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  The circular SiZer, inferred persistence of shape parameters and application to early stem cell differentiation.

Huckemann, S., Kim, K. R., Munk, A., Rehfeld, F., Sommerfeld, M., Weickert, J., et al. (2016). The circular SiZer, inferred persistence of shape parameters and application to early stem cell differentiation. Bernoulli, 22(4), 2113-2142. doi:10.3150/15-BEJ722.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-002A-E4BF-2 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-002C-C28F-2
Genre: Journal Article

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 Creators:
Huckemann, S., Author
Kim, K. R., Author
Munk, A.1, Author              
Rehfeld, F., Author
Sommerfeld , M., Author
Weickert, J., Author
Wollnik, C., Author
Affiliations:
1Research Group of Statistical Inverse-Problems in Biophysics, MPI for biophysical chemistry, Max Planck Society, ou_1113580              

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Free keywords: circular data; circular scale spaces; mode hunting; multiscale process; persistence inference; stem cell differentiation; variation diminishing; wrapped Gaussian kernel estimator
 Abstract: We generalize the SiZer of Chaudhuri and Marron (J. Amer. Statist. Assoc. 94 (1999) 807-823; Ann. Statist. 28 (2000) 408-428) for the detection of shape parameters of densities on the real line to the case of circular data. It turns out that only the wrapped Gaussian kernel gives a symmetric, strongly Lipschitz semi-group satisfying "circular" causality, that is, not introducing possibly artificial modes with increasing levels of smoothing. Some notable differences between Euclidean and circular scale space theory are highlighted. Based on this, we provide an asymptotic theory to make inference about the persistence of shape features. The resulting circular mode persistence diagram is applied to the analysis of early mechanically-induced differentiation in adult human stem cells from their actin-myosin filament structure. As a consequence, the circular SiZer based on the wrapped Gaussian kernel (WiZer) allows the verification at a controlled error level of the observation reported by Zemel et al. (Nat. Phys. 6 (2010) 468-473): Within early stem cell differentiation, polarizations of stem cells exhibit preferred directions in three different micro-environments.

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Language(s): eng - English
 Dates: 2016-05-032016-11
 Publication Status: Published in print
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Method: Peer
 Identifiers: DOI: 10.3150/15-BEJ722
 Degree: -

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Title: Bernoulli
Source Genre: Journal
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Pages: - Volume / Issue: 22 (4) Sequence Number: - Start / End Page: 2113 - 2142 Identifier: -