The circular SiZer, inferred persistence of shape parameters and application to early stem cell differentiation
| Autor: | Florian Rehfeldt, Carina Wollnik, Max Sommerfeld, Stephan Huckemann, Kwang-Rae Kim, Joachim Weickert, Axel Munk |
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| Jazyk: | angličtina |
| Rok vydání: | 2014 |
| Předmět: |
FOS: Computer and information sciences
Statistics and Probability multiscale process 02 engineering and technology 01 natural sciences Scale space Methodology (stat.ME) Causality (physics) 010104 statistics & probability symbols.namesake mode hunting Euclidean geometry persistence inference wrapped Gaussian kernel estimator 0202 electrical engineering electronic engineering information engineering Gaussian function stem cell differentiation 0101 mathematics Real line Statistics - Methodology Mathematics circular data Mathematical analysis circular scale spaces Lipschitz continuity Asymptotic theory (statistics) symbols variation diminishing 020201 artificial intelligence & image processing Smoothing |
| Zdroj: | Bernoulli 22, no. 4 (2016), 2113-2142 |
| Popis: | 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. Published at http://dx.doi.org/10.3150/15-BEJ722 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm) |
| Databáze: | OpenAIRE |
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