Relabelling Algorithms for Large Dataset Mixture Models

Mixture models are flexible tools in density estimation and classification problems. Bayesian estimation of such models typically relies on sampling from the posterior distribution using Markov chain Monte Carlo. Label switching arises because the posterior is invariant to permutations of the component parameters. Methods for dealing with label switching have been studied fairly extensively in the literature, with the most popular approaches being those based on loss functions. However, many of these algorithms turn out to be too slow in practice, and can be infeasible as the size and dimension of the data grow. In this article, we review earlier solutions which can scale up well for large data sets, and compare their performances on simulated and real datasets. In addition, we propose a new, and computationally efficient algorithm based on a loss function interpretation, and show that it can scale up well in larger problems. We conclude with some discussions and recommendations of all the methods studied

Every teacher is a language teacher: Preparing teacher candidates for English language learners through service-learning

Secondary school teachers in the United States are facing urgent challenges in their increasingly heterogeneous classrooms where the presence of English language learners (ELLs) is becoming the norm. This study reports preliminary findings of a qualitative, interpretive case study of secondary school teacher candidates learning to teach English language learners through service-learning in Northern California. In a semester-long tutoring project, candidates focused on individual ELLs in their inquiry into language learning, in which they (re)constructed their sociolinguistic knowledge of English and their tutees’ home languages in context. Moreover, the mutually beneficial relationships among members of the language community encouraged candidates’ critical reflections on language learning. The study offers instructional experiences for teachers and teacher educators to develop sociolinguistic and pedagogical tools while supporting, and being supported by, the ELL communities. Keywords: teacher education, service-learning, sociocultural perspective, English language learners, secondary schools, teacher knowledg

Lost in institution: Learning to write in Midwestern urban mainstream classrooms

How do recent immigrant students learn to write in mainstream content area classrooms? This article considers this question in the under-investigated American Midwest contexts where schooling is being reframed by rapid changing demographics. Data for this paper come from an ethnographic case study of second language learning of a Vietnamese 9th grader in an urban school setting. Grounded in a sociocultural view of learning, the author examines (1) how the student negotiated the nature and purpose of writing among inconsistent expectations, objectives and responsibilities in mainstream, and (2) how she was lost in a lack of vision in literacy and the larger institutional environment which encouraged teachers to reward formalism over substance. The author concludes with recommendations for educators in secondary schools to explicitly link pedagogical objectives to language learners literacy needs and to embedded social values of schooling

Non Parametric Confidence Intervals for Receiver Operating Characteristic Curves

We study methods for constructing confidence intervals, and confidence bands, for estimators of receiver operating characteristics. Particular emphasis is placed on the way in which smoothing should be implemented, when estimating either the characteristic itself or its variance. We show that substantial undersmoothing is necessary if coverage properties are not to be impaired. A theoretical analysis of the problem suggests an empirical, plug-in rule for bandwidth choice, optimising the coverage accuracy of interval estimators. The performance of this approach is explored. Our preferred technique is based on asymptotic approximation, rather than a more sophisticated approach using the bootstrap, since the latter requires a multiplicity of smoothing parameters all of which must be chosen in nonstandard ways. It is shown that the asymptotic method can give very good performance.Bandwidth selection, binary classification, kernel estimator, receiver operating characteristic curve.

Bayesian Symbol Detection in Wireless Relay Networks via Likelihood-Free Inference

This paper presents a general stochastic model developed for a class of cooperative wireless relay networks, in which imperfect knowledge of the channel state information at the destination node is assumed. The framework incorporates multiple relay nodes operating under general known non-linear processing functions. When a non-linear relay function is considered, the likelihood function is generally intractable resulting in the maximum likelihood and the maximum a posteriori detectors not admitting closed form solutions. We illustrate our methodology to overcome this intractability under the example of a popular optimal non-linear relay function choice and demonstrate how our algorithms are capable of solving the previously intractable detection problem. Overcoming this intractability involves development of specialised Bayesian models. We develop three novel algorithms to perform detection for this Bayesian model, these include a Markov chain Monte Carlo Approximate Bayesian Computation (MCMC-ABC) approach; an Auxiliary Variable MCMC (MCMC-AV) approach; and a Suboptimal Exhaustive Search Zero Forcing (SES-ZF) approach. Finally, numerical examples comparing the symbol error rate (SER) performance versus signal to noise ratio (SNR) of the three detection algorithms are studied in simulated examples