Cultural Consumption Patterns in South Africa: An Investigation of the Theory of Cultural Omnivores

Contrary to Bourdieu’s theory (Distinction: A social critique of the judgment of taste. Cambridge, Massachusetts: Harvard University Press (1984)) that cultural consumption of so-called “high” versus popular culture is determined by socio-economic class, Peterson (Poetics 21:243–258, 1992; Poetics 33:257–282, 2005) finds that higher income and education groups are more likely to be “cultural omnivores”—consumers of a wide variety of both high and popular cultural goods. Omnivores were also found to be much less likely to exclude other cultures and to be more open to, and tolerant of, the views of others than those with narrower cultural tastes, called “cultural univores”. This article investigates the omnivore/univore hypothesis in a South African context, using survey data collected from 500 attendees of live theatre performances at the National Arts Festival in 2008. Multiple correspondence analysis (also called perceptual mapping) shows an interesting intermediate state between Boudieu-like high culture univores and Peterson omnivores, which could have interesting implications for the development of social tolerance in multi-cultural South Africa.     

Separator-based data reduction for signed graph balancing

Polynomial-time data reduction is a classical approach to hard graph problems. Typically, particular small subgraphs are replaced by smaller gadgets. We generalize this approach to handle any small subgraph that has a small separator connecting it to the rest of the graph. The problem we study is the NP-hard Balanced Subgraph problem, which asks for a 2-coloring of a graph that minimizes the inconsistencies with given edge labels. It has applications in social networks, systems biology, and integrated circuit design. The data reduction scheme unifies and generalizes a number of previously known data reductions, and can be applied to a large number of graph problems where a coloring or a subset of the vertices is sought. To solve the instances that remain after reduction, we use a fixed-parameter algorithm based on iterative compression with a very effective heuristic speedup. Our implementation can solve biological real-world instances exactly for which previously only approximations were known. In addition, we present experimental results for financial networks and random networks.     

Bayesian Nonparametric Hidden Markov Models with application to the analysis of copy-number-variation in mammalian genomes

We consider the development of Bayesian Nonparametric methods for product partition models such as Hidden Markov Models and change point models. Our approach uses a Mixture of Dirichlet Process (MDP) model for the unknown sampling distribution (likelihood) for the observations arising in each state and a computationally efficient data augmentation scheme to aid inference. The method uses novel MCMC methodology which combines recent retrospective sampling methods with the use of slice sampler variables. The methodology is computationally efficient, both in terms of MCMC mixing properties, and robustness to the length of the time series being investigated. Moreover, the method is easy to implement requiring little or no user-interaction. We apply our methodology to the analysis of genomic copy number variation.     

Non-parametric Estimation of the Residual Distribution

Consider a heteroscedastic regression model Y = m ( X ) +σ( X )ε, where the functions m and σ are "smooth", and ε is independent of X . An estimator of the distribution of ε based on non-parametric regression residuals is proposed and its weak convergence is obtained. Applications to prediction intervals and goodness-of-fit tests are discussed.     

The non-null distributions in anoya

Under the traditional assumptions, any entry in ANOVA interpreted to include all Linear model analyses] is equivalent in disiributien to a quadratic form Q=[μ₁+σ₁Z₁]²+…+ [μ_ν+σ_νZ_ν]²]wherein Z₁..Z_ν are independent standard normal variables. Test statisics in ANOVE are distributed as ratio R of two depenbent such quadretic forms. The non-null distribution of R is a mixture of null distributions; the mixing variable is an easy generalitatlon of the Poisson variable. Fast algorithms yield the power function in both fixed and random effects models in AVOVA to user-specified accuracy.     

Robust estimation for ordinal regression

Ordinal regression is used for modelling an ordinal response variable as a function of some explanatory variables. The classical technique for estimating the unknown parameters of this model is Maximum Likelihood (ML). The lack of robustness of this estimator is formally shown by deriving its breakdown point and its influence function. To robustify the procedure, a weighting step is added to the Maximum Likelihood estimator, yielding an estimator with bounded influence function. We also show that the loss in efficiency due to the weighting step remains limited. A diagnostic plot based on the Weighted Maximum Likelihood estimator allows to detect outliers of different types in a single plot.     

Anderson's classification statistic based on a post-stratified training sample

The performance of Anderson's classification statistic based on a post-stratified random sample is examined. It is assumed that the training sample is a random sample from a stratified population consisting of two strata with unknown stratum weights. The sample is first segregated into the two strata by post-stratification. The unknown parameters for each of the two populations are then estimated and used in the construction of the plug-in discriminant. Under this procedure, it is shown that additional estimation of the stratum weight will not seriously affect the performance of Anderson's classification statistic. Furthermore, our discriminant enjoys a much higher efficiency than the procedure based on an unclassified sample from a mixture of normals investigated by Ganesalingam and McLachlan (1978).