4,994 research outputs found
Stochastic partial differential equation based modelling of large space-time data sets
Increasingly larger data sets of processes in space and time ask for
statistical models and methods that can cope with such data. We show that the
solution of a stochastic advection-diffusion partial differential equation
provides a flexible model class for spatio-temporal processes which is
computationally feasible also for large data sets. The Gaussian process defined
through the stochastic partial differential equation has in general a
nonseparable covariance structure. Furthermore, its parameters can be
physically interpreted as explicitly modeling phenomena such as transport and
diffusion that occur in many natural processes in diverse fields ranging from
environmental sciences to ecology. In order to obtain computationally efficient
statistical algorithms we use spectral methods to solve the stochastic partial
differential equation. This has the advantage that approximation errors do not
accumulate over time, and that in the spectral space the computational cost
grows linearly with the dimension, the total computational costs of Bayesian or
frequentist inference being dominated by the fast Fourier transform. The
proposed model is applied to postprocessing of precipitation forecasts from a
numerical weather prediction model for northern Switzerland. In contrast to the
raw forecasts from the numerical model, the postprocessed forecasts are
calibrated and quantify prediction uncertainty. Moreover, they outperform the
raw forecasts, in the sense that they have a lower mean absolute error
OpenCFU, a New Free and Open-Source Software to Count Cell Colonies and Other Circular Objects
Counting circular objects such as cell colonies is an important source of
information for biologists. Although this task is often time-consuming and
subjective, it is still predominantly performed manually. The aim of the
present work is to provide a new tool to enumerate circular objects from
digital pictures and video streams. Here, I demonstrate that the created
program, OpenCFU, is very robust, accurate and fast. In addition, it provides
control over the processing parameters and is implemented in an in- tuitive and
modern interface. OpenCFU is a cross-platform and open-source software freely
available at http://opencfu.sourceforge.net
Predicting Inflation: Professional Experts Versus No-Change Forecasts
We compare forecasts of United States inflation from the Survey of
Professional Forecasters (SPF) to predictions made by simple statistical
techniques. In nowcasting, economic expertise is persuasive. When projecting
beyond the current quarter, novel yet simplistic probabilistic no-change
forecasts are equally competitive. We further interpret surveys as ensembles of
forecasts, and show that they can be used similarly to the ways in which
ensemble prediction systems have transformed weather forecasting. Then we
borrow another idea from weather forecasting, in that we apply statistical
techniques to postprocess the SPF forecast, based on experience from the recent
past. The foregoing conclusions remain unchanged after survey postprocessing
A Fast Gradient Method for Nonnegative Sparse Regression with Self Dictionary
A nonnegative matrix factorization (NMF) can be computed efficiently under
the separability assumption, which asserts that all the columns of the given
input data matrix belong to the cone generated by a (small) subset of them. The
provably most robust methods to identify these conic basis columns are based on
nonnegative sparse regression and self dictionaries, and require the solution
of large-scale convex optimization problems. In this paper we study a
particular nonnegative sparse regression model with self dictionary. As opposed
to previously proposed models, this model yields a smooth optimization problem
where the sparsity is enforced through linear constraints. We show that the
Euclidean projection on the polyhedron defined by these constraints can be
computed efficiently, and propose a fast gradient method to solve our model. We
compare our algorithm with several state-of-the-art methods on synthetic data
sets and real-world hyperspectral images
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