相关论文: Chi-square and Poissonian Data: Biases Even in the…

The negative binomial distribution has been widely used as a more flexible model than the Poisson distribution for count data. However, when the true data-generating process is Poisson, it is often challenging to distinguish it from a…

The problem of fitting an event distribution when the total expected number of events is not fixed, keeps appearing in experimental studies. In a chi-square fit, if overall normalization is one of the parameters parameters to be fit, the…

Over the past 10 years Bayesian methods have rapidly grown more popular as several computationally intensive statistical algorithms have become feasible with increased computer power. In this paper, we begin with a general description of…

In particle physics, as in many areas of science, parameter inference relies on simulations to bridge the gap between theory and experiment. Recent developments in simulation-based inference have boosted the sensitivity of analyses;…

We investigate the errors in modeling the redshift-space distortion (RSD) effect at large linear scales, using data from the Millennium simulation. While standard theoretical templates, such as the Kaiser formula and the TNS method, could…

When reading peer-reviewed scientific literature describing any analysis of empirical data, it is natural and correct to proceed with the underlying assumption that experiments have made good faith efforts to ensure that their analyses…

There are several assumptions made in a standard $\chi^2$ analysis of data, including the frequent assumption that the likelihood function is well approximated by a multivariate Gaussian distribution. This article briefly reviews the…

This paper proposes a new generalized linear model with the fractional binomial distribution. Zero-inflated Poisson/negative binomial distributions are used for count data with many zeros. To analyze the association of such a count variable…

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…

It has been shown that for the analysis of X-ray spectra the C-statistic, contrary to the chi^2-statistic, provides unbiased estimates of the model parameters and their uncertainty ranges. However, it is often stated that the C-statistic…

The forthcoming generation of galaxy redshift surveys will sample the large-scale structure of the Universe over unprecedented volumes with high-density tracers. This advancement will make robust measurements of three-point clustering…

This paper concerns the development of Stein's method for chi-square approximation and its application to problems in statistics. New bounds for the derivatives of the solution of the gamma Stein equation are obtained. These bounds involve…

We describe an approximation to the widely-used Poisson-likelihood chi-square using a linear combination of Neyman's and Pearson's chi-squares, namely "combined Neyman-Pearson chi-square" ($\chi^2_{\mathrm{CNP}}$). Through analytical…

AMS-02 on the International Space Station has been releasing data of unprecedented accuracy. This poses new challenges for their interpretation. We refine the methodology to get a statistically sound determination of the cosmic-ray…

One way of revealing the nature of the coronal heating mechanism is by comparing simple theoretical one dimensional hydrostatic loop models with observations at the temperature and/or density structure along these features. The most…

When using incorrect or inaccurate signal models to perform parameter estimation on a gravitational wave signal, biased parameter estimates will in general be obtained. For a single event this bias may be consistent with the posterior, but…

The appropriateness of the Poisson model is frequently challenged when examining spatial count data marked by unbalanced distributions, over-dispersion, or under-dispersion. Moreover, traditional parametric models may inadequately capture…

In this paper, we first use the distribution of the number of records to demonstrate that the right tail probabilities of counts of rare events are generally better approximated by the right tail probabilities of Poisson distribution than…

In the real world, experimental data are rarely, if ever, distributed as a normal (Gaussian) distribution. As an example, a large set of data--such as the cross sections for particle scattering as a function of energy contained in the…

The combination of two- and three-point clustering statistics of galaxies and the underlying matter distribution has the potential to break degeneracies between cosmological parameters and nuisance parameters and can lead to significantly…