2018/1

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The relationship between anxiety and performance in a statistics class
(Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2018) Mason, S. E.; Reid, E. M.
Many students experience anxiety when taking a required statistics course. As high levels of anxiety may interfere with performance, it is desirable to identify and control factors shown to affect student anxiety. The purpose of our research was to examine the relationship between anxiety and performance and to deter- mine which aspects of course structure have the greatest effects on student anxiety levels. In a series of four studies we found self-reported anxiety levels to be neg- atively correlated with both grade expectations and final course grades. Students attributed decreases in anxiety levels to several factors, including class exercises and class atmosphere.
Sizing up the regions of unique minima in the least squares nonlinear regression
(Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2018) Khinkis, L.; Crotzer M.; Oprisan, A.
In nonlinear regression analysis, the residual sum of squares may possess multiple local minima. This complicates finding the global minimum and adversely affects reliability of the relevant statistical methods. Identifying and sizing up the regions of a readily identifiable global minimum (RIGM) is therefore of both theo- retical and practical interest. This paper addresses the issue by using equidistant function previously introduced by the first two co-authors of this paper.
Using the Seychelles child development study to cluster multiple outcomes into domains to improve estimation of the overall effect of mercury on neurodevelopment
(Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2018) LaLonde, A.; Love, T.
Environmental exposure effects on human development can be small and difficult to detect due to the nature of observational data. In the Seychelles Child Development Study, researchers examined the effect of prenatal methylmercury ex- posure using a battery of tests measuring aspects of child development [18, 20]. We build a multiple outcomes model similar to that of the previous analyses (see [18, 20]); however, our multiple outcomes model makes no assumptions of relation- ships between the testing outcomes. Instead, the nesting of outcomes into domains is a clustering problem we address with a Dirichlet process mixture model imple- mented through a Bayesian MCMC approach [12]. This model provides inference for the methylmercury exposure effect as well as greater insight into the similarities and differences across the outcomes.
Hierarchical Bayesian Bradley–Terry for applications in Major League Baseball
(Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2018) Phelan, G. C.; Whelan, J. T.
A common problem faced in statistical inference is drawing conclusions from paired comparisons, in which two objects compete and one is declared the victor. A probabilistic approach to such a problem is the Bradley–Terry model [5, 20], first studied by Zermelo in 1929 and rediscovered by Bradley and Terry in 1952. One obvious area of application for such a model is sporting events, and in particular Major League Baseball. With this in mind, we describe a hierarchical Bayesian version of Bradley–Terry suitable for use in ranking and prediction problems, and compare results from these application domains to standard maximum likelihood approaches. Our Bayesian methods outperform the MLE-based analogues, while being simple to construct, implement, and interpret.
Random Subspace Learning (RASSEL) with data driven weighting schemes
(Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2018) Elshrif, M.; Fokoué, E.
We present a novel adaptation of the random subspace learning approach to regression analysis and classification of high dimension low sample size data, in which the use of the individual strength of each explanatory variable is harnessed to achieve a consistent selection of a predictively optimal collection of base learners. In the context of random subspace learning, random forest (RF) occupies a prominent place as can be seen by the vast number of extensions of the random forest idea and the multiplicity of machine learning applications of random forest. The adaptation of random subspace learning presented in this paper differs from random forest in the following ways: (a) instead of using trees as RF does, we use multiple linear regression (MLR) as our regression base learner and the generalized linear model (GLM) as our classification base learner and (b) rather than selecting the subset of variables uniformly as RF does, we present the new concept of sampling variables based on a multinomial distribution with weights (success ’probabilities’) driven through p independent one-way analysis of variance (ANOVA) tests on the predic- tor variables. The proposed framework achieves two substantial benefits, namely, (1) the avoidance of the extra computational burden brought by the permutations needed by RF to de-correlate the predictor variables, and (2) the substantial reduc- tion in the average test error gained with the base learners used.

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