An inverse-weight acceptance bound is derived that yields a lower bound on functional mean-squared error from high retained-weight mass in discrepant states and distinguishes statistical information, retained-state functional risk, and auxiliary-computation allocation in pseudo-marginal inference.
Abstract
Pseudo-marginal MCMC is exact under nonnegative unbiased likelihood estimation, but observation design can change both posterior information and the stochastic law of the likelihood estimator. We study fixed-horizon recovery of a declared posterior functional under this joint change. For a broad fresh-estimator pseudo-marginal class, we derive an inverse-weight acceptance bound that yields a lower bound on functional mean-squared error from high retained-weight mass in discrepant states. A two-region corollary establishes an information-computation inversion: stronger exact posterior separation can coexist with worse finite-horizon recovery when the estimator law changes. The obstruction motivates an exact route-conditioned transition that allocates coupled auxiliary inheritance and independent refreshment according to a scientific pair route. In a controlled transcription experiment, a finer observation strengthens likelihood separation while degrading particle-filter reliability and finite-chain behavior. In a fresh 96-state gene-network comparison, route conditioning reduces measured particle-filter wall time by 42.4% in the frozen execution (95% retained-state bootstrap interval 39.6%-45.2%). Recovery uncertainty spans the predeclared noninferiority margin. A prospective Lotka-Volterra experiment supports portability of the retained-state route-restoration mechanism. The results distinguish statistical information, retained-state functional risk, and auxiliary-computation allocation in pseudo-marginal inference.
Constructing confidence regions for stochastic gradient descent (SGD) ideally requires estimating the asymptotic covariance matrix, a severe computational bottleneck in high dimensions. Traditional cancellation-based batch means methods bypass this estimation but require inverting a sample batch covariance matrix. This introduces strict mathematical degeneracy when the parameter dimension exceeds the number of batches. To address this problem, we utilize equal batch size batch means method and propose a simultaneous, marginal-friendly framework. The proposed marginal statistics has a asymptotic Student's $t$-distribution, and eliminates the matrix inversion step, entirely circumventing high-dimensional degeneracy. To achieve valid simultaneous coverage, we present an algorithm utilizing wild bootstrap samples drawn from a statistic as a function of only the diagonals of the variance-covariance estimator, and to further incorporate the contribution of cross-dependencies, we introduce an efficient Quasi-Monte Carlo procedure utilizing a $t$-copula approximation. Additionally, we integrate a Lugsail variance estimator to aggressively correct finite-sample bias and under-coverage. The proposed methodology delivers interpretable, simultaneous hyper-rectangular confidence regions that are statistically robust, memory-efficient, and strictly scalable for high-dimensional inference. The theoretical results are supported by extensive numerical simulation analysis through various aspects of dimension, number of batches and error structure.
Bayesian pseudo-posteriors based on moment conditions, such as Bayesian empirical likelihood (EL) and Bayesian exponentially tilted empirical likelihood (ETEL), provide a robust route to Bayesian inference when the model is specified only through moment restrictions, but their computation is often prohibitive. In this work, we address two barriers to Bayesian pseudo-inference under moment restrictions. First, scalable sampling is challenging for tall data because the pseudo-likelihoods are not log-additive across observations, so standard likelihood-subsampling methods do not apply. Second, in simulation-based and latent-variable problems, the moment function itself may be defined through an intractable expectation, making full-data pseudo-posterior inference infeasible. We develop a new family of subsampled pseudo-posteriors that replaces the full-data pseudo-posterior with an aggregate of mini-batch pseudo-posteriors. We show that naive mini-batching induces a shifted-mixture distortion, yielding aggregates that are correctly centered but overly diffuse. To remove this distortion, we introduce moment-function-level control variates that align mini-batch moment equations around a reference estimator and recover the full-data posterior shape. For Bayesian ETEL, we establish finite-sample total variation bounds to the full-data pseudo-posterior, allowing discontinuous and intractable moment functions. Numerical experiments show that the method applies broadly across moment-condition-based Bayesian pseudo-inference, closely approximates full-data pseudo-posteriors, and substantially reduces computational cost.
Sign-Corrected Bessel Debiasing (SCBD), a signed pseudo-marginal method based on independent block estimates of the loss, is introduced and its ordinary-MC and independently randomised quasi-Monte Carlo (RQMC) implementations are studied.
Yingkai Lu, J. Lee, Geoff K. Nicholls· 0 citations
Density deconvolution is an ill-posed inverse problem, as recovering the latent distribution amplifies high-frequency noise in the observed data. We propose a two-stage likelihood-based procedure. The first estimator maximizes the convolution likelihood over a regularized Gaussian-mixture sieve, while the second reuses the fitted density as an empirical prior and averages the resulting conditional latent densities over the observations. The two estimators have different population targets under misspecification: posterior reconstruction locally contracts misspecification bias under identifiable convolution, but introduces an additional first-order variance component under correct finite-dimensional specification. We establish observed- and latent-domain convergence rates under Gaussian error. Under ordinary-smooth error, the direct estimator in $L^2$ and the posterior reconstruction in $L^1$ attain the classical deconvolution exponent, up to logarithmic factors. Numerical experiments and an application to Framingham blood-pressure data illustrate their complementary finite-sample behavior.
M. Marzio, S. Fensore, Chiara Passamonti et al.· 0 citations
In this work, we explore particle learning strategies for the joint estimation of static parameters and latent states within conditional sequential Monte Carlo (CSMC) algorithms. Building on this idea, we propose the p(parameter)-CSMC algorithm, which incorporates both parameter learning and ancestor sampling, leading to much better mixing properties compared to (particle) Gibbs sampling in settings where strong internal correlations may challenge effective exploration. We also include two applications in the context of a branching process model: one using synthetic data, where we estimate the infectivity profile while assuming the reproductive number to be known, and another using real data, where we address the joint inference of the reproductive number and the infectivity profile based on daily hospital incidence from the arrival of the SARS-CoV-2 lineage B.1.1.7 (Alpha) in Norway in February 2021. We show that, in these settings, performance is dramatically enhanced, with substantially faster mixing and markedly reduced autocorrelation compared with standard particle Gibbs.
The problem of sampling from a probability distribution arises in many applications such as posterior sampling in hierarchical Bayesian inverse problems and Gaussian processes for machine learning. Markov chain Monte Carlo (MCMC) algorithms are often used for sampling from a target probability distribution, but implementations can be computationally expensive, especially for large-scale problems. In certain applications, the target distribution naturally factorizes into a lower dimensional marginal distribution and a conditional distribution that allows exact sampling. We describe an MCMC algorithm called MarCo that exploits such a structure and generates a Markov chain via Metropolis-Hastings sampling from the marginal distribution, followed by sampling from the exact conditional distribution. By design, MarCo constructs a Markov chain on the joint space that inherits the convergence behavior of the marginal MCMC algorithm. This provides multiple theoretical and computational advantages. We prove that MarCo can achieve improved mixing time upper bounds compared to direct sampling from the joint distribution. Moreover, compared to one-block methods that also exploit marginal-conditional structure, we use the framework of Peskun-Tierney ordering to show that MarCo has a larger right spectral gap and smaller asymptotic variance, thus leading to superior convergence properties. Numerical results illustrate the performance benefits of MarCo and are provided for various problems, including a semi-blind image deblurring example.
Abhijit Chowdhary, Federica Milinanni, Julianne Chung et al.· 0 citations
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