Pith. sign in

REVIEW 3 major objections 6 minor 53 references

Likelihood-Free Adaptive Bayesian Inference via Nonparametric Distribution Matching

T0 review · 3 major / 6 minor · reviewed 2026-08-15 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read ABI claims that likelihood-free inference can be made efficient and exact in the limit by comparing posterior distributions with a marginally-augmented sliced Wasserstein distance estimated by conditional quantile regression.

desk verdict A novel and empirically strong ABC method whose headline convergence theorem is unproven for p>1 due to a false convexity inequality; deserves peer review but needs a fix or a caveat. read the letter →

arxiv 2505.04603 v1 pith:ZB6L4JOG submitted 2025-05-07 stat.ME cs.LGstat.COstat.ML

Wenhui Sophia Lu , Wing Hung Wong This is my paper · ORCID
classification stat.MEcs.LGstat.COstat.ML MSC 62F1562G0862G05
keywords approximateBayesiancomputationlikelihood-freeinferenceslicedWassersteindistanceconditionalquantileregressionadaptiverejectionsamplinggenerativedensityestimationposteriormatchingsimulator-based
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Adaptive Bayesian Inference (ABI) is a new likelihood-free inference method that replaces the usual comparison of simulated and observed data with a direct comparison of the posterior distributions those data would induce. The paper claims this posterior-space comparison is more robust than data-space discrepancies when sample sizes are small, observations are dependent, or parameters are non-identifiable. It proves that, using the oracle distance, the ABI posterior converges weakly to the true posterior as the tolerance threshold shrinks to zero, and that a trimmed version of its new distance can be estimated at the parametric rate $O(m^{-1/2})$ when $p=1$. The practical algorithm estimates the distance by conditional quantile regression and refines proposals through adaptive rejection sampling with generative density estimation. A sympathetic reader would care because this recasts a notoriously inefficient rejection problem as a supervised learning problem with sequential refinement.

What carries the argument

The load-bearing object is the Marginally-augmented Sliced Wasserstein distance, defined as a convex combination of the average trimmed $p$-Wasserstein distance between coordinate marginals and the sliced $p$-Wasserstein distance averaged over random sphere projections. Its quantile representation rewrites univariate Wasserstein distances as $L^p$ differences of quantile functions, so computing MSW between posteriors becomes a sequence of one-dimensional conditional quantile regression tasks solved by a single shared ReLU network. The other component is adaptive rejection sampling: at each iteration a budget-constrained rejection step samples from the joint proposal, parameters are pruned by the estimated MSW threshold, and a generative model fitted to the accepted draws becomes the next proposal. This mechanism converts posterior matching into a supervised distributional regression problem and permits sequential refinement without explicit prior density evaluation.

What would settle it

For a model with a tractable exact posterior, compute the oracle MSW distance between posteriors for simulated datasets close to $x^*$ and compare it to the quantile-network estimate; if the network systematically misorders candidate datasets near $x^*$, ABI's acceptance region is mis-specified and its output will diverge from the true posterior even as the tolerance shrinks.

Watch

Extended reading notes

Core claim

The central claim is that approximate Bayesian inference can be done by matching full posterior distributions rather than data summaries. ABI defines the approximate posterior as the law of $\theta$ conditional on the event that the simulated data's induced posterior $\pi(\theta \mid X)$ lies within tolerance $\epsilon$ of the observed posterior $\pi(\theta \mid x^*)$ under the Marginally-augmented Sliced Wasserstein (MSW) distance. Theorem 3.5 shows that as $\epsilon \downarrow 0$ this oracle ABI posterior converges weakly in $P_p(\Omega)$ to the true posterior $\pi(\theta \mid x^*)$. The MSW distance is a metric that metrizes weak convergence on $P_p(\mathbb{R}^d)$, is an integral probability metric when $p=1$, and its trimmed empirical version converges to the population value at rate $O(m^{-1/(2p)})$, recovering the parametric rate at $p=1$. These guarantees are established for the oracle distance; the implemented algorithm replaces it with a quantile-regression network estimate.

Load-bearing premise

The approximate algorithm's accuracy depends on the quantile regression network estimating the true MSW distance accurately, especially near observed $x^*$; the paper proves guarantees for the oracle MSW only, not for the network-estimated version.

