Check the extended Schwartz conditions and return the resulting bound

Prior mass on a Kullback-Leibler neighbourhood AND a test rate beating its radius are both required; either alone is insufficient. The margin C - c governs the bound.

Usage

Kldsupp(prior_mass, kl_radius, test_rate, n)

Arguments

prior_mass

Pi(P_0), in (0, 1].

kl_radius

c, the Kullback-Leibler radius.

test_rate

C, the exponential rate of the test.

n

Sample size.

Value

List with holds, margin, bound, prior_mass, n.

Details

Formula: Pi(P_0) > 0 and K(p_0; P_0) <= c and C > c imply consistency; the working bound is e^{-(C - c) n} / Pi(P_0)

References

Ghosal & van der Vaart (2017), Fundamentals of Nonparametric Bayesian Inference, Theorem 6.17 (Extended Schwartz) together with Theorem 6.16. Read from the copy of the book held in the corpus.

Examples

Kldsupp(prior_mass = 0.5, kl_radius = 0.1, test_rate = 0.2, n = 100)
#> $holds
#> [1] 1
#> 
#> $margin
#> [1] 0.1
#> 
#> $bound
#> [1] 9.079986e-05
#> 
#> $prior_mass
#> [1] 0.5
#> 
#> $n
#> [1] 100
#> 
#> $method
#> [1] "Extended Schwartz conditions, Ghosal Theorem 6.17"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"