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Register a new userBayesian data analysis tools for atomic physics
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Added by
Martino Trassinelli
Publication date
2016
fields
Physics
and research's language is
English
Authors
Martino Trassinelli
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We present an introduction to some concepts of Bayesian data analysis in the context of atomic physics. Starting from basic rules of probability, we present the Bayes theorem and its applications. In particular we discuss about how to calculate simple and joint probability distributions and the Bayesian evidence, a model dependent quantity that allows to assign probabilities to different hypotheses from the analysis of a same data set. To give some practical examples, these methods are applied to two concrete cases. In the first example, the presence or not of a satellite line in an atomic spectrum is investigated. In the second example, we determine the most probable model among a set of possible profiles from the analysis of a statistically poor spectrum. We show also how to calculate the probability distribution of the main spectral component without having to determine uniquely the spectrum modeling. For these two studies, we implement the program Nested fit to calculate the different probability distributions and other related quantities. Nested fit is a Fortran90/Python code developed during the last years for analysis of atomic spectra. As indicated by the name, it is based on the nested algorithm, which is presented in details together with the program itself.
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The Collaborative Analysis Versioning Environment System (CAVES) project concentrates on the interactions between users performing data and/or computing intensive analyses on large data sets, as encountered in many contemporary scientific disciplines. In modern science increasingly larger groups of researchers collaborate on a given topic over extended periods of time. The logging and sharing of knowledge about how analyses are performed or how results are obtained is important throughout the lifetime of a project. Here is where virtual data concepts play a major role. The ability to seamlessly log, exchange and reproduce results and the methods, algorithms and computer programs used in obtaining them enhances in a qualitative way the level of collaboration in a group or between groups in larger organizations. The CAVES project takes a pragmatic approach in assessing the needs of a community of scientists by building series of prototypes with increasing sophistication. In extending the functionality of existing data analysis packages with virtual data capabilities these prototypes provide an easy and habitual entry point for researchers to explore virtual data concepts in real life applications and to provide valuable feedback for refining the system design. The architecture is modular based on Web, Grid and other services which can be plugged in as desired. As a proof of principle we build a first system by extending the very popular data analysis framework ROOT, widely used in high energy physics and other fields, making it virtual data enabled.
A selection of unfolding methods commonly used in High Energy Physics is compared. The methods discussed here are: bin-by-bin correction factors, matrix inversion, template fit, Tikhonov regularisation and two examples of iterative methods. Two procedures to choose the strength of the regularisation are tested, namely the L-curve scan and a scan of global correlation coefficients. The advantages and disadvantages of the unfolding methods and choices of the regularisation strength are discussed using a toy example.
VISPA is a novel development environment for high energy physics analyses, based on a combination of graphical and textual steering. The primary aim of VISPA is to support physicists in prototyping, performing, and verifying a data analysis of any complexity. We present example screenshots, and describe the underlying software concepts.
texttt{GooStats} is a software framework that provides a flexible environment and common tools to implement multi-variate statistical analysis. The framework is built upon the texttt{CERN ROOT}, texttt{MINUIT} and texttt{GooFit} packages. Running a multi-variate analysis in parallel on graphics processing units yields a huge boost in performance and opens new possibilities. The design and benchmark of texttt{GooStats} are presented in this article along with illustration of its application to statistical problems.
Modern analysis of high energy physics (HEP) data needs advanced statistical tools to separate signal from background. A C++ package has been implemented to provide such tools for the HEP community. The package includes linear and quadratic discriminant analysis, decision trees, bump hunting (PRIM), boosting (AdaBoost), bagging and random forest algorithms, and interfaces to the standard backpropagation neural net and radial basis function neural net implemented in the Stuttgart Neural Network Simulator. Supplemental tools such as bootstrap, estimation of data moments, and a test of zero correlation between two variables with a joint elliptical distribution are also provided. The package offers a convenient set of tools for imposing requirements on input data and displaying output. Integrated in the BaBar computing environment, the package maintains a minimal set of external dependencies and therefore can be easily adapted to any other environment. It has been tested on many idealistic and realistic examples.
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