Editorial extensions

If this is right

  • When the data are fixed and the tolerance vanishes, the oracle ABI posterior converges weakly to the exact posterior instead of merely to a summary-based approximation.
  • The trimmed MSW distance can be estimated from finite samples at the parametric $O(m^{-1/2})$ rate for $p=1$, whereas ordinary Wasserstein ABC suffers the slow $O(n^{-1/s})$ rate for data dimension $s\ge 3$.
  • Because samples are compared in posterior space, ABI remains meaningful for small observed sample sizes, dependent observations, and non-identifiable parameters where data-space IPM comparisons degrade.
  • The approximate rejection sampling error decays exponentially in the simulation budget $R$ under a local-positivity condition, so the adaptive scheme's bias can be controlled explicitly.
  • The sequential generative update allows inference when the prior is intractable, requiring only a simulator for the prior rather than its density.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the quantile-network estimate is accurate, the same posterior-matching kernel could be plugged into sequential Monte Carlo or population Monte Carlo schemes; the paper suggests this direction but does not develop it.
  • The key open question the theory leaves is whether the MSW estimate from the network is close enough to the oracle; a direct numerical comparison of estimated vs oracle MSW near $x^*$ would test this and could guide network capacity and tolerance schedules.
  • One could test whether the marginal augmentation term or the sliced term drives the empirical gains by ablating $\lambda$; the paper reports performance for fixed choices but does not isolate these contributions.
  • The posterior-space view suggests a general recipe: any distributional metric with a quantile or dual representation could replace data-space discrepancies; comparing MSW with an energy-distance analogue would clarify how much of the gain is specific to slicing versus posterior matching itself.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. The paper introduces Adaptive Bayesian Inference (ABI), a likelihood-free inference framework that replaces data-space ABC discrepancies with a distance between posterior distributions, called the Marginally-augmented Sliced Wasserstein (MSW) distance. MSW combines coordinate marginals with random one-dimensional projections and admits a quantile representation, which the authors estimate by deep conditional quantile regression. The algorithm performs adaptive rejection sampling with decreasing tolerance thresholds and updates proposals via generative density estimation. The theoretical sections establish metricity, an IPM representation for p=1, topological equivalence with the Wasserstein distance, a convergence rate for the empirical trimmed MSW distance, and convergence of the oracle ABI posterior to the true posterior as the tolerance vanishes. Experiments compare ABI with WABC, ABC-SS, SNLE, SNPE, and WGAN-GP on four benchmark models.

Significance. The posterior-space matching idea is timely and potentially influential: it avoids hand-crafted summary statistics, remains meaningful for non-identifiable parameters and dependent observations, and the reduction of MSW to conditional quantile regression is a clean and practical algorithmic insight. The martingale-based proof of ABC posterior continuity (Theorem 3.6) is a genuine technical contribution. The empirical study is broad and the results are encouraging. However, the central theoretical guarantee is currently established only for p=1 in the oracle setting, and the implemented quantile-network estimator is not covered by the stated convergence theorems; these gaps must be repaired before the paper's main claims are fully supported.

