SUMMARY We propose a new method for estimation in linear models. The 'lasso' minimizes the residual sum of squares subject to the sum of the absolute value of the coefficients being less than a constant. Because of the nature of this constraint it tends to produce some coefficients that are exactly 0 and hence gives interpretable models. Our simulation studies suggest that the lasso enjoys some of the favourable properties of both subset selection and ridge regression. It produces interpretable models like subset selection and exhibits the stability of ridge regression. There is also an interesting relationship with recent work in adaptive function estimation by Donoho and Johnstone. The lasso idea is quite general and can be applied in a variety of statistical models: extensions to generalized regression models and tree-based models are briefly described.

/pdf/regression-shrinkage-and-selection-via-the-lasso-6mx35txfr5.pdf

Regression Shrinkage and Selection via the Lasso

We describe a model-based clustering method for using multilocus genotype data to infer population structure and assign individuals to populations. We assume a model in which there are K populations (where K may be unknown), each of which is characterized by a set of allele frequencies at each locus. Individuals in the sample are assigned (probabilistically) to populations, or jointly to two or more populations if their genotypes indicate that they are admixed. Our model does not assume a particular mutation process, and it can be applied to most of the commonly used genetic markers, provided that they are not closely linked. Applications of our method include demonstrating the presence of population structure, assigning individuals to populations, studying hybrid zones, and identifying migrants and admixed individuals. We show that the method can produce highly accurate assignments using modest numbers of loci— e.g. , seven microsatellite loci in an example using genotype data from an endangered bird species. The software used for this article is available from http://www.stats.ox.ac.uk/~pritch/home.html.

/pdf/inference-of-population-structure-using-multilocus-genotype-1x75ku6urs.pdf

Inference of population structure using multilocus genotype data

We propose a generative model for text and other collections of discrete data that generalizes or improves on several previous models including naive Bayes/unigram, mixture of unigrams [6], and Hof-mann's aspect model, also known as probabilistic latent semantic indexing (pLSI) [3]. In the context of text modeling, our model posits that each document is generated as a mixture of topics, where the continuous-valued mixture proportions are distributed as a latent Dirichlet random variable. Inference and learning are carried out efficiently via variational algorithms. We present empirical results on applications of this model to problems in text modeling, collaborative filtering, and text classification.

/pdf/latent-dirichlet-allocation-rkwbqihm3p.pdf

Latent Dirichlet Allocation

Summary: The program MRBAYES performs Bayesian inference of phylogeny using a variant of Markov chain Monte Carlo. Availability: MRBAYES, including the source code, documentation, sample data files, and an executable, is available at http://brahms.biology.rochester.edu/software.html.

http://webpages.icav.up.pt/PTDC/BIA-BEC/104097/2008/23.pdf

MRBAYES: Bayesian inference of phylogenetic trees

The Gibbs sampler, the algorithm of Metropolis and similar iterative simulation methods are potentially very helpful for summarizing multivariate distributions. Used naively, however, iterative simulation can give misleading answers. Our methods are simple and generally applicable to the output of any iterative simulation; they are designed for researchers primarily interested in the science underlying the data and models they are analyzing, rather than for researchers interested in the probability theory underlying the iterative simulations themselves. Our recommended strategy is to use several independent sequences, with starting points sampled from an overdispersed distribution. At each step of the iterative simulation, we obtain, for each univariate estimand of interest, a distributional estimate and an estimate of how much sharper the distributional estimate might become if the simulations were continued indefinitely. Because our focus is on applied inference for Bayesian posterior distributions in real problems, which often tend toward normality after transformations and marginalization, we derive our results as normal-theory approximations to exact Bayesian inference, conditional on the observed simulations. The methods are illustrated on a random-effects mixture model applied to experimental measurements of reaction times of normal and schizophrenic patients.

/pdf/inference-from-iterative-simulation-using-multiple-sequences-f65bwr81f3.pdf

Inference from Iterative Simulation Using Multiple Sequences

Markov chain Monte Carlo methods for Bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some fixed standard underlying measure. They have therefore not been available for application to Bayesian model determination, where the dimensionality of the parameter vector is typically not fixed. This paper proposes a new framework for the construction of reversible Markov chain samplers that jump between parameter subspaces of differing dimensionality, which is flexible and entirely constructive. It should therefore have wide applicability in model determination problems. The methodology is illustrated with applications to multiple change-point analysis in one and two dimensions, and to a Bayesian comparison of binomial experiments.

Reversible jump Markov chain Monte Carlo computation and Bayesian model determination

Celiac Disease

Refence centile curves show the distribution of a measurement as it changes according to some covariate, often age The LMS method summarizes the changing distribution by three curves representing the median, coefficient of variation and skewness, the latter expressed as a Box-Cox power Using penalized likelihood the three curves can be fitted as cubic splines by non-linear regression, and the extent of smoothing required can be expressed in terms of smoothing parameters or equivalent degrees of freedom The method is illustrated with data on triceps skinfold in Gambian girls and women, and body weight in USA girls

Smoothing reference centile curves: The lms method and penalized likelihood

New methodology for fully Bayesian mixture analysis is developed, making use of reversible jump Markov chain Monte Carlo methods that are capable of jumping between the parameter subspaces corresponding to different numbers of components in the mixture A sample from the full joint distribution of all unknown variables is thereby generated, and this can be used as a basis for a thorough presentation of many aspects of the posterior distribution The methodology is applied here to the analysis of univariate normal mixtures, using a hierarchical prior model that offers an approach to dealing with weak prior information while avoiding the mathematical pitfalls of using improper priors in the mixture context

On Bayesian Analysis of Mixtures with an Unknown Number of Components (with discussion)

Of course, from childhood to forever, we are always thought to love reading. It is not only reading the lesson book but also reading everything good is the choice of getting new inspirations. Religion, sciences, politics, social, literature, and fictions will enrich you for not only one aspect. Having more aspects to know and understand will lead you become someone more precious. Yea, becoming precious can be situated with the presentation of how your knowledge much.

Peter H.R. Green

Papers

Reversible jump Markov chain Monte Carlo computation and Bayesian model determination

Celiac Disease

Smoothing reference centile curves: The lms method and penalized likelihood

On Bayesian Analysis of Mixtures with an Unknown Number of Components (with discussion)

Nonparametric regression and generalized linear models