Statistics Seminar - Fall 2018

We introduce a novel framework for model-free variable selection with matrix-valued predictors. To test the importance of rows, columns, and submatrices of the predictor matrix in terms of predicting the response, three types of hypotheses are formulated under a unified framework, and a simple permutation test procedure is used to approximate the null distribution of the test statistics for all three tests. A nonparametric maximum ratio criteria (MRC) is proposed for the purpose of model-free variable selection. Unlike the traditional stepwise regression procedures that require calculating p-values at each step, MRC is a non-iterative procedure that does not require p-value calculation. The effectiveness of the proposed methods are evaluated through extensive numerical studies and an application to the electroencephalography (EEG) dataset.

Randomized controlled trials (RCT's) are an indispensable source of information about efficacy of treatments in almost any disease area. With the availability of multiple treatment options, comparative effectiveness research (CER) is gaining importance for better and informed health care decisions. However, design and analysis of effectiveness trial is much more complex than the efficacy trial. The effect of including an active comparator arm/s in a RCT is immense. This gives rise to superiority and non-inferiority trials. The non-inferiority (NI) RCT design plays a fundamental role in CER, which will be also focus of this talk. We will primarily focus on three-arm NI trial design. Testing in such setup is not unique and there exist two competing approaches under Frequentist framework namely fraction margin and fixed margin based approach. We will discuss the advantage and issues of each approach. We will also talk about Bayesian approach and discuss some interesting open problems related to CER using NI trial.

One of the main tasks of statistical models is to characterize the dependence structures of multi-dimensional distributions. Latent variable model takes advantage of the fact that the dependence of a high dimensional random vector is often induced by just a few latent (unobserved) factors. Such models are employed in the analysis of educational and psychological assessment, political sciences, marketing, finance, and many other fields where human behaviors are observed and are summarized to a few characteristics. In this talk, we present three real data examples in psychology, finance, and political sciences. In these examples, a common problem is that the dimension grows higher and the dependence structure becomes more complicated. It is hardly possible to find a low dimensional parametric latent variable model that fits well. We enrich the model by including a graphical structure on top of the latent structure. The graph captures the remaining dependence and is often more interpretable than graphs built on marginal dependence.

Uncertainty in real life takes on many forms. An analyst can hesitate to specify a prior for a Bayesian model, or be ignorant of the mechanism that gave rise to the missing data. Such kinds of uncertainty cannot be faithfully captured by a single probability but by a set of probabilities, and in special cases, by a capacity function and/or a belief function. Sets of probabilities present an attractive modeling strategy that alleviates the need to concoct unwarranted assumptions, and in so doing reduces irreplicable findings.

In this talk, I motivate the use of sets of probabilities and showcase their ability to capture low-resolution information in both data and model aspects. I present a belief function model for multinomial inference that is prior-free, computationally efficient, and delivers posterior inference as a class of random convex polytopes. I discuss challenges that arise with the employment of belief and capacity functions, specifically, the choice of conditioning rules and how they reconcile among a trio of unsettling phenomena: dilation, contraction and sure loss. These findings underscores the invaluable role of judicious judgment in handling low-resolution probabilistic information.

We consider statistical inference for the explained variance under the high-dimensional linear model in the semi-supervised setting. A calibrated estimator, which efficiently integrates both labelled and unlabelled data, is proposed. It is shown that the estimator achieves the minimax optimal rate of convergence in the general semi-supervised framework. The optimality result characterizes how the unlabelled data affects the minimax optimal rate. Moreover, the limiting distribution for the proposed estimator is established and data-driven confidence intervals for the explained variance are constructed. We further develop a randomized calibration technique for statistical inference in the presence of weak signals and apply the obtained inference results to a range of important statistical problems, including signal detection and global testing, prediction accuracy evaluation, and confidence ball construction. The numerical performance of the proposed methodology is demonstrated in simulation studies and an analysis of estimating heritability for a yeast segregant data set with multiple traits.

Computer experiments have become ubiquitous in various applications from rocket injector designs to weather forecasting. In spite of the extensive research literature, computer experiments with binary time-series outputs have received scant attention. Motivated by the analysis of a class of cell adhesion experiments, we introduce a new emulator as well as a new calibration framework for binary time-series outputs. We provide their theoretical properties to ensure the estimation performance in an asymptotic setting. The application to the cell adhesion experiments illustrates that the proposed emulator and calibration framework can not only provide an efficient alternative for the computer simulation, but also reveal important insight on the underlying adhesion mechanism, which cannot be directly observed through existing methods.

Statistics is a much versatile subject which can be applied in almost any activity in life. Statistics has been introduced in almost all degree courses in universities. However, studies in different countries have shown that there is a high level of statistics anxiety among the under graduates. The degree of anxiety varied on the type of the degree program. This study was therefore initiated to study the statistics anxiety of the Social Science undergraduates in government universities in the Western Province in Sri Lanka. To achieve this objective a survey was carried out with 319 undergraduates. Necessary information was acquired through structural questionnaire after pre tested. Chi-square analyses for 2-way contingency tables and Factor Analysis (FA) were performed. It was found that the percentage of statistic anxiety among males is significantly higher than that of females. Factors were extracted using principal axis factoring method and both orthogonal and non-orthogonal methods of rotation were applied. Validity of data for FA was confirmed using both statistical and non-statistical methods. Fear for Mathematics, Statistical Software, Computers, Statistics, Less Support, Misunderstanding, Negative Self Perception, Less Guidance, Less Cognitive Capacity and Class Anxiety were the factors identified as the reasons for statistics anxiety irrespective of gender and age. Validity of factors were also confirmed by the Cronbach’s reliability index. Of those ten factors “fear for mathematics” is the most important factor. This factor is formed due to the reasons of “never enjoyed working with numbers”, “hard to understand conclusions based on mathematics solutions”, “not good at mathematics”, and “difficulty with the vocabulary of math”. Furthermore, it was identified that “more support and help” and “cognitive capacity” were the two significant factors to mitigate the student’s anxiety in statistics. The results identified are useful to the decision makers in the respective departments and it is recommended to carry out similar studies for other universities as well.