290 research outputs found
Comment: Bibliometrics in the Context of the UK Research Assessment Exercise
Research funding and reputation in the UK have, for over two decades, been
increasingly dependent on a regular peer-review of all UK departments. This is
to move to a system more based on bibliometrics. Assessment exercises of this
kind influence the behavior of institutions, departments and individuals, and
therefore bibliometrics will have effects beyond simple measurement.
[arXiv:0910.3529]Comment: Published in at http://dx.doi.org/10.1214/09-STS285A the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Empirical Bayes selection of wavelet thresholds
This paper explores a class of empirical Bayes methods for level-dependent
threshold selection in wavelet shrinkage. The prior considered for each wavelet
coefficient is a mixture of an atom of probability at zero and a heavy-tailed
density. The mixing weight, or sparsity parameter, for each level of the
transform is chosen by marginal maximum likelihood. If estimation is carried
out using the posterior median, this is a random thresholding procedure; the
estimation can also be carried out using other thresholding rules with the same
threshold. Details of the calculations needed for implementing the procedure
are included. In practice, the estimates are quick to compute and there is
software available. Simulations on the standard model functions show excellent
performance, and applications to data drawn from various fields of application
are used to explore the practical performance of the approach. By using a
general result on the risk of the corresponding marginal maximum likelihood
approach for a single sequence, overall bounds on the risk of the method are
found subject to membership of the unknown function in one of a wide range of
Besov classes, covering also the case of f of bounded variation. The rates
obtained are optimal for any value of the parameter p in (0,\infty],
simultaneously for a wide range of loss functions, each dominating the L_q norm
of the \sigmath derivative, with \sigma\ge0 and 0<q\le2.Comment: Published at http://dx.doi.org/10.1214/009053605000000345 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
EbayesThresh: R Programs for Empirical Bayes Thresholding
Suppose that a sequence of unknown parameters is observed sub ject to independent Gaussian noise. The EbayesThresh package in the S language implements a class of Empirical Bayes thresholding methods that can take advantage of possible sparsity in the sequence, to improve the quality of estimation. The prior for each parameter in the sequence is a mixture of an atom of probability at zero and a heavy-tailed density. Within the package, this can be either a Laplace (double exponential) density or else a mixture of normal distributions with tail behavior similar to the Cauchy distribution. The mixing weight, or sparsity parameter, is chosen automatically by marginal maximum likelihood. If estimation is carried out using the posterior median, this is a random thresholding procedure; the estimation can also be carried out using other thresholding rules with the same threshold, and the package provides the posterior mean, and hard and soft thresholding, as additional options. This paper reviews the method, and gives details (far beyond those previously published) of the calculations needed for implementing the procedures. It explains and motivates both the general methodology, and the use of the EbayesThresh package, through simulated and real data examples. When estimating the wavelet transform of an unknown function, it is appropriate to apply the method level by level to the transform of the observed data. The package can carry out these calculations for wavelet transforms obtained using various packages in R and S-PLUS. Details, including a motivating example, are presented, and the application of the method to image estimation is also explored. The final topic considered is the estimation of a single sequence that may become progressively sparser along the sequence. An iterated least squares isotone regression method allows for the choice of a threshold that depends monotonically on the order in which the observations are made. An alternative possibility, also discussed in detail, is a particular parametric dependence of the sparsity parameter on the position in the sequence.
Julian Ernst Besag, 26 March 1945 -- 6 August 2010, a biographical memoir
Julian Besag was an outstanding statistical scientist, distinguished for his
pioneering work on the statistical theory and analysis of spatial processes,
especially conditional lattice systems. His work has been seminal in
statistical developments over the last several decades ranging from image
analysis to Markov chain Monte Carlo methods. He clarified the role of
auto-logistic and auto-normal models as instances of Markov random fields and
paved the way for their use in diverse applications. Later work included
investigations into the efficacy of nearest neighbour models to accommodate
spatial dependence in the analysis of data from agricultural field trials,
image restoration from noisy data, and texture generation using lattice models.Comment: 26 pages, 14 figures; minor revisions, omission of full bibliograph
Warping Functional Data in R and C via a Bayesian Multiresolution Approach
Phase variation in functional data obscures the true amplitude variation when a typical cross-sectional analysis of these responses would be performed. Time warping or curve registration aims at eliminating the phase variation, typically by applying transformations, the warping functions τn, to the function arguments. We propose a warping method that jointly estimates a decomposition of the warping function in warping components, and amplitude components. For the estimation routine, adaptive MCMC calculations are performed and implemented in C rather than R to increase computational speed. The R-C interface makes the program user-friendly, in that no knowledge of C is required and all input and output will be handled through R. The R package MRwarping contains all needed files
Bootstrapping multiple systems estimates to account for model selection
Multiple systems estimation is a standard approach to quantifying hidden
populations where data sources are based on lists of known cases. A typical
modelling approach is to fit a Poisson loglinear model to the numbers of cases
observed in each possible combination of the lists. It is necessary to decide
which interaction parameters to include in the model, and information criterion
approaches are often used for model selection. Difficulties in the context of
multiple systems estimation may arise due to sparse or nil counts based on the
intersection of lists, and care must be taken when information criterion
approaches are used for model selection due to issues relating to the existence
of estimates and identifiability of the model. Confidence intervals are often
reported conditional on the model selected, providing an over-optimistic
impression of the accuracy of the estimation.
A bootstrap approach is a natural way to account for the model selection
procedure. However, because the model selection step has to be carried out for
every bootstrap replication, there may be a high or even prohibitive
computational burden. We explore the merit of modifying the model selection
procedure in the bootstrap to look only among a subset of models, chosen on the
basis of their information criterion score on the original data. This provides
large computational gains with little apparent effect on inference. Another
model selection approach considered and investigated is a downhill search
approach among models, possibly with multiple starting points.Comment: 21 pages, 5 figures, 6 table
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