In survey research, researchers often add up a finite number of binary responses to form an index of some political attitude or behavior, such as political knowledge and political participation. Indices of this sort are called grouped binary variables in political science research; they comprise finite and countable binary items that take on only integer values ranging from zero to the total number of survey items. Commonly-used distributions for modeling these kinds of indices are the binomial, beta binomial, and extended beta binomial distributions. But whether these distributions are appropriate depends on the assumptions that the binary responses are identically and independently distributed Bernoulli random variables. If these assumptions are violated, the binomial, beta binomial, and extended beta binomial models are rendered questionable, and it may be more useful to turn to other distributions of sums of Bernoulli variables, called generalized binomial distributions. To facilitate the use of generalized binomial distributions in political science research, this report is a review of the various probability distributions of grouped binary variables. This report clarifies the nature of the distributions of sums of Bernoulli variables in survey research by considering whether the Bernoulli variables are independently and/or identically distributed, whether there is heterogeneity across survey items and/or across respondents, and the consequences of these considerations for the relative dispersion of each generalized binomial distribution. / text

A determination of Parton Distribution Functions (PDFs) from a global fit to a dataset including measurements from the LHC has been performed for the first time. The determinations have been performed according to the NNPDF methodology, leading to a fit relatively free of parametrisation bias and with an accurate account of PDF uncertainty. In this thesis the importance of QCD measurements at the LHC to PDF extraction are discussed, and we summarise some of the technical difficulties in their inclusion into PDF fits. A number of methods are presented that permit the efficient inclusion of these observables into PDF determinations. Firstly a Bayesian reweighting procedure taking advantage of the Monte Carlo representation of PDF uncertainties in NNPDF sets is discussed. The utility of the Bayesian reweighting method is demonstrated by a study of the impact of early W production asymmetry measurements from ATLAS, CMS and LHCb upon an earlier PDF set. A package for the fast computation of observables in an automated NLO framework is presented, providing an interface between Monte Carlo event generators and NLO interpolation tools. Finally, a new method of combining PDF evolution with interpolating codes for hadronic observable computation is also described. This method largely overcomes the computational difficulties in performing fast perturbative QCD predictions for collider observables. The method has been applied to the determination of PDFs from a global dataset including electroweak vector boson production data from LHCb, ATLAS and CMS along with inclusive jet data from ATLAS. The resulting set, NNPDF2.3 provides the most accurate determination of parton distributions via the NNPDF methodology to date. Finally, the method of closure testing is introduced, and the method is applied to the study of the NNPDF methodology. A number of improvements are found in the minimisation and stopping procedures, which are adopted for the development of the next NNPDF release, NNPDF3.0. Alongside the sounder methodological basis, the NNPDF3.0 PDF set will provide a determination based upon an expanded datfits.

published_or_final_version / Mathematics / Doctoral / Doctor of Philosophy

No description available.

Thesis--Ph. D., University of Hong Kong, 1983.

published_or_final_version / Applied Statistics / Master / Master of Social Sciences

No description available.

Thesis, Ph.D., University of Hong Kong, 1983. / Also available in print.

Thesis (M. Soc. Sc.)--University of Hong Kong, 1993. / Includes bibliographical references.

Thesis (M.Soc.Sc.)--University of Hong Kong, 1993. / Includes bibliographical references. Also available in print.