1 Naive Bayes, 20 points Problem 1. Basic concepts, 10 points Naive Bayes reduces the number of parameters that must be estimated for a Bayesian classifier, by making a conditional independence assumption when modeling P (X|Y). The definition for conditional independence is the following: Given this definition, please answer the following questions:

cDNA microarrays are used in many contexts to compare mRNA levels between samples of cells. Microarray experiments typically give us expression measurements on 1000-20 000 genes, but with few replicates for each gene. Traditional methods using means and standard deviations to detect differential expression are not satisfactory in this context. A handful of alternative statistics have been devel...

Compressive Sensing (CS) provides a new paradigm of sub-Nyquist sampling which can be considered as an alternative to Nyquist sampling theorem. In particular, providing that signals are with sparse representations in some known space (or domain), information can be perfectly preserved even with small amount of measurements captured by random projections. Besides sparsity prior of signals, the i...

Bayes and empirical Bayes methods have proven eeective in smoothing crude maps of disease risk, eliminating the instability of estimates in low-population areas while maintaining overall geographic trends and patterns. Recent work applies these methods to the analysis of areal data which are spatially misaligned, i.e., involving variables (typically counts or rates) which are aggregated over di...

BACKGROUND Rodent hippocampal population codes represent important spatial information about the environment during navigation. Computational methods have been developed to uncover the neural representation of spatial topology embedded in rodent hippocampal ensemble spike activity. NEW METHOD We extend our previous work and propose a novel Bayesian nonparametric approach to infer rat hippocam...

a two-factor experiment with interaction between factors wherein observations follow an inverse gaussian model is considered. analysis of the experiment is approached via an empirical bayes procedure. the conjugate family of prior distributions is considered. bayes and empirical bayes estimators are derived. application of the procedure is illustrated on a data set, which has previously been an...

The paper introduces the ‘Bayes transform’, a mathematical procedure for putting data into a hierarchical representation. Applicable to any type of data, the procedure yields interesting results when applied to sequences. In this case, the representation obtained implicitly models the repetition hierarchy of the source. There are then natural applications to music. Derivation of Bayes transform...

BACKGROUND Multilevel modelling, also known as hierarchical regression, generalizes ordinary regression modelling to distinguish multiple levels of information in a model. Use of multiple levels gives rise to an enormous range of statistical benefits. To aid in understanding these benefits, this article provides an elementary introduction to the conceptual basis for multilevel modelling, beginn...

We analyze a hierarchical Bayes model which is related to the usual empirical Bayes formulation of James-Stein estimators. We consider running a Gibbs sampler on this model. Using previous results about convergence rates of Markov chains, we provide rigorous, numerical, reasonable bounds on the running time of the Gibbs sampler, for a suitable range of prior distributions. We apply these result...