major comments (3)
  1. [Section 3.2 / Appendix E.3.1, Eq. (E.16)] Theorem 3.5 is stated for all p in [1,∞), but the proof hinges on inequality (E.16), which is a Jensen-type convexity inequality for MSW_p in its first argument. This inequality is valid for p=1, since W_1 and hence MSW_1 admit an IPM dual representation (Theorem 3.1), but it fails for p>1. For example, on R with d=1, take mu1=delta_0, mu2=delta_2, nu=delta_0, and lambda=1/2; then 0.5*W_2(delta_0,nu)+0.5*W_2(delta_2,nu)=1, while W_2(0.5*delta_0+0.5*delta_2,nu)=sqrt(2)>1. Since W_2=MSW_2 for d=1, Eq. (E.16) is false for p>1, and no alternative proof for p>1 is supplied. This is a load-bearing gap in the oracle convergence guarantee. Please either restrict Theorem 3.5 to p=1, or prove convergence for p>1 through a different argument, for example by combining Theorem 3.6 with a separate bound on MSW_p(pi_{Theta|X in A_epsilon}, pi*) that does not use the Jensen step.
  2. [Sections 2.1.2 and 2.2 vs. Theorems 3.4 and 3.5] The theoretical guarantees in Theorems 3.4 and 3.5 concern the oracle MSW distance, while the deployed algorithm (Algorithm 2, Eq. (2.4)) uses the estimated distance \hat{MSW}_{p,delta,K,H} obtained from a neural quantile regression network trained on samples from the current proposal. The manuscript provides no bound on the error between \hat{MSW} and the true MSW, and no statement that the estimated acceptance region approximates the oracle region A_t. Consequently, Theorem 2.2 (the sample complexity of ARS) and Theorem 3.5 do not apply to the implemented procedure, and the sequence of partial posteriors could be driven by a systematically biased metric. Please either provide an estimation-error bound under the stated network and training assumptions, or clearly state in Sections 2 and 5 that the convergence guarantees apply only to the oracle MSW and that the neural estimator is an approximation validated only empirically.
  3. [Section 3.1.2, Theorem 3.4 and Remark 3.2] The advertised parametric rate O(m^{-1/(2p)}) in Remark 3.2 is a rate for the oracle empirical MSW distance between i.i.d. samples from fixed measures, not for the estimator used in Algorithm 3. The practical estimator additionally depends on the number of projections K, the number of quantile levels H, the network architecture, the Huber threshold kappa, and the optimization error, none of which appear in the bound. Since Algorithm 2 makes acceptance decisions using this estimated distance, the claim that ABI achieves a parametric convergence rate is not supported for the implemented method. The manuscript should either extend the analysis to the full estimator or explicitly restrict the rate claim to the oracle quantity.
minor comments (6)
  1. [Theorem 3.4 and Appendix E.2.5] The symbol delta is used both for the trimming parameter and for the confidence level in the assumptions and in the bound of Theorem 3.4, which makes formulas such as sqrt(log(16d/delta)) ambiguous. Rename the confidence level, for example to eta, and use it consistently with the theorem statement's \bar{delta}.
  2. [Section 2.2.2] In the paragraph on determining the sequence of tolerance levels, the displayed chain is ϵ0(alpha)>ϵ1(alpha)>...>ϵT(alpha), while Algorithm 2 and the surrounding text define the sequence as ϵ1>...>ϵT. Please align the indexing.
  3. [Algorithm 2 and Section 2.1.2] Algorithm 2 line 3 uses the notation pi_X and pi_{x*} before the shorthand pi_x is defined in Section 2.1.2 after Eq. (2.4). Define this notation immediately after Definition 2.2 or when the algorithm is first presented.
  4. [Appendix E.2.3, Proposition E.2] The constant in the proof is written as Cd,lambda, but the symbol Cd,lambda is also used for the constant in Proposition E.1; the proof defines it as ~Cd(1-lambda)^{-1/(d+1)} after previously using Cd,p,lambda. Please use distinct names to avoid confusion.
  5. [Appendix E.3.1] There is a typo in the citation: 'Thoerem 3.4, Kallenberg and Kallenberg 1997' should be 'Theorem 3.4, Kallenberg and Kallenberg (1997)'.
  6. [Table 2] The caption states that the best results are in bold, but for parameters theta2 and theta5 the best values belong to SNLE and WGAN, respectively, and are not bolded. Please either adjust the bolding or clarify the statement in the text.

Circularity Check

0 steps flagged · score 1.0 of 10

No material circularity: the practical ABI loop does not fit the target posterior, and the oracle convergence theorem is a definitional sanity check rather than a fitted prediction; the notable issue is a proof gap for p>1, not circularity.

full rationale

I walked the claimed derivation chain. In the implemented ABI, no parameter is calibrated to the target posterior: the tuning constants (lambda, delta, K, H) are user-chosen, the tolerance sequence is set by empirical quantiles of the estimated MSW values, and the conditional quantile network is trained on samples from the current proposal to estimate conditional quantiles of theta given X, not to match the target posterior. The adaptive refinement uses the algorithm's own previous estimates to update proposals, which is a declared bootstrap; the theoretical guarantees are stated for the oracle MSW, so the practical estimation error is a separate gap, not a circular reduction. The self-citations are non-load-bearing: POTNet (Lu et al., 2025) is only one permissible generative model, and ABC-SS (Jiang et al., 2017) is used as a baseline; the framework and the oracle analysis do not depend on them. The one near-tautological element is Theorem 3.5: the oracle ABI posterior is defined by conditioning on the event MSW_p(pi_{Theta|x}, pi_{Theta|x*}) <= epsilon, so the claimed convergence as epsilon to 0 is, when the proof's Jensen-type inequality (E.16) is valid, a direct consequence of the definition of the acceptance region. This is a sanity-check theorem rather than an independent empirical prediction, and it does not drive the practical claims. Separate correctness note, not circularity: the proof of Theorem 3.5 for p>1 relies on inequality (E.16), which asserts a convexity/Jensen property of MSW_p in its first argument; that property is true for p=1 via the dual representation of W_1 but is false for p>1 (e.g., W_2 on R is not convex in its first argument), so Theorem 3.5 is unproven as stated for p>1. Overall, I find no significant circularity, only a definitional oracle statement and minor non-load-bearing self-citations.

