White-noise full Bernstein-von Mises

In the white-noise model dY = theta dt + dW/sqrt(n) with a nearly flat Gaussian prior the posterior is N(Y, I/n) EXACTLY, not asymptotically. The white-noise model is the one place where the BvM statement can be checked as an identity rather than a limit, which is why the chapter uses it to isolate what does and does not survive in infinite dimensions.

Usage

Ghosalwnfullbvm(y = c(0.5, -0.2, 0.1), n = 400, prior_var = 1e+06)

Arguments

y

Observed coordinates.

n

Precision (sample size).

prior_var

Prior variance per coordinate; large means flat.

Value

List with estimate (max deviation of the posterior mean from Y), mean_matches_Y, var_matches_In, method.

Details

Formula: posterior mean = Y prior_var / (prior_var + 1/n); posterior variance = 1 / (1/prior_var + n).

References

Ghosal & van der Vaart (2017), Fundamentals of Nonparametric Bayesian Inference, CUP, section 12.4.1.

Examples

Ghosalwnfullbvm()
#> $estimate
#> [1] 1.25e-09
#> 
#> $mean_matches_Y
#> [1] TRUE
#> 
#> $var_matches_In
#> [1] TRUE
#> 
#> $method
#> [1] "white-noise full BvM (GvdV 2017 sec. 12.4.1)"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"