Related papers: Statistically optimal fitting of astrometric signa…

A tool for representation of the one-dimensional astrometric signal of Gaia is described and investigated in terms of fit discrepancy and astrometric performance with respect to number of parameters required. The proposed basis function is…

A goodness-of-fit test for the fitting of a parametric model to data obtained from a detector with finite resolution and limited acceptance is proposed. The parameters of the model are found by minimization of a statistic that is used for…

Optimal estimation of signal amplitude, background level, and photocentre location is crucial to the combined extraction of astrometric and photometric information from focal plane images, and in particular from the one-dimensional…

This thesis investigates algorithms regarding their applicability for highly nonlinear model fitting on big datasets. Various mathematical methods are presented with which a model fit using the least squares criterion is possible. Special…

Transforming the instrumental photometry of ground-based telescopes into a calibrated physical flux in a well-defined passband is a major challenge in astronomy. Along with the intrinsic instrumental difference between telescopes sharing…

I discuss the effects of measurement error on regression and density estimation. I review the statistical methods that have been developed to correct for measurement error that are most popular in astronomical data analysis, discussing…

Statistical modeling plays a fundamental role in understanding the underlying mechanism of massive data (statistical inference) and predicting the future (statistical prediction). Although all models are wrong, researchers try their best to…

In this review, the state-of-the-art for goodness-of-fit testing for spatial point processes is summarized. Test statistics based on classical functional summary statistics and recent contributions from topological data analysis are…

Astronomical data is often uncertain with errors that are heteroscedastic (different for each data point) and covariant between different dimensions. Assuming that a set of D-dimensional data points can be described by a (D - 1)-dimensional…

In real telescopes, the optical parameters evolve with time, and the degradation is often not uniform. This introduces variations in the image profile and therefore photo-centre displacements which, unless corrected, may result in…

The aim of this paper, triggered by some discussions in the astrophysics community raised by astro-ph/0508529, is to introduce the issue of `fits' from a probabilistic perspective (also known as Bayesian), with special attention to the…

Spatial point processes are used as models in many different fields ranging from ecology and forestry to cosmology and materials science. In recent years, model validation, and in particular goodness-of-fit testing of a proposed point…

The problem of error analysis is addressed in stages beginning with the case of uncorrelated parameters and proceeding to the Bayesian problem that takes into account all possible correlations when a great deal of prior information about…

The high accuracy of modern space astrometry requires the use of General Relativity to model the propagation of stellar light through the gravitational field encountered from a source to a given observer inside the Solar System. In this…

While considerable advance has been made to account for statistical uncertainties in astronomical analyses, systematic instrumental uncertainties have been generally ignored. This can be crucial to a proper interpretation of analysis…

In its all-sky survey, the ESA global astrometry mission Gaia will perform high-precision astrometry and photometry for 1 billion stars down to $V = 20$ mag. The data collected in the Gaia catalogue, to be published by the end of the next…

Using a time series model to mimic an observed time series has a long history. However, with regard to this objective, conventional estimation methods for discrete-time dynamical models are frequently found to be wanting. In fact, they are…

We are developing automated systems to provide homogeneous calibration meta-data for heterogeneous imaging data, using the pixel content of the image alone where necessary. Standardized and complete calibration meta-data permit generative…

The methods of obtaining the average spectral shape in a low statistics regime are presented. Different approaches to averaging are extensively tested with simulated spectra, based on the ASCA responses. The issue of binning up the spectrum…

I describe an approach to fitting and comparison of radio spectra based on Bayesian analysis and realised using a new implementation of the nested sampling algorithm. Such an approach improves on the commonly used maximum-likelihood fitting…