BF(H1, H0) = p(X | H1) / p(X | H0) tends to infinity under H1 and to
zero under H0. Both evidences are exact here (normal means, H0
keeping no coordinates and H1 keeping two), so the demonstration is
arithmetic rather than simulation: only the data are random.
Usage
Ghosalmodselbic(truth_in_H1 = TRUE, n = 2000, seed = 42)
Arguments
- truth_in_H1
If TRUE the truth has nonzero mean, so H1 holds.
- n
Precision (sample size) of each coordinate.
- seed
Seed for the deterministic draw.
Value
List with estimate (log Bayes factor),
supports_H1, method.
Details
Formula: log BF = log m_2(y) - log m_0(y).
References
Ghosal & van der Vaart (2017), Fundamentals of
Nonparametric Bayesian Inference, CUP, section 10.5.
Examples
Ghosalmodselbic()
#> $estimate
#> [1] 957.4621
#>
#> $supports_H1
#> [1] TRUE
#>
#> $method
#> [1] "Bayes factor consistency (GvdV 2017 sec. 10.5)"
#>
#> attr(,"class")
#> [1] "morie_rich_result" "list"
