37,604 research outputs found
Adaptive numerical designs for the calibration of computer codes
Making good predictions of a physical system using a computer code requires
the inputs to be carefully specified. Some of these inputs called control
variables have to reproduce physical conditions whereas other inputs, called
parameters, are specific to the computer code and most often uncertain. The
goal of statistical calibration consists in estimating these parameters with
the help of a statistical model which links the code outputs with the field
measurements. In a Bayesian setting, the posterior distribution of these
parameters is normally sampled using MCMC methods. However, they are
impractical when the code runs are high time-consuming. A way to circumvent
this issue consists of replacing the computer code with a Gaussian process
emulator, then sampling a cheap-to-evaluate posterior distribution based on it.
Doing so, calibration is subject to an error which strongly depends on the
numerical design of experiments used to fit the emulator. We aim at reducing
this error by building a proper sequential design by means of the Expected
Improvement criterion. Numerical illustrations in several dimensions assess the
efficiency of such sequential strategies
Surrogate time series
Before we apply nonlinear techniques, for example those inspired by chaos
theory, to dynamical phenomena occurring in nature, it is necessary to first
ask if the use of such advanced techniques is justified "by the data". While
many processes in nature seem very unlikely a priori to be linear, the possible
nonlinear nature might not be evident in specific aspects of their dynamics.
The method of surrogate data has become a very popular tool to address such a
question. However, while it was meant to provide a statistically rigorous,
foolproof framework, some limitations and caveats have shown up in its
practical use. In this paper, recent efforts to understand the caveats, avoid
the pitfalls, and to overcome some of the limitations, are reviewed and
augmented by new material. In particular, we will discuss specific as well as
more general approaches to constrained randomisation, providing a full range of
examples. New algorithms will be introduced for unevenly sampled and
multivariate data and for surrogate spike trains. The main limitation, which
lies in the interpretability of the test results, will be illustrated through
instructive case studies. We will also discuss some implementational aspects of
the realisation of these methods in the TISEAN
(http://www.mpipks-dresden.mpg.de/~tisean) software package.Comment: 28 pages, 23 figures, software at
http://www.mpipks-dresden.mpg.de/~tisea
Boosting Functional Response Models for Location, Scale and Shape with an Application to Bacterial Competition
We extend Generalized Additive Models for Location, Scale, and Shape (GAMLSS)
to regression with functional response. This allows us to simultaneously model
point-wise mean curves, variances and other distributional parameters of the
response in dependence of various scalar and functional covariate effects. In
addition, the scope of distributions is extended beyond exponential families.
The model is fitted via gradient boosting, which offers inherent model
selection and is shown to be suitable for both complex model structures and
highly auto-correlated response curves. This enables us to analyze bacterial
growth in \textit{Escherichia coli} in a complex interaction scenario,
fruitfully extending usual growth models.Comment: bootstrap confidence interval type uncertainty bounds added; minor
changes in formulation
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