Related papers: A quasi-Gaussian approximation for the probability…
In science and engineering, we often work with models designed for accurate prediction of variables of interest. Recognizing that these models are approximations of reality, it becomes desirable to apply multiple models to the same data and…
Fitting a theoretical model to experimental data in a Bayesian manner using Markov chain Monte Carlo typically requires one to evaluate the model thousands (or millions) of times. When the model is a slow-to-compute physics simulation,…
Data with uncertain, missing, censored, and correlated values are commonplace in many research fields including astronomy. Unfortunately, such data are often treated in an ad hoc way in the astronomical literature potentially resulting in…
The interpretation of cosmological observables requires the use of increasingly sophisticated theoretical models. Since these models are becoming computationally very expensive and display non-trivial uncertainties, the use of standard…
We apply Bayesian statistics to the estimation of correlation functions. We give the probability distributions of auto- and cross-correlations as functions of the data. Our procedure uses the measured data optimally and informs about the…
We propose a Likelihood Matching approach for training diffusion models by first establishing an equivalence between the likelihood of the target data distribution and a likelihood along the sample path of the reverse diffusion. To…
A method providing optimal estimate of probability density functions (PDFs) from time series is proposed. It allows almost arbitrary resolution PDFs when applied to either, sampled analytic functions or digitized data from experiments. When…
Approximating complex probability distributions, such as Bayesian posterior distributions, is of central interest in many applications. We study the expressivity of geometric Gaussian approximations. These consist of approximations by…
We consider Bayesian inference problems with computationally intensive likelihood functions. We propose a Gaussian process (GP) based method to approximate the joint distribution of the unknown parameters and the data. In particular, we…
The normalized probability density function (PDF) of global measures of a large class of highly correlated systems has previously been demonstrated to fall on a single non-Gaussian "universal" curve. We derive the functional form of the…
We perform high resolution ray-tracing simulations to investigate probability distribution functions (PDFs) of lensing convergence, shear, and magnification on distant sources up to the redshift of $z_s=20$. We pay particular attention to…
Due to their flexibility, Gaussian processes (GPs) have been widely used in nonparametric function estimation. A prior information about the underlying function is often available. For instance, the physical system (computer model output)…
Random processes play a crucial role in scientific research, often characterized by distribution functions or probability density functions (PDFs). These PDFs serve as essential approximations of the actual and frequently undisclosed…
We study the significance of non-Gaussianity in the likelihood of weak lensing shear two-point correlation functions, detecting significantly non-zero skewness and kurtosis in one-dimensional marginal distributions of shear two-point…
We propose a new sampling-based approach for approximate inference in filtering problems. Instead of approximating conditional distributions with a finite set of states, as done in particle filters, our approach approximates the…
A product of two Gaussians (or normal distributions) is another Gaussian. That's a valuable and useful fact! Here we use it to derive a refactoring of a common product of multivariate Gaussians: The product of a Gaussian likelihood times a…
A set of probabilities along with corresponding quantiles are often used to define predictive distributions or probabilistic forecasts. These quantile predictions offer easily interpreted uncertainty of an event, and quantiles are generally…
In a Cox model, the partial likelihood, as the product of a series of conditional probabilities, is used to estimate the regression coefficients. In practice, those conditional probabilities are approximated by risk score ratios based on a…
Given a decision process based on the approximate probability density function returned by a data assimilation algorithm, an interaction level between the decision making level and the data assimilation level is designed to incorporate the…
We study Bayesian inference methods for solving linear inverse problems, focusing on hierarchical formulations where the prior or the likelihood function depend on unspecified hyperparameters. In practice, these hyperparameters are often…