Circular statistics Maximum likelihood Local likelihood Kenneth D. Harris 4/3/2015.

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Presentation transcript:

Circular statistics Maximum likelihood Local likelihood Kenneth D. Harris 4/3/2015

Relationship of cells to oscillations Klausberger & Somogyi, Science 2008

Relationship of cells to oscillations O’Keefe & Recce, Hippocampus 1993

How do we quantify: A cell’s average phase of firing? How phase depends on other variables?

Computing instantaneous phase Hilbert transform Peak fitting

Phase histogram Different cells prefer different phases How do we compute each cell’s mean phase?

Linear mean doesn’t work

Circular mean R

von Mises distribution

Maximum likelihood estimation

Maximum likelihood von Mises

How does phase depend on another variable? Don’t use linear regression!

Locally-weighted likelihood

Kernel smoother

Place field estimation

Phase field Local likelihood estimation for von Mises Physical space Abstract space Harris et al Nature 2002

Confirmatory statistics: How to test that phase is independent of place? Shuffling method? Test statistic?