Related papers: An Approximation to the Likelihood Function for Ba…
We discuss the problem of constraining cosmological parameters with cosmic microwave background band--power estimates. Because these latter are variances, they do not have gaussian distribution functions and, hence, the standard…
Most parameter constraints obtained from cosmic microwave background (CMB) anisotropy data are based on power estimates and rely on approximate likelihood functions; computational difficulties generally preclude an exact analysis based on…
The primary results of most observations of cosmic microwave background (CMB) anisotropy are estimates of the angular power spectrum averaged through some broad band, called band-powers. These estimates are in turn what are used to produce…
Powerful constraints on theories can already be inferred from existing CMB anisotropy data. But performing an exact analysis of available data is a complicated task and may become prohibitively so for upcoming experiments with \gtrsim10^4…
The majority of present efforts to constrain cosmological parameters with cosmic microwave background (CMB) anisotropy data employ approximate likelihood functions, the time consuming nature of a complete analysis being a major obstacle. We…
Microwave background temperature and polarization observations are a powerful way to constrain cosmological parameters if the likelihood function can be calculated accurately. The temperature and polarization fields are correlated, partial…
A maximum-likelihood method is presented for estimating the power spectrum of anisotropies in the cosmic microwave background (CMB) from interferometer observations. The method calculates flat band-power estimates in separate bins in…
The likelihood function is a crucial element of parameter estimation. In analyses of galaxy overdensities and weak lensing shear, one often approximates the likelihood of the power spectrum with a Gaussian distribution. The posterior…
The estimation of cosmological parameters from a given data set requires a construction of a likelihood function which, in general, has a complicated functional form. We adopt a Gaussian copula and constructed a copula likelihood function…
Application of a Goodness--of--fit (GOF) statistic is an essential element of parameter estimation. We discuss the computation of GOF when estimating parameters from anisotropy measurements of the cosmic microwave background (CMB), and we…
As the Cosmic Microwave Background (CMB) radiation is observed to higher and higher angular resolution the size of the resulting datasets becomes a serious constraint on their analysis. In particular current algorithms to determine the…
We explore power spectrum estimation in the context of a Gaussian approximation to the likelihood function. Using the Saskatoon data, we estimate the power averaged through a set of ten filters designed to make the errors on the power…
We propose a formalism for estimating the skewness and angular power spectrum of a general Cosmic Microwave Background data set. We use the Edgeworth Expansion to define a non-Gaussian likelihood function that takes into account the…
Much attention has been given to the problem of estimating cosmological parameters from the $C_l$ measured by future experiments. Many of the approaches which are being used either invoke poorly controlled approximations or are…
We discuss the effects of finite sky coverage and the uncertainty in extracting information about the power spectrum from experiments on small angular scales. In general the cosmic variance is enhanced by a factor of $4\pi/A$, where $A$ is…
I develop a method for assessing the ability of an instrument, coupled with an observing strategy, to measure the angular power spectrum of the cosmic microwave background (CMB). It allows for efficient calculation of expected parameter…
We describe our methodology for comparing the WMAP measurements of the cosmic microwave background (CMB) and other complementary data sets to theoretical models. The unprecedented quality of the WMAP data, and the tight constraints on…
We develop two methods for estimating the power spectrum, C_l, of the cosmic microwave background (CMB) from data and apply them to the COBE/DMR and Saskatoon datasets. One method involves a direct evaluation of the likelihood function, and…
As the era of high precision cosmology approaches, the empirically determined power spectrum of the microwave background anisotropy, $C_l$, will provide a crucial test for cosmological theories. We present a unified semi-analytic framework…
We investigate whether a Gaussian likelihood is sufficient to obtain accurate parameter constraints from a Euclid-like combined tomographic power spectrum analysis of weak lensing, galaxy clustering and their cross-correlation. Testing its…