Related papers: Uncertainty Quantification in density estimation f…

Anomaly detection is a field of intense research. Identifying low probability events in data/images is a challenging problem given the high-dimensionality of the data, especially when no (or little) information about the anomaly is…

We investigate the errors in modeling the redshift-space distortion (RSD) effect at large linear scales, using data from the Millennium simulation. While standard theoretical templates, such as the Kaiser formula and the TNS method, could…

Compressive sensing has become a powerful addition to uncertainty quantification when only limited data is available. In this paper we provide a general framework to enhance the sparsity of the representation of uncertainty in the form of…

Uncertainty quantification of the photogrammetry process is essential for providing per-point accuracy credentials of the point clouds. Unlike airborne LiDAR, whose accuracy generally remains consistent with objects with varying geometric…

Diffusion posterior sampling solves inverse problems by combining a pretrained diffusion prior with measurement-consistency guidance, but it often fails to recover fine details because measurement terms are applied in a manner that is…

Suppose $X_1,\dots, X_n$ is a random sample from a bounded and decreasing density $f_0$ on $[0,\infty)$. We are interested in estimating such $f_0$, with special interest in $f_0(0)$. This problem is encountered in various statistical…

The paper studies an imaging problem in the diffusive ultrasound-modulated bioluminescence tomography with partial boundary measurement in an anisotropic medium. Assuming plane-wave modulation, we transform the imaging problem to an inverse…

This work considers a problem of estimating a mixing probability density $f$ in the setting of discrete mixture models. The paper consists of three parts. The first part focuses on the construction of an $L_1$ consistent estimator of $f$.…

Establishing dense correspondences between a pair of images is an important and general problem. However, dense flow estimation is often inaccurate in the case of large displacements or homogeneous regions. For most applications and…

A density estimation method in a Bayesian nonparametric framework is presented when recorded data are not coming directly from the distribution of interest, but from a length biased version. From a Bayesian perspective, efforts to…

Numerical models based on partial differential equations (PDE), or integro-differential equations, are ubiquitous in engineering and science, making it possible to understand or design systems for which physical experiments would be…

Computing polarised intensities from noisy data in Stokes U and Q suffers from a positive bias that should be suppressed. To develop a correction method that, when applied to maps, should provide a distribution of polarised intensity that…

Uncertainties from model parameters and model discrepancy from small-scale models impact the accuracy and reliability of predictions of large-scale systems. Inadequate representation of these uncertainties may result in inaccurate and…

A key factor in ensuring the accuracy of computer simulations that model physical systems is the proper calibration of their parameters based on real-world observations or experimental data. Inevitably, uncertainties arise, and Bayesian…

We propose a method for variable selection in the intensity function of spatial point processes that combines sparsity-promoting estimation with noise-robust model selection. As high-resolution spatial data becomes increasingly available…

In this paper, we consider the problem of propagating an uncertain distribution by a possibly non-linear function and quantifying the resulting uncertainty. We measure the uncertainty using the Wasserstein distance, and for a given input…

Uncertainty quantification for image data is dominated by complex deep learning methods, yet the field lacks an interpretable, mathematically grounded baseline. We propose Bayesian scattering to fill this gap, serving as a first-step…

The use of photometric redshifts in cosmology is increasing. Often, however these photo-zs are treated like spectroscopic observations, in that the peak of the photometric redshift, rather than the full probability density function (PDF),…

The fusion of multiple sensor modalities, especially through deep learning architectures, has been an active area of study. However, an under-explored aspect of such work is whether the methods can be robust to degradations across their…

Recent advances in deep learning have led to its widespread adoption across diverse domains, including medical imaging. This progress is driven by increasingly sophisticated model architectures, such as ResNets, Vision Transformers, and…