相关论文: The Crossing Statistic: Dealing with Unknown Error…
I present an analysis for fitting cosmological parameters from a Hubble Diagram of a standard candle with unknown intrinsic magnitude dispersion. The dispersion is determined from the data themselves, simultaneously with the cosmological…
By using the Sloan Digital Sky Survey (SDSS) first year type Ia supernova (SN Ia) compilation, we compare two different approaches (traditional \chi^2 and complete likelihood) to determine parameter constraints when the magnitude dispersion…
This paper presents a new method to estimate systematic errors in the maximum-likelihood regression of count data. The method is applicable in particular to X-ray spectra in situations where the Poisson log-likelihood, or the Cash…
We demonstrate that two approximations to the chi^2 statistic as popularly employed by observational astronomers for fitting Poisson-distributed data can give rise to intrinsically biased model parameter estimates, even in the high counts…
We discuss a novel approach to identifying cosmic events in separate and independent observations. In our focus are the true events, such as supernova explosions, that happen once, hence, whose measurements are not repeatable. Their…
The median statistic has recently been discussed by Gott \textit{et al.} as a more reliable alternative to the standard $\chi^2$ likelihood analysis, in the sense of requiring fewer assumptions about the data and being almost as…
For testing goodness of fit it is very popular to use either the chi square statistic or G statistics (information divergence). Asymptotically both are chi square distributed so an obvious question is which of the two statistics that has a…
By introducing Crossing functions and hyper-parameters I show that the Bayesian interpretation of the Crossing Statistics [1] can be used trivially for the purpose of model selection among cosmological models. In this approach to falsify a…
The C statistics, also known as the Cash statistic, is often used in astronomy for the analysis of low-count Poisson data. One of the challenges of the C statistic is that its probability distribution, under the null hypothesis that the…
In statistical inference, uncertainty is unknown and all models are wrong. That is to say, a person who makes a statistical model and a prior distribution is simultaneously aware that both are fictional candidates. To study such cases,…
A new test statistic based on success runs of weighted deviations is introduced. Its use for observations sampled from independent normal distributions is worked out in detail. It supplements the classic $\chi^{2}$ test which ignores the…
Cosmological parameter fitting remains crucial, especially with the abundance of available data. While many parameters have been tightly constrained, discrepancies-most notably the Hubble tension-persist between measurements obtained from…
The likelihood ratio statistic, with its asymptotic $\chi^2$ distribution at regular model points, is often used for hypothesis testing. At model singularities and boundaries, however, the asymptotic distribution may not be $\chi^2$, as…
In this paper we compare the performances of the chi-square and median likelihood analysis in the determination of cosmological constraints using type Ia supernovae data. We perform a statistical analysis using the 307 supernovae of the…
The question of testing for equality in distribution between two linear models, each consisting of sums of distinct discrete independent random variables with unequal numbers of observations, has emerged from the biological research. In…
The nature of random errors in any data set that is Gaussian is a well established fact according to the Central Limit Theorem. Supernovae type Ia data have played a crucial role in major discoveries in cosmology. Unlike in laboratory…
The scatter in the apparent magnitude of type Ia supernovae induced by stochastic gravitational lensing is highly dependent on the nonlinear growth of cosmological structure. In this paper, we show that such a dependence can potentially be…
We use the $\Delta_{\chi^2}$ statistic introduced in \cite{gup08,gup10} to study directional dependence, in the high-z supernovae data. This dependence could arise due to departures from the cosmological principle or from direction…
Thousands of experiments are analyzed and papers are published each year involving the statistical analysis of grouped data. While this area of statistics is often perceived -- somewhat naively -- as saturated, several misconceptions still…
We study linear statistics of a class of determinantal processes which interpolate between Poisson and GUE/Ginibre statistics in dimension 1 or 2. These processes are obtained by performing an independent Bernoulli percolation on the…