Assumptions & free parameters 7 free parameters · 5 assumptions · 0 invented entities

The central claim (ABI posterior converges to true posterior, and the method outperforms baselines) rests on user-chosen distance hyperparameters, two structural assumptions about the model (finite moment, local positivity), and two unverified bridges between theory and practice: the network's quantile fidelity and a convexity property of MSW_p that only provably holds for p=1. No new physical entities are postulated.

free parameters (7)
  • λ (mixing parameter) = not reported
    User-specified weight between marginal and sliced components in MSW (Eq. 2.2). No default or sensitivity analysis is given.
  • δ (trimming parameter) = not reported
    User-specified trimming fraction in MSW (Definition 2.2). Affects the distance and the constants in Theorem 3.4.
  • K (number of projections) = 5 in experiments
    Number of random slices used to approximate the spherical integral (Algorithm 3).
  • H (number of quantile levels) = 10 in experiments
    Discretization points for quantile integration (Eq. 2.4).
  • α (tolerance quantile threshold) = not reported
    Determines the adaptive tolerance schedule ε_t as the α-th quantile of estimated MSW values (Section 2.2.2).
  • R (rejection budget) = not reported
    Maximum number of simulator calls per parameter draw in Algorithm 4.
  • Network architecture and Huber loss threshold κ = not reported
    Details of the quantile ReLU network and loss smoothness parameter are used in Algorithm 3 but not specified.
assumptions (5)
  • domain assumption Existence of joint density f_Θ,X and marginal f_X with f_X(x*)>0 and f_X continuous at x*
    Invoked in Theorem 3.5 to define the oracle ABI posterior and prove convergence (Section 3.2).
  • domain assumption Moment bound M = sup_x ∫ ||θ||^p f_Θ,X(θ,x) dθ < ∞
    Used in Theorem 3.5 and Theorem 3.6 for convergence in P_p(Ω) (Section 3.2).
  • domain assumption Local Positivity: P_θ(A_t) ≥ c ε_t^γ uniformly over the proposal support
    Assumption 2.1 in Section 2.2.1 is necessary for the ARS bias bound in Theorem 2.2. It may fail for diffuse priors or non-identifiable models.
  • ad hoc to paper The quantile regression network accurately and uniformly estimates the conditional posterior quantiles over the data space region relevant to acceptance
    The practical ABI algorithm replaces true MSW with an estimate from a trained network (Algorithm 3). The theory only treats the oracle MSW, so this fidelity assumption is the bridge between theory and the method as run.
  • ad hoc to paper Convexity inequality MSW_p(∫ π_x dλ, ν) ≤ ∫ MSW_p(π_x, ν) dλ holds for the relevant p
    Used with no proof in Eq. (E.16) of the proof of Theorem 3.5; it holds for p=1 but is false in general for p>1, so Theorem 3.5 is only established for p=1.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Likelihood-Free Adaptive Bayesian Inference via Nonparametric Distribution Matching." pith.science (2026). https://pith.science/paper/ZB6L4JOG

@misc{pith2026250504603,
  author       = {Pith},
  title        = {Pith review of: Likelihood-Free Adaptive Bayesian Inference via Nonparametric Distribution Matching},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZB6L4JOG}},
  note         = {Machine review of arXiv:2505.04603}
}
read the original abstract

