\Vert _{2}^{2}

The technicity of the proof is quite involved, with a special kind of coupling, to the point the authors provide a roadmap, as reproduced left.

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