LOGIN TO YOUR ACCOUNT

Username
Password
Remember Me
Or use your Academic/Social account:

CREATE AN ACCOUNT

Or use your Academic/Social account:

Congratulations!

You have just completed your registration at OpenAire.

Before you can login to the site, you will need to activate your account. An e-mail will be sent to you with the proper instructions.

Important!

Please note that this site is currently undergoing Beta testing.
Any new content you create is not guaranteed to be present to the final version of the site upon release.

Thank you for your patience,
OpenAire Dev Team.

Close This Message

CREATE AN ACCOUNT

Name:
Username:
Password:
Verify Password:
E-mail:
Verify E-mail:
*All Fields Are Required.
Please Verify You Are Human:
fbtwitterlinkedinvimeoflicker grey 14rssslideshare1
Baaqeel, Hanan (2015)
Languages: English
Types: Unknown
Subjects:
Random graphs and networks are of great importance in any fields including mathematics, computer science, statistics, biology and sociology. This research aims to develop statistical theory and methods of statistical inference for random graphs in novel directions. A major strand of the research is the development of conditional goodness-of-fit tests for random graph models and for random block graph models. On the theoretical side, this entails proving a new conditional central limit theorem for a certain graph statistics, which are closely related to the number of two-stars and the number of triangles, and where the conditioning is on the number of edges in the graph. A second strand of the research is to develop composite likelihood methods for estimation of the parameters in exponential random graph models. Composite likelihood methods based on edge data have previously been widely used. A novel contribution of the thesis is the development of composite likelihood methods based on more complicated data structures. The goals of this PhD thesis also include testing the numerical performance of the novel methods in extensive simulation studies and through applications to real graphical data sets.
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

    • 2 Review of Background and relevant Techniques 5 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Background on Random Graph Models . . . . . . . . . . . . . . . 5 2.2.1 Basic Terminology in Graph Theory . . . . . . . . . . . . . 6 2.2.2 Random Graph Models . . . . . . . . . . . . . . . . . . . . 8 2.3 Relevant Mathematical Techniques and Results . . . . . . . . . . 14 2.3.1 Spectral Decomposition Theorem in Linear Algebra . . . . 14 2.3.2 Equivalence Relation and Partitions . . . . . . . . . . . . . 15 2.4 Background in Probability and Statistics . . . . . . . . . . . . . . 16 2.4.1 Univariate and Multivariate Normal Distributions . . . . . 17 2.4.2 Dierent Types of Stochastic Convergence . . . . . . . . . 18 2.4.3 Central Limit Theorem . . . . . . . . . . . . . . . . . . . . 19 2.4.4 Projections . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.4.5 The Method of Moments . . . . . . . . . . . . . . . . . . . 23 2.4.6 Conditional Expectation . . . . . . . . . . . . . . . . . . . 23 2.5 Composite Likelihood Methods . . . . . . . . . . . . . . . . . . . 24 2.5.1 Types of Composite Likelihood . . . . . . . . . . . . . . . 24 2.5.2 Asymptotic behavior of Composite Likelihood estimators . 25 2.6 More Advanced Topics . . . . . . . . . . . . . . . . . . . . . . . . 27
    • Chatterjee, S., Diaconis, P. and Sly, A. (2011), 'Random graphs with a given degree sequence', The Annals of Applied Probability 21, 14001435.
    • Robins, G., Pattison, P., Kalish, Y. and Lusher, D. (2007), 'An introduction to exponential random graph models for social networks', Social Networks 29, 173 191.
    • Robins, G., Snijders, T., Wang, P., Handcock, M. and Pattison, P. (2007), 'Recent developments in exponential random graph models for social networks', Social networks 29, 192215.
    • Snijders, T. A. (2002), 'Markov chain monte carlo estimation of exponential random graph models', Journal of Social Structure 3, 140.
  • No related research data.
  • No similar publications.

Share - Bookmark

Cite this article