Related papers: Tweedie Calculus
Diffusion models have achieved remarkable success in generating samples from unknown data distributions. Most popular stochastic differential equation-based diffusion models perturb the target distribution by adding Gaussian noise,…
Diffusion generative models unlock new possibilities for inverse problems as they allow for the incorporation of strong empirical priors in scientific inference. Recently, diffusion models are repurposed for solving inverse problems using…
Empirical Bayes methods are widely used for large-scale inference, yet most classical approaches assume homoscedastic observations and focus primarily on posterior mean estimation. We develop a nonparametric empirical Bayes framework for…
Tweedie distributions are a special case of exponential dispersion models, which are often used in classical statistics as distributions for generalized linear models. Here, we reveal that Tweedie distributions also play key roles in modern…
Score-driven models update time-varying parameters using conditional likelihood scores. This paper develops a Bayesian interpretation of such updates through Tweedie's formula, which connects posterior mean corrections with marginal scores.…
The Tweedie Compound Poisson-Gamma model is routinely used for modeling non-negative continuous data with a discrete probability mass at zero. Mixed models with random effects account for the covariance structure related to the grouping…
This paper investigates the consistency of a posterior distribution in the single-measurement fractional Calder\'on problem with additive Gaussian noise. We consider a Bayesian framework with rescaled and Gaussian sieve priors, using a…
Diffusion models have been firmly established as principled zero-shot solvers for linear and nonlinear inverse problems, owing to their powerful image prior and iterative sampling algorithm. These approaches often rely on Tweedie's formula,…
While diffusion models excel at generating continuous data such as images, adapting them to discrete tasks has relied on indirect approaches that either operate in continuous embedding spaces or use token masking mechanisms, both of which…
Likelihood-based deep generative models have recently been shown to exhibit pathological behaviour under the manifold hypothesis as a consequence of using high-dimensional densities to model data with low-dimensional structure. In this…
The Tweedie generalized linear models are commonly applied in the insurance industry to analyze semicontinuous claim data. For better prediction of the aggregated claim size, the mean and dispersion of the Tweedie model are often estimated…
We introduce a class of two-parameter discrete dispersion models, obtained by combining convolution with a factorial tilting operation, similar to exponential dispersion models which combine convolution and exponential tilting. The…
We propose a new class of discrete generalized linear models based on the class of Poisson-Tweedie factorial dispersion models with variance of the form $\mu + \phi\mu^p$, where $\mu$ is the mean, $\phi$ and $p$ are the dispersion and…
The statistical inverse problem of estimating the probability distribution of an infinite-dimensional unknown given its noisy indirect observation is studied in the Bayesian framework. In practice, one often considers only…
We adopt Gaussian Processes (GPs) as latent functions for probabilistic forecasting of intermittent time series. The model is trained in a Bayesian framework that accounts for the uncertainty about the latent function. We couple the latent…
In this paper, we present a new statistical approach to the problem of incorporating experimental observations into a mathematical model described by linear partial differential equations (PDEs) to improve the prediction of the state of a…
We propose a methodology for modeling and comparing probability distributions within a Bayesian nonparametric framework. Building on dependent normalized random measures, we consider a prior distribution for a collection of discrete random…
Bayesian approach to inverse problems is studied in the case where the forward map is a linear hypoelliptic pseudodifferential operator and measurement error is additive white Gaussian noise. The measurement model for an unknown Gaussian…
We propose a novel adaptive importance sampling scheme for Bayesian inversion problems where the inference of the variables of interest and the power of the data noise is split. More specifically, we consider a Bayesian analysis for the…
Ambient diffusion is a recently proposed framework for training diffusion models using corrupted data. Both Ambient Diffusion and alternative SURE-based approaches for learning diffusion models from corrupted data resort to approximations…