H ~ int BP(c, H0_lambda) dPi(lambda) mixes over the base hazard. The
prior mean is then the weighted mixture of the component means,
E H(t) = sum_j w_j H0_{lambda_j}(t) – mixing enlarges the support
without disturbing the mean structure, which is why it is the standard
way to make a beta process prior less committal.
Usage
Ghosalmixbp(lambdas = c(0.5, 1, 2), weights = NULL, c = 3, t = 1)
Arguments
- lambdas
Component hazard rates.
- weights
Mixing weights; uniform when NULL.
- c
Concentration (does not enter the mean).
- t
Time point.
Value
List with estimate (mixture mean hazard),
component_means, method.
Details
Formula: E H(t) = sum_j w_j lambda_j t, with w the normalised
weights.
References
Ghosal & van der Vaart (2017), Fundamentals of
Nonparametric Bayesian Inference, CUP, section 13.3.4.
Examples
Ghosalmixbp()
#> $estimate
#> [1] 1.166667
#>
#> $component_means
#> [1] 0.5 1.0 2.0
#>
#> $method
#> [1] "mixture of beta processes (GvdV 2017 sec. 13.3.4)"
#>
#> attr(,"class")
#> [1] "morie_rich_result" "list"
