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.
Conditional density estimation describes how the entire distribution of a response changes with covariates, and in imaging studies also with location. Logistic Gaussian processes (LGP) give a flexible prior for such densities. However, the normalizing constant of an LGP has no closed form, so existing methods approxima...
Jae-Hyun Kim, Indrajit Ghosh, D. Pati et al.· 1 citation
Estimating spectral density matrices for future space-based gravitational-wave detectors such as LISA is challenging due to the long duration of the data and the correlated instrumental noise across multiple time-delay interferometry channels. In this work, we investigate a specialized mean-field stochastic gradient va...
Jianan Liu, A. Vajpeyi, Renate Meyer et al.· 0 citations
Conditional density estimation targets the full distribution of a response given covariates, as required, for example, for per-galaxy photometric redshifts. We develop a scalable Bayesian estimator based on the logistic Gaussian process. The log conditional density has a separable covariance: a Mat\'ern kernel along th...
Daniel Paulin, Á. Jung, András A. Benczúr· 0 citations
Probability density functions are commonly estimated through preliminary smoothing or aggregation procedures, e.g., histograms or kernel density estimation, before subsequent functional representation and functional data analyses. Such a two-stage approach can lead to additional approximation bias and weaken the direct...
Bayesian data assimilation combines model forecasts with noisy observations, but sampling high-dimensional, non-Gaussian posteriors remains challenging. We introduce an observation-interpolant framework that turns pretrained stochastic interpolant, flow matching, and diffusion models into posterior samplers without ret...
Sampling from the posterior is the central task of computational Bayesian inverse problems. The standard workhorse in Bayesian inference - Markov chain Monte Carlo (MCMC) - is sequential, yields correlated samples, and must be rerun for each observation. Conditional flow matching offers an amortized alternative: a tran...
Jan Blechschmidt, O. Ernst, Moritz Poguntke et al.· 0 citations
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