6,977 research outputs found
Automated analysis of quantitative image data using isomorphic functional mixed models, with application to proteomics data
Image data are increasingly encountered and are of growing importance in many
areas of science. Much of these data are quantitative image data, which are
characterized by intensities that represent some measurement of interest in the
scanned images. The data typically consist of multiple images on the same
domain and the goal of the research is to combine the quantitative information
across images to make inference about populations or interventions. In this
paper we present a unified analysis framework for the analysis of quantitative
image data using a Bayesian functional mixed model approach. This framework is
flexible enough to handle complex, irregular images with many local features,
and can model the simultaneous effects of multiple factors on the image
intensities and account for the correlation between images induced by the
design. We introduce a general isomorphic modeling approach to fitting the
functional mixed model, of which the wavelet-based functional mixed model is
one special case. With suitable modeling choices, this approach leads to
efficient calculations and can result in flexible modeling and adaptive
smoothing of the salient features in the data. The proposed method has the
following advantages: it can be run automatically, it produces inferential
plots indicating which regions of the image are associated with each factor, it
simultaneously considers the practical and statistical significance of
findings, and it controls the false discovery rate.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS407 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Locally stationary long memory estimation
There exists a wide literature on modelling strongly dependent time series
using a longmemory parameter d, including more recent work on semiparametric
wavelet estimation. As a generalization of these latter approaches, in this
work we allow the long-memory parameter d to be varying over time. We embed our
approach into the framework of locally stationary processes. We show weak
consistency and a central limit theorem for our log-regression wavelet
estimator of the time-dependent d in a Gaussian context. Both simulations and a
real data example complete our work on providing a fairly general approach
- …