When the likelihood is analytically unavailable and computationally intractable, approximate Bayesian computation (ABC) has emerged as a widely used methodology for approximate posterior inference; however, it suffers from severe computational inefficiency in high-dimensional settings or under diffuse priors. To overcome these limitations, we propose Adaptive Bayesian Inference (ABI), a framework that bypasses traditional data-space discrepancies and instead compares distributions directly in posterior space through nonparametric distribution matching. By leveraging a novel Marginally-augmented Sliced Wasserstein (MSW) distance on posterior measures and exploiting its quantile representation, ABI transforms the challenging problem of measuring divergence between posterior distributions into a tractable sequence of one-dimensional conditional quantile regression tasks. Moreover, we introduce a new adaptive rejection sampling scheme that iteratively refines the posterior approximation by updating the proposal distribution via generative density estimation. Theoretically, we establish parametric convergence rates for the trimmed MSW distance and prove that the ABI posterior converges to the true posterior as the tolerance threshold vanishes. Through extensive empirical evaluation, we demonstrate that ABI significantly outperforms data-based Wasserstein ABC, summary-based ABC, and state-of-the-art likelihood-free simulators, especially in high-dimensional or dependent observation regimes.

Figures

Figures reproduced from arXiv: 2505.04603 by the authors.

Figure 1
Figure 1. Comparison of approximate posterior densities obtained from [PITH_FULL_IMAGE:figures/full_fig_p026_1.png] view at source ↗
Figure 2
Figure 2. Comparison of marginal posteriors generated by [PITH_FULL_IMAGE:figures/full_fig_p026_2.png] view at source ↗
Figure 3
Figure 3. Evolution of the sample path over successive iterations of [PITH_FULL_IMAGE:figures/full_fig_p026_3.png] view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: Comparison of approximate posterior densities under the M/G/1 queuing example. [PITH_FULL_IMAGE:figures/full_fig_p028_4.png]
Figure 5
Figure 5. Figure 5: 30 trajectories simulated from the cosine model with parameter values [PITH_FULL_IMAGE:figures/full_fig_p028_5.png]
Figure 6
Figure 6. Figure 6: Comparison of approximate posterior densities under the cosine model. The true [PITH_FULL_IMAGE:figures/full_fig_p029_6.png]
Figure 7
Figure 7. Figure 7: Approximate posterior densities generated by [PITH_FULL_IMAGE:figures/full_fig_p029_7.png]
Figure 8
Figure 8. Figure 8: 30 trajectories sampled from the Lotka-Volterra model, each corresponding to one of [PITH_FULL_IMAGE:figures/full_fig_p030_8.png]
Figure 9
Figure 9. Figure 9: Comparison of approximate posterior distributions for the Lotka-Volterra model. True [PITH_FULL_IMAGE:figures/full_fig_p031_9.png]
Figure 10
Figure 10. Figure 10: Adaptive inference on the univariate Gaussian model. [PITH_FULL_IMAGE:figures/full_fig_p040_10.png]
Figure 11
Figure 11. Figure 11: Bivariate density plot of the posterior distribution. [PITH_FULL_IMAGE:figures/full_fig_p059_11.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

53 extracted references · 32 canonical work pages

  1. [1]

    A general method for numerically simulating the stochastic time evolution of coupled chemical reactions

    Daniel T Gillespie. A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. Journal of computational physics, 22 0 (4): 0 403--434, 1976

    work page 1976

  2. [2]

    On Bayesian inference for the M/G/1 queue with efficient MCMC sampling

    Alexander Y Shestopaloff and Radford M Neal. On bayesian inference for the m/g/1 queue with efficient mcmc sampling. arXiv preprint arXiv:1401.5548, 2014

    work page Pith review arXiv 2014

  3. [3]

    Massive optimal data compression and density estimation for scalable, likelihood-free inference in cosmology

    Justin Alsing, Benjamin Wandelt, and Stephen Feeney. Massive optimal data compression and density estimation for scalable, likelihood-free inference in cosmology. Monthly Notices of the Royal Astronomical Society, 477 0 (3): 0 2874--2885, 2018

    work page 2018

  4. [4]

    Trimmed comparison of distributions

    Pedro C \'e sar Alvarez-Esteban, Eustasio Del Barrio, Juan Antonio Cuesta-Albertos, and Carlos Matran. Trimmed comparison of distributions. Journal of the American Statistical Association, 103 0 (482): 0 697--704, 2008

    work page 2008

  5. [5]

    The rate of convergence for approximate bayesian computation

    Stuart Barber, Jochen Voss, and Mark Webster. The rate of convergence for approximate bayesian computation. Electronic Journal of Statistics., 2015

    work page 2015

  6. [6]

    Adaptive approximate bayesian computation

    Mark A Beaumont, Jean-Marie Cornuet, Jean-Michel Marin, and Christian P Robert. Adaptive approximate bayesian computation. Biometrika, 96 0 (4): 0 983--990, 2009

    work page 2009

  7. [7]

