Description Usage Arguments Details Value Methods (by class) Supported Conjugate PriorLikelihood Pairs References Examples
Calculates the Effective Sample Size (ESS) for a mixture prior. The ESS indicates how many experimental units the prior is roughly equivalent to.
1 2 3 4 5 6 7 8 9 10  ess(mix, method = c("elir", "moment", "morita"), ...)
## S3 method for class 'betaMix'
ess(mix, method = c("elir", "moment", "morita"), ..., s = 100)
## S3 method for class 'gammaMix'
ess(mix, method = c("elir", "moment", "morita"), ..., s = 100, eps = 1e04)
## S3 method for class 'normMix'
ess(mix, method = c("elir", "moment", "morita"), ..., sigma, s = 100)

mix 
Prior (mixture of conjugate distributions). 
method 
Selects the used method. Can be either 
... 
Optional arguments applicable to specific methods. 
s 
For 
eps 
Probability mass left out from the numerical integration of the expected information for the PoissonGamma case of Morita method (defaults to 1E4). 
sigma 
reference scale. 
The ESS is calculated using either the expected local information ratio (elir) Neuenschwander et al. (submitted), the moments approach or the method by Morita et al. (2008).
The elir approach is the only ESS which fulfills predictive consistency. The predictive consistency of the ESS requires that the ESS of a prior is the same as averaging the posterior ESS after a fixed amount of events over the prior predictive distribution from which the number of forward simulated events is subtracted. The elir approach results in ESS estimates which are neither conservative nor liberal whereas the moments method yields conservative and the morita method liberal results. See the example section for a demonstration of predictive consistency.
For the moments method the mean and standard deviation of the mixture are calculated and then approximated by the conjugate distribution with the same mean and standard deviation. For conjugate distributions, the ESS is well defined. See the examples for a stepwise calculation in the beta mixture case.
The Morita method used here evaluates the mixture prior at the mode instead of the mean as proposed originally by Morita. The method may lead to very optimistic ESS values, especially if the mixture contains many components. The calculation of the Morita approach here follows the approach presented in Neuenschwander B. et all (2019) which avoids the need for a minimization and does not restrict the ESS to be an integer.
Returns the ESS of the prior as floating point number.
betaMix
: ESS for beta mixtures.
gammaMix
: ESS for gamma mixtures.
normMix
: ESS for normal mixtures.
Prior/Posterior  Likelihood  Predictive  Summaries 
Beta  Binomial  BetaBinomial  n , r 
Normal  Normal (fixed σ)  Normal  n , m , se 
Gamma  Poisson  GammaPoisson  n , m 
Gamma  Exponential  GammaExp (not supported)  n , m

Morita S, Thall PF, Mueller P. Determining the effective sample size of a parametric prior. Biometrics 2008;64(2):595602.
Neuenschwander B, Weber S, Schmidli H, O'Hagen A. Predictively Consistent Prior Effective Sample Sizes. preprint 2019; arXiv:1907.04185
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53  # Conjugate Beta example
a < 5
b < 15
prior < mixbeta(c(1, a, b))
ess(prior)
(a+b)
# Beta mixture example
bmix < mixbeta(rob=c(0.2, 1, 1), inf=c(0.8, 10, 2))
ess(bmix, "elir")
ess(bmix, "moment")
# moments method is equivalent to
# first calculate moments
bmix_sum < summary(bmix)
# then calculate a and b of a matching beta
ab_matched < ms2beta(bmix_sum["mean"], bmix_sum["sd"])
# finally take the sum of a and b which are equivalent
# to number of responders/nonresponders respectivley
round(sum(ab_matched))
ess(bmix, method="morita")
# Predictive consistency of elir
n_forward < 1E2
bmixPred < preddist(bmix, n=n_forward)
pred_samp < rmix(bmixPred, 1E3)
pred_ess < sapply(pred_samp, function(r) ess(postmix(bmix, r=r, n=n_forward), "elir") )
ess(bmix, "elir")
mean(pred_ess)  n_forward
# Normal mixture example
nmix < mixnorm(rob=c(0.5, 0, 2), inf=c(0.5, 3, 4), sigma=10)
ess(nmix, "elir")
ess(nmix, "moment")
## the reference scale determines the ESS
sigma(nmix) < 20
ess(nmix)
# Gamma mixture example
gmix < mixgamma(rob=c(0.3, 20, 4), inf=c(0.7, 50, 10))
ess(gmix) ## interpreted as appropriate for a Poisson likelihood (default)
likelihood(gmix) < "exp"
ess(gmix) ## interpreted as appropriate for an exponential likelihood

Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.