Related papers: Analytic Methods for Cosmological Likelihoods
We describe the Bayesian-based signal-to-noise eigenmode method for cosmological parameter estimation, show how it can be used to optimally compress large CMB anisotropy data sets to manageable sizes, and apply it to the DMR 4-year, South…
It is well understood that Bayesian decision theory and average case analysis are essentially identical. However, if one is interested in performing uncertainty quantification for a numerical task, it can be argued that standard approaches…
This review article considers some of the most common methods used in astronomy for regressing one quantity against another in order to estimate the model parameters or to predict an observationally expensive quantity using trends between…
A novel data-driven methodology is presented for the joint selection of prior parameters for both fixed and random effects in Linear Mixed Models (LMMs). This approach facilitates the estimation of complex random-effects structures, as well…
In this paper, we use The Quijote simulations in order to extract the cosmological parameters through Bayesian Neural Networks. This kind of model has a remarkable ability to estimate the associated uncertainty, which is one of the ultimate…
To estimate cosmological parameters from a given dataset, we need to construct a likelihood function, which sometimes has a complicated functional form. We introduce the copula, a mathematical tool to construct an arbitrary multivariate…
A major problem in numerical weather prediction (NWP) is the estimation of high-dimensional covariance matrices from a small number of samples. Maximum likelihood estimators cannot provide reliable estimates when the overall dimension is…
We study parameter estimation in linear Gaussian covariance models, which are $p$-dimensional Gaussian models with linear constraints on the covariance matrix. Maximum likelihood estimation for this class of models leads to a non-convex…
For nearly any challenging scientific problem evaluation of the likelihood is problematic if not impossible. Approximate Bayesian computation (ABC) allows us to employ the whole Bayesian formalism to problems where we can use simulations…
We develop a method for constructing exact cosmological solutions of the Einstein equations based on representing them as a second-order linear differential equation. In particular, the method allows using an arbitrary known solution to…
The Linear Ballistic Accumulator (Brown & Heathcote, 2008) model is used as a measurement tool to answer questions about applied psychology. The analyses based on this model depend upon the model selected and its estimated parameters.…
A grand challenge of the 21st century cosmology is to accurately estimate the cosmological parameters of our Universe. A major approach to estimating the cosmological parameters is to use the large-scale matter distribution of the Universe.…
We present a new approach to parameter inference targeted on generic situations where the evaluation of the likelihood $\mathcal{L}$ (i.e., the probability to observe the data given a fixed model configuration) is numerically expensive.…
Maximum likelihood estimation for parameter-fitting given observations from a Gaussian process in space is a computationally-demanding task that restricts the use of such methods to moderately-sized datasets. We present a framework for…
The study of cosmic expansion history and the late time cosmic acceleration from observational data depends on the nuisance parameters associated with the data. For example, the absolute peak magnitude of type Ia supernova associated with…
In Bayesian optimization, accounting for the importance of the output relative to the input is a crucial yet challenging exercise, as it can considerably improve the final result but often involves inaccurate and cumbersome entropy…
The ability to calculate precise likelihood ratios is fundamental to many STEM areas, such as decision-making theory, biomedical science, and engineering. However, there is no assumption-free statistical methodology to achieve this. For…
We discuss the possibility of applying some standard statistical methods (the least square method, the maximum likelihood method, the method of statistical moments for estimation of parameters) to deterministically chaotic low-dimensional…
Relations between categorical variables can be analyzed conveniently by multiple correspondence analysis (MCA). %It is well suited to discover relations that may exist between categories of different variables. The graphical representation…
Marginal likelihoods for the cosmic expansion rates are evaluated using the `Constitution' data of 397 supernovas, thereby updating the results in some previous works. Even when beginning with a very strong prior probability that favors an…