    The likelihood principle

    James O Berger and Robert L Wolpert. The likelihood principle. IMS, 1988

    1988

  8. [8]

    Approximate bayesian computation with the wasserstein distance

    Espen Bernton, Pierre E Jacob, Mathieu Gerber, and Christian P Robert. Approximate bayesian computation with the wasserstein distance. Journal of the Royal Statistical Society Series B: Statistical Methodology, 81 0 (2): 0 235--269, 2019

    work page 2019

Show all 53 references
  1. [9]

    New insights into approximate bayesian computation

    G \'e rard Biau, Fr \'e d \'e ric C \'e rou, and Arnaud Guyader. New insights into approximate bayesian computation. In Annales de l'IHP Probabilit \'e s et statistiques , volume 51, pages 376--403, 2015

    2015

  2. [10]

    Sequential monte carlo with adaptive weights for approximate bayesian computation

    Fernando V Bonassi and Mike West. Sequential monte carlo with adaptive weights for approximate bayesian computation. Bayesian Analysis, 2015

    2015

  3. [11]

    Unidimensional and evolution methods for optimal transportation

    Nicolas Bonnotte. Unidimensional and evolution methods for optimal transportation. PhD thesis, Universit \'e Paris Sud-Paris XI; Scuola normale superiore (Pise, Italie), 2013

    2013

  4. [12]

    Approximate bayesian computation for astronomical model analysis: a case study in galaxy demographics and morphological transformation at high redshift

    Ewan Cameron and AN Pettitt. Approximate bayesian computation for astronomical model analysis: a case study in galaxy demographics and morphological transformation at high redshift. Monthly Notices of the Royal Astronomical Society, 425 0 (1): 0 44--65, 2012

    2012

  5. [13]

    Approximate bayesian computation for physical inverse modeling

    Neel Chatterjee, Somya Sharma, Sarah Swisher, and Snigdhansu Chatterjee. Approximate bayesian computation for physical inverse modeling. arXiv preprint arXiv:2111.13296, 2021

    2021 arXiv

  6. [14]

    Univariate-guided sparse regression

    Sourav Chatterjee, Trevor Hastie, and Robert Tibshirani. Univariate-guided sparse regression. arXiv preprint arXiv:2501.18360, 2025

    2025 arXiv

  7. [15]

    Manuel Chiachío-Ruano, Juan Chiachío-Ruano, and María L. Jalón. Solving inverse problems by approximate bayesian computation. In Bayesian Inverse Problems. 2021

    2021

  8. [16]

    Implicit quantile networks for distributional reinforcement learning

    Will Dabney, Georg Ostrovski, David Silver, and R \'e mi Munos. Implicit quantile networks for distributional reinforcement learning. In International conference on machine learning, pages 1096--1105. PMLR, 2018

    2018

  9. [17]

    An adaptive sequential monte carlo method for approximate bayesian computation

    Pierre Del Moral, Arnaud Doucet, and Ajay Jasra. An adaptive sequential monte carlo method for approximate bayesian computation. Statistics and computing, 22: 0 1009--1020, 2012

    2012

  10. [18]

    Dynamics of a discrete lotka-volterra model

    Qamar Din. Dynamics of a discrete lotka-volterra model. Advances in Difference Equations, 2013: 0 1--13, 2013

    2013

  11. [19]

    Improving the accuracy of marginal approximations in likelihood-free inference via localization

    Christopher Drovandi, David J Nott, and David T Frazier. Improving the accuracy of marginal approximations in likelihood-free inference via localization. Journal of Computational and Graphical Statistics, 33 0 (1): 0 101--111, 2024

    2024

  12. [20]

    Constructing abc summary statistics: semi-automatic abc

    Paul Fearnhead and Dennis Prangle. Constructing abc summary statistics: semi-automatic abc. Nature Precedings, pages 1--1, 2011

    2011

  13. [21]

    Constructing summary statistics for approximate bayesian computation: semi-automatic approximate bayesian computation

    Paul Fearnhead and Dennis Prangle. Constructing summary statistics for approximate bayesian computation: semi-automatic approximate bayesian computation. Journal of the Royal Statistical Society Series B: Statistical Methodology, 74 0 (3): 0 419--474, 2012

    2012

  14. [22]

