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Strict semiparametric Bernstein-von Mises conditions

Source: R/gh_c12_7.R
Ghosalstrictsbvm.Rd

The exact semiparametric BvM needs three separate things: prior mass around the least-favourable direction, a LAN remainder tending to zero, and a change-of-measure (prior invariance) condition. They are independent – a model can satisfy any two and fail the theorem – so the three are reported separately rather than as one verdict.

Usage

Ghosalstrictsbvm(
  prior_mass_ok = TRUE,
  lan_remainder = 0.01,
  change_of_measure_gap = 0.02,
  tol = 0.05
)

Arguments

prior_mass_ok

Logical; the prior-mass condition.

lan_remainder

Size of the LAN remainder, non-negative.

change_of_measure_gap

Size of the invariance gap.

tol

Tolerance both gaps must fall under.

Value

List with estimate (aggregate score), bvm_holds, conditions, method.

Details

Formula: score = 1{prior mass ok} - lan_remainder

  • change_of_measure_gap; holds iff all three checks pass at tol.

References

Ghosal & van der Vaart (2017), Fundamentals of Nonparametric Bayesian Inference, CUP, section 12.3.2.

Examples

Ghosalstrictsbvm()
#> $estimate
#> [1] 0.97
#> 
#> $bvm_holds
#> [1] TRUE
#> 
#> $conditions
#> [1] TRUE TRUE TRUE
#> 
#> $method
#> [1] "strict semiparametric BvM (GvdV 2017 sec. 12.3.2)"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"