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i.i.d. posterior contraction theorem

Source: R/ghosal_native.R
morie_contraction_conditions.Rd

A rate \(\varepsilon_n\) holds when THREE conditions hold together: entropy \(\lesssim n\varepsilon_n^2\), prior mass \(\ge e^{-Cn\varepsilon_n^2}\), and a sieve remainder (Sec. 8.2). All three are calibrated by the same \(n\varepsilon_n^2\), and that is the content – neither alone gives a rate. Mirrors morie.fn.gh_c8_6.

Usage

morie_contraction_conditions(
  x,
  eps = NULL,
  n = NULL,
  prior_mass = NULL,
  entropy = NULL,
  C = 1
)

Arguments

x

numeric observations, for the sample size.

eps

candidate rate.

n

sample size.

prior_mass, entropy

measured quantities, when available.

C

constant in the prior-mass condition.

Value

list: n, eps, n_eps_squared, entropy_budget, prior_mass_budget, entropy_ok, prior_mass_ok, all_conditions_checked, metric, conditions, method.

References

Ghosal and van der Vaart, Sec. 8.2; Ghosal, Ghosh and van der Vaart (2000).

Examples

morie_contraction_conditions(numeric(9), eps = 0.1, n = 1000)$n_eps_squared
#> [1] 10