Abstract:
We consider the generic problem of performing a global fit to many independent data sets each with a different overall multiplicative normalization uncertainty. We show that the methods in common use to treat multiplicative uncertainties lead to systematic biases. We develop a method which is unbiased, based on a self--consistent iterative procedure. We demonstrate the use of this method by applying it to the determination of parton distribution functions with the NNPDF methodology, which uses a Monte Carlo method for uncertainty estimation.

Abstract:
We present a method for determining the background of Fermi GBM GRBs using the satellite positional information and a physical model. Since the polynomial fitting method typically used for GRBs is generally only indicative of the background over relatively short timescales, this method is particularly useful in the cases of long GRBs or those which have Autonomous Repoint Request (ARR) and a background with much variability on short timescales. We give a Direction Dependent Background Fitting (DDBF) method for separating the motion effects from the real data and calculate the duration (T90 and T50, as well as confidence intervals) of the nine example bursts, from which two resulted an ARR. We also summarize the features of our method and compare it qualitatively with the official GBM Catalogue. Our background filtering method uses a model based on the physical information of the satellite position. Therefore, it has many advantages compared to previous methods. It can fit long background intervals, remove all the features caused by the rocking behaviour of the satellite, and search for long emissions or not-triggered events. Furthermore, many part of the fitting have now been automatised, and the method have been shown to work for both Sky Survey mode and ARR mode data. Future work will provide a burst catalogue with DDBF.

Abstract:
The operation of AMS-02 opens a new era for the study of cosmic ray physics with unprecedentedly precise data which are comparable with the laboratory measurements. The high precision data allow a quantitative study on the cosmic ray physics and give strict constraints on the nature of cosmic ray sources. However, the intrinsic errors from the theoretical models to interpret the data become dominant over the errors in the data. In the present work we try to give a systematic study on the uncertainties of the models to explain the AMS-02 positron fraction data, which shows the cosmic ray $e^+e^-$ excesses together with the PAMELA and Fermi-LAT measurements. The excesses can be attributed to contributions from the extra $e^+e^-$ sources, such as pulsars or the dark matter annihilation. The possible systematic uncertainties of the theoretical models considered include the cosmic ray propagation, the treatment of the low energy data, the solar modulation, the $pp$ interaction models, the nuclei injection spectrum and so on. We find that in general a spectral hardening of the primary electron injection spectrum above $\sim50-100$ GeV is favored by the data. Furthermore, the present model uncertainties may lead to a factor of $\sim2$ enlargement in the determination of the parameter regions of the extra source, such as the dark matter mass, annihilation rate and so on.

Abstract:
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 plane with intrinsic scatter, we derive the general likelihood function to be maximised to recover the best fitting model. Alongside the mathematical description, we also release the hyper-fit package for the R statistical language (github.com/asgr/hyper.fit) and a user-friendly web interface for online fitting (hyperfit.icrar.org). The hyper-fit package offers access to a large number of fitting routines, includes visualisation tools, and is fully documented in an extensive user manual. Most of the hyper-fit functionality is accessible via the web interface. In this paper we include applications to toy examples and to real astronomical data from the literature: the mass-size, Tully-Fisher, Fundamental Plane, and mass-spin-morphology relations. In most cases the hyper-fit solutions are in good agreement with published values, but uncover more information regarding the fitted model.

Abstract:
Using the likelihood ratio test statistic, we present a method which can be employed to test the hypothesis of a single Higgs boson using the matrix of measured signal strengths. This method can be applied in the presence of incomplete data and takes into account uncertainties on the measurements. The p-value against the hypothesis of a single Higgs boson is defined from the expected distribution of the test statistic, generated using pseudo-experiments. The applicability of the likelihood-based test is demonstrated using numerical examples with uncertainties and missing matrix elements.

Abstract:
We present a procedure for determination of positions and orbital elements, and associated uncertainties, of outer Solar System planets. The orbit-fitting procedure is greatly streamlined compared to traditional methods because acceleration can be treated as a perturbation to the inertial motion of the body. These techniques are immediately applicable to Kuiper Belt Objects, for which recovery observations are costly. Our methods produce positional estimates and uncertainty ellipses even in the face of the substantial degeneracies of short-arc orbit fits; the sole a priori assumption is that the orbit should be bound or nearly so. We use these orbit-fitting techniques to derive a strategy for determining Kuiper Belt orbits with a minimal number of observations.

Abstract:
The Fermi Gamma-ray Burst Monitor (GBM) detects gamma-rays in the energy range 8 keV - 40 MeV. We developed a new background fitting process of these data, based on the motion of the satellite. Here we summarize this method, called Direction Dependent Background Fitting (DDBF), regarding the GBM triggered catalog. We also give some preliminary results and compare the duration parameters with the 2-years Fermi Burst Catalog.

Abstract:
Kinematic fitting is a well-established tool to improve jet energy and invariant mass resolutions by fitting the measured values under constraints (e.g. energy conservation). However, in the presence of substantial ISR and Beamstrahlung, naive energy and (longitudinal) momentum constraints fail due to the a priori unknown amount of undetected momentum carried away by collinear photons. It is possible to take care of those two effects and thus obtain significantly higher mass resolutions.

Abstract:
We discuss fitting correlated data - with the example of hadron mass spectroscopy in mind. The main conclusion is that the method of minimising correlated $\chi^2$ is unreliable if the data sample is too small.

Abstract:
Given a dense set of points lying on or near an embeddedsubmanifold M0⊂ℝn of Euclideanspace, the manifold fitting problem is to find anembedding F:M→ℝn that approximatesM0 in the sense of least squares. When the dataset is modeledby a probability distribution, the fitting problem reduces tothat of finding an embedding that minimizes Ed[F], theexpected square of the distance from a point in ℝnto F(M). It is shown that this approach to the fitting problemis guaranteed to fail because the functional Ed has no localminima. This problem is addressed by adding a small multiple kof the harmonic energy functional to the expected square of thedistance. Techniques from the calculus of variations are thenused to study this modified functional.