Data-processing inequality for a Markov chain X -> Y -> Z

$$X \to Y \to Z \Rightarrow I(X;Y) \ge I(X;Z)$$ Cover & Thomas (2006), Section 2.8, Theorem 2.8.1, p. 34. A deterministic identity, not a hypothesis test.

Usage

Dpineq(pxyz, cdf = NULL, base = 2)

Arguments

pxyz

Joint pmf as a 3-D array or nested list; normalised here.

cdf

Accepted and ignored; kept so older call sites keep working.

base

Log base; 2 gives bits.

Value

Named list with estimate (the gap), ixy, ixz, markov_gap, holds, n, method.

References

Cover & Thomas (2006), Theorem 2.8.1.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Dpineq(V)
#> $estimate
#> [1] 0
#> 
#> $ixy
#> [1] 0
#> 
#> $ixz
#> [1] 0
#> 
#> $markov_gap
#> [1] 0
#> 
#> $holds
#> [1] TRUE
#> 
#> $n
#> [1] 8
#> 
#> $method
#> [1] "Data-processing inequality I(X;Y) >= I(X;Z) -- Cover & Thomas (2006) Thm 2.8.1"
#>