Statistics

We study maximum likelihood estimation for the statistical model for undirected random graphs, known as the β -model, in which the degree sequences are minimal sufficient statistics. We derive necessary and sufficient conditions, based on the polytope of degree sequences, for the existence of the maximum likelihood estimator (MLE) of the model parameters. We characterize in a combinatorial fashion sample points leading to a nonexistent MLE, and nonestimability of the probability parameters under a nonexistent MLE. We formulate conditions that guarantee that the MLE exists with probability tending to one as the number of nodes increases.

Modern students encounter big, messy data sets long before setting foot in our classrooms. Many of our students need to develop skills in exploratory data analysis and multivariate analysis techniques for their jobs after college, but these topics are not covered in introductory statistics courses. This case study describes my experience in designing and teaching a course on multivariate data analysis with no pre-requisites, using real data, active learning, and other activities to help students tackle the material.

The last half-dozen years have seen The American Statistician publish well-argued and provocative calls to change our thinking about statistics and how we teach it, among them Brown and Kass (2009), Nolan and Temple-Lang (2010), and Legler et al. (2010). Within this past year, the ASA has issued a new and comprehensive set of guidelines for undergraduate programs (ASA 2014). Accepting (and applauding) all this as background, the current article argues the need to rethink our curriculum from the ground up, and offers five principles and two caveats intended to help us along the path toward a new synthesis. These principles and caveats rest on my sense of three parallel evolutions: the convergence of trends in the roles of mathematics, computation, and context within statistics education. These ongoing changes, together with the articles cited above and the seminal provocation by Leo Breiman (2001) call for a deep rethinking of what we teach to undergraduates. In particular, following Brown and Kass, we should put priority on two goals, to make fundamental concepts accessible and to minimize prerequisites to research.

In this paper, we propose methods for the estimation of parameters for the three-parameter Reflected Weibull distribution. The Moment estimator , Maximum likelihood estimator and Location and Scale Parameters free maximum likelihood estimator. The Location and Scale Parameters free maximum likelihood estimator is based on a data transformation, which avoids the problem of unbounded likelihood estimator. Through Mont Carlo simulations, we further show that the Location and Scale Parameters free maximum likelihood estimator performs better than methods moment and maximum likelihood estimator in terms of bias and root mean squared error. Finally, two examples based on real data sets are presented to illustrate methods.

Structure learning in random fields has attracted considerable attention due to its difficulty and importance in areas such as remote sensing, computational biology, natural language processing, protein networks, and social network analysis. We consider the problem of estimating the probabilistic graph structure associated with a Gaussian Markov Random Field (GMRF), the Ising model and the Potts model, by extending previous work on l 1 regularized neighborhood estimation to include the elastic net l 1 + l 2 penalty. Additionally, we show numerical evidence that the edge density plays a role in the graph recovery process. Finally, we introduce a novel method for augmenting neighborhood estimation by leveraging pair-wise neighborhood union estimates.

The Healthy Life Years Lost Methodology (HLYL) is introduced to model and estimate the Health Expenditure in Japan in 2011. The HLYL theory and estimation methods are presented in our books in the Springer Series on Demographic Methods and Population Analysis vol. 45 and 46 titled: Exploring the Health State of a Population by Dynamic Modeling Methods and Demography and Health Issues: Population Aging, Mortality and Data Analysis. Special applications appear in Chapters of these books as in The Health-Mortality Approach in Estimating the Healthy Life Years Lost Compared to the Global Burden of Disease Studies and Applications in World, USA and Japan and in Estimation of the Healthy Life Expectancy in Italy Through a Simple Model Based on Mortality Rate by Skiadas and Arezzo. Here further to present the main part of the methodology with more details and illustrations, we develop and extend a life table important to estimate the healthy life years lost along with the fitting to the health expenditure in the related case. The application results are quite promising and important to support decision makers and health agencies with a powerful tool to improve the health expenditure allocation and the future predictions.

Investment approaches in financial instruments have been varied and often produce unpredictable results. Many investors in the earlier days of investment banking suffered catastrophical losses due to poor strategy and lack of understanding of the financial market. With the development of investment banking, many innovative investment strategies have been proposed to make portfolio returns higher than the overall market. One of the most famous theories of portfolio creation and management is the modern portfolio theory proposed by Harry Markowitz. In this paper, we shall apply the theory in creating a portfolio of stocks as well as managing it.

This paper proposes an on-line multiple object tracking algorithm that can operate in unknown background. In a majority of multiple object tracking applications, model parameters for background processes such as clutter and detection are unknown and vary with time, hence the ability of the algorithm to adaptively learn the these parameters is essential in practice. In this work, we detail how the Generalized Labeled Multi Bernouli (GLMB) filter a tractable and provably Bayes optimal multi-object tracker can be tailored to learn clutter and detection parameters on the fly while tracking. Provided that these background model parameters do not fluctuate rapidly compared to the data rate, the proposed algorithm can adapt to the unknown background yielding better tracking performance.

We use the Enron email corpus to study relationships in a network by applying six different measures of centrality. Our results came out of an in-semester undergraduate research seminar. The Enron corpus is well suited to statistical analyses at all levels of undergraduate education. Through this note's focus on centrality, students can explore the dependence of statistical models on initial assumptions and the interplay between centrality measures and hierarchical ranking, and they can use completed studies as springboards for future research. The Enron corpus also presents opportunities for research into many other areas of analysis, including social networks, clustering, and natural language processing.

Dynamic extinction colonisation models (also called contact processes) are widely studied in epidemiology and in metapopulation theory. Contacts are usually assumed to be possible only through a network of connected patches. This network accounts for a spatial landscape or a social organisation of interactions. Thanks to social network literature, heterogeneous networks of contacts can be considered. A major issue is to assess the influence of the network in the dynamic model. Most work with this common purpose uses deterministic models or an approximation of a stochastic Extinction-Colonisation model (sEC) which are relevant only for large networks. When working with a limited size network, the induced stochasticity is essential and has to be taken into account in the conclusions. Here, a rigorous framework is proposed for limited size networks and the limitations of the deterministic approximation are exhibited. This framework allows exact computations when the number of patches is small. Otherwise, simulations are used and enhanced by adapted simulation techniques when necessary. A sensitivity analysis was conducted to compare four main topologies of networks in contrasting settings to determine the role of the network. A challenging case was studied in this context: seed exchange of crop species in the Réseau Semences Paysannes (RSP), an emergent French farmers' organisation. A stochastic Extinction-Colonisation model was used to characterize the consequences of substantial changes in terms of RSP's social organisation on the ability of the system to maintain crop varieties.