相关论文: Non-Gaussian Likelihood Function

One of the major goals of cosmological observations is to test theories of structure formation. The most straightforward way to carry out such tests is to compute the likelihood function L, the probability of getting the data given the…

We propose a new asymptotic expansion method for nonlinear filtering, based on a small parameter in the system noise. The conditional expectation is expanded as a power series in the noise level, with each coefficient computed by solving a…

A new algorithm is developed to tackle the issue of sampling non-Gaussian model parameter posterior probability distributions that arise from solutions to Bayesian inverse problems. The algorithm aims to mitigate some of the hurdles faced…

The first purpose of this article is to obtain a.s. asymptotic properties of the maximum likelihood estimator in the autoregressive process driven by a stationary Gaussian noise. The second purpose is to show the local asymptotic normality…

Higher criticism is a large-scale testing procedure that can attain the optimal detection boundary for sparse and faint signals. However, there has been a lack of knowledge in most existing works about its asymptotic distribution for more…

Many problems arising in applications result in the need to probe a probability distribution for functions. Examples include Bayesian nonparametric statistics and conditioned diffusion processes. Standard MCMC algorithms typically become…

We study the problem of estimating the intensity function of a covariate-driven point process based on observations of the points and covariates over a large window. We consider the nonparametric Bayesian approach, and show that a wide…

The statistics of multi-field inflation are investigated using the stochastic approach. We analytically obtain the probability distribution function of fields with the scaling approximation by extending the previous work by Amendola. The…

This paper considers a multivariate spatial random field, with each component having univariate marginal distributions of the skew-Gaussian type. We assume that the field is defined spatially on the unit sphere embedded in $\mathbb{R}^3$,…

We study estimation and prediction of Gaussian random fields with covariance models belonging to the generalized Wendland (GW) class, under fixed domain asymptotics. As the Mat\'ern case, this class allows a continuous parameterization of…

We propose a rigorous, non-perturbative, Bayesian framework which enables one jointly to test Gaussianity and estimate the power spectrum of CMB anisotropies. It makes use of the Hilbert space of an harmonic oscillator to set up an exact…

In this work, we study probability functions associated with Gaussian mixture models. Our primary focus is on extending the use of spherical radial decomposition for multivariate Gaussian random vectors to the context of Gaussian mixture…

We study nonparametric Bayesian inference for the intensity function of a covariate-driven point process. We extend recent results from the literature, showing that a wide class of Gaussian priors, combined with flexible link functions,…

Non-Gaussian distributions of cosmic microwave background (CMB) anisotropies have been proposed to reconcile the discrepancies between different experiments at half-degree scales (Coulson et al. 1994). Each experiment probes a different…

A large class of statistics can be formulated as smooth functions of sample means of random vectors. In this paper, we propose a general partial Cram\'{e}r's condition (GPCC) and apply it to establish the validity of the Edgeworth expansion…

The complex Gaussian distribution has been widely used as a fundamental spectral and noise model in signal processing and communication. However, its Gaussian structure often limits its ability to represent the diverse amplitude…

In this Letter, we strengthen and extend the connection between simulation and estimation to exploit simulation routines that do not exactly compute the probability of experimental data, known as the likelihood function. Rather, we provide…

The asymptotic law for the expected nodal volume of random non-Gaussian monochromatic band-limited functions is determined in vast generality. Our methods combine microlocal analytic techniques and modern probability theory. A particularly…

The Gaussian linear model provides a unique way to obtain the posterior probability distribution as well as the Bayesian evidence analytically. Considering the expansion rate data, the Gaussian linear model can be applied for $\Lambda$CDM,…

In Gaussian graphical models, the likelihood equations must typically be solved iteratively. We investigate two algorithms: A version of iterative proportional scaling which avoids inversion of large matrices, and an algorithm based on…