85,333 research outputs found
Monte Carlo Implementation of Gaussian Process Models for Bayesian Regression and Classification
Gaussian processes are a natural way of defining prior distributions over
functions of one or more input variables. In a simple nonparametric regression
problem, where such a function gives the mean of a Gaussian distribution for an
observed response, a Gaussian process model can easily be implemented using
matrix computations that are feasible for datasets of up to about a thousand
cases. Hyperparameters that define the covariance function of the Gaussian
process can be sampled using Markov chain methods. Regression models where the
noise has a t distribution and logistic or probit models for classification
applications can be implemented by sampling as well for latent values
underlying the observations. Software is now available that implements these
methods using covariance functions with hierarchical parameterizations. Models
defined in this way can discover high-level properties of the data, such as
which inputs are relevant to predicting the response
Quantum field theory with an interaction on the boundary
We consider quantum theory of fields \phi defined on a D dimensional manifold
(bulk) with an interaction V(\phi) concentrated on a d<D dimensional surface
(brane). Such a quantum field theory can be less singular than the one in d
dimensions with the interaction . It is shown that scaling properties
of fields on the brane are different from the ones in the bulk.Comment: 15 page
Sensitivity of a Barotropic Ocean Model to Perturbations of the Bottom Topography
In this paper, we look for an operator that describes the relationship
between small errors in representation of the bottom topography in a barotropic
ocean model and the model's solution. The study shows that the model's solution
is very sensitive to topography perturbations in regions where the flow is
turbulent. On the other hand, the flow exhibits low sensitivity in laminar
regions. The quantitative measure of sensitivity is influenced essentially by
the error growing time. At short time scales, the sensitivity exhibits the
polynomial dependence on the error growing time. And in the long time limit,
the dependence becomes exponential
Shape of an elastica under growth restricted by friction
We investigate the quasi-static growth of elastic fibers in the presence of
dry or viscous friction. An unusual form of destabilization beyond a critical
length is described. In order to characterize this phenomenon, a new definition
of stability against infinitesimal perturbations over finite time intervals is
proposed and a semi-analytical method for the determination of the critical
length is developed. The post-critical behavior of the system is studied by
using an appropriate numerical scheme based on variational methods. We find
post-critical shapes for uniformly distributed as well as for concentrated
growth and demonstrate convergence to a figure-8 shape for large lengths when
self-crossing is allowed. Comparison with simple physical experiments yields
reasonable accuracy of the theoretical predictions
Approximate Bayesian Computation with composite score functions
Both Approximate Bayesian Computation (ABC) and composite likelihood methods
are useful for Bayesian and frequentist inference, respectively, when the
likelihood function is intractable. We propose to use composite likelihood
score functions as summary statistics in ABC in order to obtain accurate
approximations to the posterior distribution. This is motivated by the use of
the score function of the full likelihood, and extended to general unbiased
estimating functions in complex models. Moreover, we show that if the composite
score is suitably standardised, the resulting ABC procedure is invariant to
reparameterisations and automatically adjusts the curvature of the composite
likelihood, and of the corresponding posterior distribution. The method is
illustrated through examples with simulated data, and an application to
modelling of spatial extreme rainfall data is discussed.Comment: Statistics and Computing (final version
Geometry of Winter Model
By constructing the Riemann surface controlling the resonance structure of
Winter model, we determine the limitations of perturbation theory. We then
derive explicit non-perturbative results for various observables in the
weak-coupling regime, in which the model has an infinite tower of long-lived
resonant states. The problem of constructing proper initial wavefunctions
coupled to single excitations of the model is also treated within perturbative
and non-perturbative methods.Comment: latex file, 56 pages, 15 figure
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
- …