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Multivariate Granger Causality (Barrett 2010)

research, journalclub
by Syed Ashrafulla on 15 September 2011

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Transcript of Multivariate Granger Causality (Barrett 2010)

Multivariate Granger Causality Spectral Domain Granger Causality Trace or Det? Adam Barrett, Lionel Barnett, Anil Seth Ideas Univariate error when using past x AND y error when using past x ONLY Multivariate error when using past x AND y error when using past x ONLY What scalar do we want? Choices Causal Density trvMVGC MVGC Entropy No such analogue for = uncertainty in a given b Marginality No such analogue for Let x be a scalar; then, Stability determinant -> biased by zero eigenvalue? / Key identity: Set of variables Want to look at whole network Causal density from all subsets of size k
to all subsets of size r
given the rest Bipartition causal density from all subsets of size k
to all subsets of size n-k Scaled causal density from all subsets of size k
to all subsets of size s-k think "bcd" but subset of data Tripartition causal density from all subsets of size k
to all subsets of size s-k
for all total sets of size s Bundled Connections ONE transmission trace/det is 5 on 5
max eigenvalue is best combination
canonical AR? Constraints known 0 how to add zeros to A? estimate x given only weighted sum of y
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