7,395 research outputs found
Locally Adaptive Bayesian P-Splines with a Normal-Exponential-Gamma Prior
The necessity to replace smoothing approaches with a global amount of smoothing arises in a variety of situations such as effects with highly varying curvature or effects with discontinuities. We present an implementation of locally adaptive spline smoothing using a class of heavy-tailed shrinkage priors. These priors utilize scale mixtures of normals with locally varying exponential-gamma distributed variances for the differences of the P-spline coefficients. A fully Bayesian hierarchical structure is derived with inference about the posterior being based on Markov Chain Monte Carlo techniques. Three increasingly flexible and automatic approaches are introduced to estimate the spatially varying structure of the variances. In an extensive simulation study, the performance of our approach on a number of benchmark functions is shown to be at least equivalent, but mostly better than previous approaches and fits both functions of smoothly varying complexity and discontinuous functions well. Results from two applications also reflecting these two situations support the simulation results
Natural and Projectively Invariant Quantizations on Supermanifolds
The existence of a natural and projectively invariant quantization in the
sense of P. Lecomte [Progr. Theoret. Phys. Suppl. (2001), no. 144, 125-132] was
proved by M. Bordemann [math.DG/0208171], using the framework of
Thomas-Whitehead connections. We extend the problem to the context of
supermanifolds and adapt M. Bordemann's method in order to solve it. The
obtained quantization appears as the natural globalization of the
-equivariant quantization on
constructed by P. Mathonet and F. Radoux in [arXiv:1003.3320]. Our quantization
is also a prolongation to arbitrary degree symbols of the projectively
invariant quantization constructed by J. George in [arXiv:0909.5419] for
symbols of degree two
Conformational selection in protein binding and function
Protein binding and function often involves conformational changes. Advanced
NMR experiments indicate that these conformational changes can occur in the
absence of ligand molecules (or with bound ligands), and that the ligands may
'select' protein conformations for binding (or unbinding). In this review, we
argue that this conformational selection requires transition times for ligand
binding and unbinding that are small compared to the dwell times of proteins in
different conformations, which is plausible for small ligand molecules. Such a
separation of timescales leads to a decoupling and temporal ordering of
binding/unbinding events and conformational changes. We propose that
conformational-selection and induced-change processes (such as induced fit) are
two sides of the same coin, because the temporal ordering is reversed in
binding and unbinding direction. Conformational-selection processes can be
characterized by a conformational excitation that occurs prior to a binding or
unbinding event, while induced-change processes exhibit a characteristic
conformational relaxation that occurs after a binding or unbinding event. We
discuss how the ordering of events can be determined from relaxation rates and
effective on- and off-rates determined in mixing experiments, and from the
conformational exchange rates measured in advanced NMR or single-molecule FRET
experiments. For larger ligand molecules such as peptides, conformational
changes and binding events can be intricately coupled and exhibit aspects of
conformational-selection and induced-change processes in both binding and
unbinding direction.Comment: review article; 10 pages, 4 figures, Protein Sci. 201
Penalized Likelihood and Bayesian Function Selection in Regression Models
Challenging research in various fields has driven a wide range of
methodological advances in variable selection for regression models with
high-dimensional predictors. In comparison, selection of nonlinear functions in
models with additive predictors has been considered only more recently. Several
competing suggestions have been developed at about the same time and often do
not refer to each other. This article provides a state-of-the-art review on
function selection, focusing on penalized likelihood and Bayesian concepts,
relating various approaches to each other in a unified framework. In an
empirical comparison, also including boosting, we evaluate several methods
through applications to simulated and real data, thereby providing some
guidance on their performance in practice
Representation by Integrating Reproducing Kernels
Based on direct integrals, a framework allowing to integrate a parametrised
family of reproducing kernels with respect to some measure on the parameter
space is developed. By pointwise integration, one obtains again a reproducing
kernel whose corresponding Hilbert space is given as the image of the direct
integral of the individual Hilbert spaces under the summation operator. This
generalises the well-known results for finite sums of reproducing kernels;
however, many more special cases are subsumed under this approach: so-called
Mercer kernels obtained through series expansions; kernels generated by
integral transforms; mixtures of positive definite functions; and in particular
scale-mixtures of radial basis functions. This opens new vistas into known
results, e.g. generalising the Kramer sampling theorem; it also offers
interesting connections between measurements and integral transforms, e.g.
allowing to apply the representer theorem in certain inverse problems, or
bounding the pointwise error in the image domain when observing the pre-image
under an integral transform
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