1,847 research outputs found
Design of Boolean LUM Smoothers through Permutation Coloring Concept
Rank-order based LUM (lower-upper-middle) smoothers distinguishes by wide range of smoothing characteristics given by filter parameter. Thus, for the capability to achieve the best balance between noise suppression and signal details preservation, the LUM smoothers are preferred in smoothing applications. Thanks to threshold decomposition and stacking properties, the LUM smoothers belong to the class of stack filters. This paper is focused to the derivation of minimal positive Boolean function for LUM smoothers through permutation groups and a coloring concept
Robust Kalman tracking and smoothing with propagating and non-propagating outliers
A common situation in filtering where classical Kalman filtering does not
perform particularly well is tracking in the presence of propagating outliers.
This calls for robustness understood in a distributional sense, i.e.; we
enlarge the distribution assumptions made in the ideal model by suitable
neighborhoods. Based on optimality results for distributional-robust Kalman
filtering from Ruckdeschel[01,10], we propose new robust recursive filters and
smoothers designed for this purpose as well as specialized versions for
non-propagating outliers. We apply these procedures in the context of a GPS
problem arising in the car industry. To better understand these filters, we
study their behavior at stylized outlier patterns (for which they are not
designed) and compare them to other approaches for the tracking problem.
Finally, in a simulation study we discuss efficiency of our procedures in
comparison to competitors.Comment: 27 pages, 12 figures, 2 table
The output distribution of important LULU-operators
Two procedures to compute the output distribution phi_S of certain stack
filters S (so called erosion-dilation cascades) are given. One rests on the
disjunctive normal form of S and also yields the rank selection probabilities.
The other is based on inclusion-exclusion and e.g. yields phi_S for some
important LULU-operators S. Properties of phi_S can be used to characterize
smoothing properties of S. One of the methods discussed also allows for the
calculation of the reliability polynomial of any positive Boolean function
(e.g. one derived from a connected graph).Comment: 20 pages, up to trivial differences this is the final version to be
published in Quaestiones Mathematicae 201
Just Another Gibbs Additive Modeller: Interfacing JAGS and mgcv
The BUGS language offers a very flexible way of specifying complex
statistical models for the purposes of Gibbs sampling, while its JAGS variant
offers very convenient R integration via the rjags package. However, including
smoothers in JAGS models can involve some quite tedious coding, especially for
multivariate or adaptive smoothers. Further, if an additive smooth structure is
required then some care is needed, in order to centre smooths appropriately,
and to find appropriate starting values. R package mgcv implements a wide range
of smoothers, all in a manner appropriate for inclusion in JAGS code, and
automates centring and other smooth setup tasks. The purpose of this note is to
describe an interface between mgcv and JAGS, based around an R function,
`jagam', which takes a generalized additive model (GAM) as specified in mgcv
and automatically generates the JAGS model code and data required for inference
about the model via Gibbs sampling. Although the auto-generated JAGS code can
be run as is, the expectation is that the user would wish to modify it in order
to add complex stochastic model components readily specified in JAGS. A simple
interface is also provided for visualisation and further inference about the
estimated smooth components using standard mgcv functionality. The methods
described here will be un-necessarily inefficient if all that is required is
fully Bayesian inference about a standard GAM, rather than the full flexibility
of JAGS. In that case the BayesX package would be more efficient.Comment: Submitted to the Journal of Statistical Softwar
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