With Pi = pi_0 Pi_0 + (1 - pi_0) Pi_1 the posterior weight of whichever
model contains the truth tends to one. Both evidences are conjugate
and exact here, so the weight is a plain logistic transform of their
log-ratio: the small model keeps one coordinate, the large model six.
Usage
Ghosaltwomodeladp(n = 500, truth_dim = 1, pi0 = 0.5, seed = 42)
Arguments
- n
Precision (sample size) of each coordinate.
- truth_dim
Number of nonzero coordinates in the truth.
- pi0
Prior weight of the small model, in (0, 1).
- seed
Seed for the deterministic draw.
Value
List with estimate,
posterior_weight_small_model, small_model_wins,
method.
Details
Formula: w_0 = 1 / (1 + exp(l_1 - l_0)),
l_j = log m_{K_j}(y) + log prior weight of model j.
References
Ghosal & van der Vaart (2017), Fundamentals of
Nonparametric Bayesian Inference, CUP, section 10.2.3.
Examples
Ghosaltwomodeladp()
#> $estimate
#> [1] 0.9999881
#>
#> $posterior_weight_small_model
#> [1] 0.9999881
#>
#> $small_model_wins
#> [1] TRUE
#>
#> $method
#> [1] "two-model adaptation (GvdV 2017 sec. 10.2.3)"
#>
#> attr(,"class")
#> [1] "morie_rich_result" "list"