    Robust and efficient approximate bayesian computation: A minimum distance approach

    David T Frazier. Robust and efficient approximate bayesian computation: A minimum distance approach. arXiv preprint arXiv:2006.14126, 2020

    2006 arXiv

  15. [23]

    Exponential tail bounds for chisquared random variables

    Malay Ghosh. Exponential tail bounds for chisquared random variables. Journal of Statistical Theory and Practice, 15 0 (2): 0 35, 2021

    2021

  16. [24]

    Bayesian sufficiency in survey-sampling

    VP Godambe. Bayesian sufficiency in survey-sampling. Annals of the Institute of Statistical Mathematics, 20 0 (1): 0 363--373, 1968

    1968

  17. [25]

    Automatic posterior transformation for likelihood-free inference

    David Greenberg, Marcel Nonnenmacher, and Jakob Macke. Automatic posterior transformation for likelihood-free inference. In International conference on machine learning, pages 2404--2414. PMLR, 2019

    2019

  18. [26]

    Improved training of wasserstein gans

    Ishaan Gulrajani, Faruk Ahmed, Martin Arjovsky, Vincent Dumoulin, and Aaron C Courville. Improved training of wasserstein gans. Advances in neural information processing systems, 30, 2017

    2017

  19. [27]

    Robust estimation of a location parameter

    Peter J Huber. Robust estimation of a location parameter. The Annals of Mathematical Statistics, 35 0 (1): 0 73--101, 1964

    1964

  20. [28]

    Approximate bayesian computation with kullback-leibler divergence as data discrepancy

    Bai Jiang. Approximate bayesian computation with kullback-leibler divergence as data discrepancy. In International conference on artificial intelligence and statistics, pages 1711--1721. PMLR, 2018

    2018

  21. [29]

    Learning summary statistic for approximate bayesian computation via deep neural network

    Bai Jiang, Tung-yu Wu, Charles Zheng, and Wing H Wong. Learning summary statistic for approximate bayesian computation via deep neural network. Statistica Sinica, pages 1595--1618, 2017

    2017

  22. [30]

    Foundations of modern probability, volume 2

    Olav Kallenberg and Olav Kallenberg. Foundations of modern probability, volume 2. Springer, 1997

    1997

  23. [31]

    Deep generative quantile bayes

    Jungeum Kim, Percy S Zhai, and Veronika Ro c kov \'a . Deep generative quantile bayes. arXiv preprint arXiv:2410.08378, 2024

    2024 arXiv

  24. [32]

    Regression quantiles

    Roger Koenker and Gilbert Bassett Jr. Regression quantiles. Econometrica: journal of the Econometric Society, pages 33--50, 1978

    1978

  25. [33]

    Concentration of discrepancy-based abc via rademacher complexity

    Sirio Legramanti, Daniele Durante, and Pierre Alquier. Concentration of discrepancy-based abc via rademacher complexity. arXiv preprint arXiv:2206.06991, 2022

    2022 arXiv

  26. [34]

    Efficient generative modeling via penalized optimal transport network

    Wenhui Sophia Lu, Chenyang Zhong, and Wing Hung Wong. Efficient generative modeling via penalized optimal transport network. arXiv preprint arXiv:2402.10456v2, 2025

    2025 arXiv

  27. [35]

    Minimax confidence intervals for the sliced wasserstein distance

    Tudor Manole, Sivaraman Balakrishnan, and Larry Wasserman. Minimax confidence intervals for the sliced wasserstein distance. Electronic Journal of Statistics, 16 0 (1): 0 2252--2345, 2022

    2022

  28. [36]

    Approximate bayesian computational methods

    Jean-Michel Marin, Pierre Pudlo, Christian P Robert, and Robin J Ryder. Approximate bayesian computational methods. Statistics and computing, 22 0 (6): 0 1167--1180, 2012

    2012

  29. [37]

    Reconstruction and simulation of neocortical microcircuitry

    Henry Markram, Eilif Muller, Srikanth Ramaswamy, Michael W Reimann, Marwan Abdellah, Carlos Aguado Sanchez, Anastasia Ailamaki, Lidia Alonso-Nanclares, Nicolas Antille, Selim Arsever, et al. Reconstruction and simulation of neocortical microcircuitry. Cell, 163 0 (2): 0 456--492, 2015

    2015

  30. [38]

    Elicitation of multivariate prior distributions: A nonparametric bayesian approach

