Archive for ABC
Straßburger Abenrot
Posted in pictures, Running, Travel, University life with tags ABC, Alsace, bitcoin, blockchain, city walk, day trip, German, habilitation, high speed train, homonym, Ill River, jatp, jury, Jussieu, Petite France, Saint Paul's church, Strasbourg, sunset on April 27, 2026 by xi'anlikelihood-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 ABC, Approximate Bayesian computation, Columbus, Coventry, dawn, deep learning, generative model, intractable likelihood, KASPE, Kenilworth, likelihood-free inference, Ohio State University, OWABI, posterior distribution, simulation-based inference, University of Warwick, webinar on April 17, 2026 by xi'anThe 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.
OWABI⁷, 25 March 2026: Robust Simulation Based Inference (10am EST time)
Posted in Books, Statistics, University life with tags ABC, approximate Bayesian inference, arXiv, Carnegie Mellon University, exponential tilting, generalised Bayesian inference, generative model, Larry Wasserman, maximum mean discrepancy, model misspecification, OWABI, robust Bayesian procedures, Safe Anytime-Valid Inference, simulation-based inference, University of Warwick, webinar on March 9, 2026 by xi'anSpeaker: 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
robust simulation-based inference
Posted in Books, pictures, Statistics, University life with tags ABC, Bayesian classification, Bayesian p-values, Carnegie Mellon University, Charlie Geyer, discrepancies, exponential tilting, goodness of fit, intractable likelihood, maximum mean discrepancy, misspecified model, OWABI, Series B, tequila, webinar on March 7, 2026 by xi'anThis new arXival by Lorenzo Tomaselli, Valérie Ventura, and Larry Wasserman (from CMU) considers simulation-based inference under model misspecification (as we did for ABC in our 2020 Series B paper). Which is almost always the case. In the paper, SBI is defined as producing N parameters and N samples from the prior and the corresponding sampling distribution, respectively, and then doubling the resulting samples by permuting at random the parameters θ. This means that the second half is distributed from the product of the prior and of the marginal, hence that the classification odds ratio is equal to the likelihood, hence providing an estimation method (andlikelihood trick) à la Geyer. From this estimate, an ABC p-value can be derived, but it is incorrect as such when the model is misspecified. Hence the use of the Hellinger discrepancy, the power divergence and the kernel distance (or MMD) as alternatives to the misspecified MLE.
The paper then expands on approximating density ratios by virtue of a reproducing kernel Hilbert space, using a Gaussian kernel. (With a nice remark on requiring only one single ratio estimator for all values of θ, albeit in the joint space.) And focus on a studentized MMD estimator (à la e-value) to build a confidence set that remains valid under model misspecification. And without regularity assumptions.
Another approach is further explored, based on exponential tilting—of which I am not a great fan, from being highly dependent on the choice of the pseudo-sufficient statistic to require an intractable normalising constant, to requiring an extra optimization, even though I appreciate the mathematical appeal of the construct. Which seems to require a sample simulation for each value of θ at the learning stage, albeit relying on the same likelihood trick. The appropriateness of the tilting can be tested by a goodness of fit test tailored for the SBI structure, which sounds rather greedy in the required simulations.
Besides the g-and-k distribution example (which, as pointed out several times on the ‘Og, is not intractable, strictly speaking!), the paper studies a mixture example, despite Larry dubbing them as evil as tequila a long while ago! (The paper also offers a section called accoutrements, which is my first encounter with this use of the term, usually found in medieval contexts!)
Note that Larry will present the paper at the OWABI webinar next 25 March!
OWABI⁷, 26 February 2026: Prequential posteriors (11am UK time)
Posted in Books, Statistics, University life with tags ABC, approximate Bayesian inference, diffusion model, generalised Bayesian inference, generative model, OWABI, prequential loss, reinforcement learning, score function, sequential ABC, sequential Monte Carlo, simulation-based inference, SMC, University of Warwick, webinar on February 25, 2026 by xi'anSpeaker: Shreya Sinha Roy (University of Warwick)
Title: Prequential posteriors
Abstract: Data assimilation is a fundamental task in updating forecasting models upon observing new data, with applications ranging from weather prediction to online reinforcement learning. Deep generative forecasting models (DGFMs) have shown excellent performance in these areas, but assimilating data into such models is challenging due to their intractable likelihood functions. This limitation restricts the use of standard Bayesian data assimilation methodologies for DGFMs. To overcome this, we introduce prequential posteriors, based upon a predictive-sequential (prequential) loss function; an approach naturally suited for temporally dependent data which is the focus of forecasting tasks. Since the true data-generating process often lies outside the assumed model class, we adopt an alternative notion of consistency and prove that, under mild conditions, both the prequential loss minimizer and the prequential posterior concentrate around parameters with optimal predictive performance. For scalable inference, we employ easily parallelizable wastefree sequential Monte Carlo (SMC) samplers with preconditioned gradient-based kernels, enabling efficient exploration of high-dimensional parameter spaces such as those in DGFMs. We validate our method on both a synthetic multi-dimensional time series and a real-world meteorological dataset; highlighting its practical utility for data assimilation for complex dynamical systems.
Keywords: diffusion models, simulation based inference, sequential methods.
Reference: S. S. Roy, R. Everitt, C. P Robert, R. Dutta. Prequential posteriors. Preprint at ArXiv:2511.17721, 202
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