| dc.contributor.advisor | Munk, Axel Prof. Dr. | |
| dc.contributor.author | Pein, Florian | |
| dc.date.accessioned | 2018-02-09T09:34:38Z | |
| dc.date.available | 2018-02-09T09:34:38Z | |
| dc.date.issued | 2018-02-09 | |
| dc.identifier.uri | http://hdl.handle.net/11858/00-1735-0000-002E-E34A-7 | |
| dc.identifier.uri | http://dx.doi.org/10.53846/goediss-6719 | |
| dc.language.iso | eng | de |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | |
| dc.subject.ddc | 510 | de |
| dc.title | Heterogeneous Multiscale Change-Point Inference and its Application to Ion Channel Recordings | de |
| dc.type | doctoralThesis | de |
| dc.contributor.referee | Munk, Axel Prof. Dr. | |
| dc.date.examination | 2017-10-20 | |
| dc.description.abstracteng | Ion channel recordings by the patch clamp technique are a major tool to quantify the
electrophysiological dynamics of ion channels in the cell membrane, which is for instance
important in medicine for the development of new drugs. In this work, we model these
recordings as a time series which is equidistantly sampled from the convolution of a piecewise
constant signal disturbed by white noise with a lowpass filter. We focus on nonparametric
estimation of the underlying signal, but also discuss how to use these estimations
to analyze the recordings. Estimating the underlying signal requires to detect
multiple change-points in noisy and filtered Gaussian observations. The variance can be
constant in time, but also a varying variance is observed in some measurements. Since
this change-point regression problem is very difficult, we start with independent Gaussian
observations but with heterogeneous noise. Such a model is of its own interest and has
further applications for instance in genetics. For this model, we propose the heterogeneous simultaneous multiscale change-point
estimator, H-SMUCE. It estimates the piecewise constant function by minimizing the
number of change-points over the acceptance region of a multiscale test which locally
adapts to changes in the variance. The multiscale test is a combination of local likelihood
ratio tests which are properly calibrated by scale dependent critical values in order to keep
a global nominal level alpha, even for finite samples.
We show that H-SMUCE controls over- and underestimation of the number of change-points
at a given probability for finitely many observations. To this end, new deviation
bounds for F-type statistics are derived. We also bound the implicitly defined critical
values. By combining these bounds, we obtain simultaneous confidence intervals for the
change-point locations and a confidence band for the whole signal. Moreover, it allows us
to show that H-SMUCE achieves the optimal detection rate and estimates the number of
change-points consistently for vanishing signals, even when the number of change-points
is unbounded. The only extra assumption we have to suppose is that the length of the
constant segments does not vanished too fast. We compare the performance of H-SMUCE
with several state of the art methods in simulations and show how it can be computed
efficiently by a pruned dynamic program. An R-package is provided.
In a second step we combine these multiscale regression techniques with deconvolution
to obtain non-parametric estimators for the ion channel recordings. Truncating the filter
kernel and pre-estimating the function values on longer constant segments enable us to
perform the deconvolution locally which allows fast computation. Simulations and real
data applications confirm that the proposed segmentation methods, JULES and JILTAD, estimate the underlying signal very accurately, even when events occur on small temporal
scales, where the smoothing effect of the filter hinders estimation by common methods.
Moreover, JILTAD shows still good results when the noise is heterogeneous, a situation
for which previously no non-parametric estimation method existed. Also these methods
are implemented in R.
The usage of these methods is demonstrated in a biochemical study against the context
of multidrug-resistant bacteria. We showed statistically significant differences for the interaction
of the antibiotic ampicillin with the wild type and with the mutant G103K of
the outer membrane channel PorB. These results improves the understanding of potential
sources for bacterial resistance and might help to develop new drugs against it to alleviate
the severe consequences of multidrug-resistant bacteria. | de |
| dc.contributor.coReferee | Krajina, Andrea Prof. Dr. | |
| dc.subject.eng | change-point regression | de |
| dc.subject.eng | deconvolution | de |
| dc.subject.eng | deviation bounds | de |
| dc.subject.eng | dynamic programming | de |
| dc.subject.eng | flickering event detection | de |
| dc.subject.eng | heterogeneous noise | de |
| dc.subject.eng | honest confidence sets | de |
| dc.subject.eng | inverse problems | de |
| dc.subject.eng | multidrug-resistant bacteria | de |
| dc.subject.eng | multiscale methods | de |
| dc.subject.eng | planar patch clamp | de |
| dc.subject.eng | robustness | de |
| dc.subject.eng | scale dependent critical values | de |
| dc.identifier.urn | urn:nbn:de:gbv:7-11858/00-1735-0000-002E-E34A-7-7 | |
| dc.affiliation.institute | Fakultät für Mathematik und Informatik | de |
| dc.subject.gokfull | Mathematics (PPN61756535X) | de |
| dc.identifier.ppn | 1013634802 | |