The Temporal Logic of Causal Structures

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Significance testing

Our tests as well as the Granger tests each return a set of causal hypotheses with some associated test statistics. One must still choose a threshold at which a result will be called significant (or causal). Here we include the set of histograms for each pattern depicting the number of results with a given test value. For the granger test, which returned both p-values and f-statistics, we graph both.

Links to graphs below

Our tests:

One (scatter gather), Two (two separate scatter gather graphs), Three (a chain of scatter gather relationships), Four (a binary tree), and Five (a long chain of neurons).

Granger tests:

One, Two, Three, Four, and Five.

Our tests

Pattern 1

Pattern 1 z-values


Pattern 1 z-values (zoomed in view of tail area)

Pattern 1 z-values


Pattern 1 z-values full graph

 

Pattern 2

Pattern 2 z-values


Pattern 2 z-values (zoomed in view of tail area)

Pattern 2 z-values


Pattern 2 z-values full graph

 

Pattern 3

Pattern 3 z-values


Pattern 3 z-values (zoomed in view of tail area)

Pattern 3 z-values


Pattern 3 z-values full graph

 

Pattern 4

Pattern 4 z-values


Pattern 4 z-values (zoomed in view of tail area)

Pattern 4 z-values


Pattern 4 z-values full graph

 

Pattern 5

Pattern 5 z-values


Pattern 5 z-values (zoomed in view of tail area)

Pattern 5 z-values


Pattern 5 z-values full graph

 

Granger tests

Pattern 1

Pattern 1 f-statistics


Pattern 1 f-statistics (zoomed in view to show tail area. Click for full graph)

Pattern 1 p-values


Pattern 1 p-values

 

Pattern 2

Pattern 2 f-statistics


Pattern 2 f-statistics (zoomed in view to show tail area. Click for full graph)

Pattern 2 p-values


Pattern 2 p-values

 

Pattern 3

Pattern 3 f-statistics


Pattern 3 f-statistics (zoomed in view to show tail area. Click for full graph)

Pattern 3 p-values


Pattern 3 p-values

 

Pattern 4

Pattern 4 f-statistics


Pattern 4 f-statistics (zoomed in view to show tail area. Click for full graph)

Pattern 4 p-values


Pattern 4 p-values

 

Pattern 5

Pattern 5 f-statistics


Pattern 5 f-statistics (zoomed in view to show tail area. Click for full graph)

Pattern 5 p-values


Pattern 5 p-values