    Fernando A Moala and Anthony O’Hagan. Elicitation of multivariate prior distributions: A nonparametric bayesian approach. Journal of Statistical Planning and Inference, 140 0 (7): 0 1635--1655, 2010

    2010

  31. [39]

    Asymptotic guarantees for learning generative models with the sliced-wasserstein distance

    Kimia Nadjahi, Alain Durmus, Umut Simsekli, and Roland Badeau. Asymptotic guarantees for learning generative models with the sliced-wasserstein distance. Advances in Neural Information Processing Systems, 32, 2019

    2019

  32. [40]

    Quantile regression with relu networks: Estimators and minimax rates

    Oscar Hernan Madrid Padilla, Wesley Tansey, and Yanzhen Chen. Quantile regression with relu networks: Estimators and minimax rates. Journal of Machine Learning Research, 23 0 (247): 0 1--42, 2022

    2022

  33. [41]

    Fast -free inference of simulation models with bayesian conditional density estimation

    George Papamakarios and Iain Murray. Fast -free inference of simulation models with bayesian conditional density estimation. Advances in neural information processing systems, 29, 2016

    2016

  34. [42]

    Sequential neural likelihood: Fast likelihood-free inference with autoregressive flows

    George Papamakarios, David Sterratt, and Iain Murray. Sequential neural likelihood: Fast likelihood-free inference with autoregressive flows. In The 22nd international conference on artificial intelligence and statistics, pages 837--848. PMLR, 2019

    2019

  35. [43]

    Generative ai for bayesian computation

    Nicholas G Polson and Vadim Sokolov. Generative ai for bayesian computation. arXiv preprint arXiv:2305.14972, 2023

    2023 arXiv

  36. [44]

    Adapting the abc distance function

    Dennis Prangle. Adapting the abc distance function. Bayesian Analysis, 2017

    2017

  37. [45]

    Wasserstein barycenter and its application to texture mixing

    Julien Rabin, Gabriel Peyr \'e , Julie Delon, and Marc Bernot. Wasserstein barycenter and its application to texture mixing. In Scale Space and Variational Methods in Computer Vision: Third International Conference, SSVM 2011, Ein-Gedi, Israel, May 29--June 2, 2011, Revised Se...

    2011

  38. [46]

    The transportation cost from the uniform measure to the empirical measure in dimension 3

    Michel Talagrand. The transportation cost from the uniform measure to the empirical measure in dimension 3 . The Annals of Probability, pages 919--959, 1994

    1994

  39. [47]

    On the history of abc

    Simon Tavar \'e . On the history of abc. In Handbook of Approximate Bayesian Computation, pages 55--69. Chapman and Hall/CRC, 2018

    2018

  40. [48]

    Gonçalves, David S

    Alvaro Tejero-Cantero, Jan Boelts, Michael Deistler, Jan-Matthis Lueckmann, Conor Durkan, Pedro J. Gonçalves, David S. Greenberg, and Jakob H. Macke. sbi: A toolkit for simulation-based inference. Journal of Open Source Software, 5 0 (52): 0 2505, 2020. doi:10.21105/joss.02505...

    2020 doi

  41. [49]

    Optimal transport: old and new, volume 338

    C \'e dric Villani et al. Optimal transport: old and new, volume 338. Springer, 2009

    2009

  42. [50]

    Adversarial bayesian simulation

    Yuexi Wang and Veronika Ro c kov \'a . Adversarial bayesian simulation. arXiv preprint arXiv:2208.12113, 2022

    2022

  43. [51]

    Statistical inference for noisy nonlinear ecological dynamic systems

    Simon N Wood. Statistical inference for noisy nonlinear ecological dynamic systems. Nature, 466 0 (7310): 0 1102--1104, 2010

    2010

  44. [52]

    A novel adaptive approximate bayesian computation method for inverse heat conduction problem

    Yang Zeng, Hu Wang, Shuai Zhang, Yong Cai, and Enying Li. A novel adaptive approximate bayesian computation method for inverse heat conduction problem. International Journal of Heat and Mass Transfer, 134: 0 185--197, 2019

    2019

  45. [53]

    A deep generative approach to conditional sampling

    Xingyu Zhou, Yuling Jiao, Jin Liu, and Jian Huang. A deep generative approach to conditional sampling. Journal of the American Statistical Association, 118 0 (543): 0 1837--1848, 2023

    2023

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.