README.md

In wiesenfa/ESS: Quantification of prior informativeness in terms of prior effective and effective current sample size

Quantification of prior impact in terms of effective current sample size

• Installation
• Visualization of the impact of priors in terms of effective sample size
• References

Computes prior effective and effective current sample size. The concept of prior effective sample sizes (prior ESS) is convenient to quantify and communicate informativeness of prior distributions as it equates the information provided by a prior to a sample size. Prior information can arise from historical observations, thus the traditional approach identifies the ESS with such historical sample size (prior ESS). However, this measure is independent from newly observed data, and thus would not capture an actual ``loss of information’’ induced by the prior in case of prior-data conflict. The effective current sample size (ECSS) of a prior relates prior information to a number of (virtual) samples from the current data model and describes the impact of the prior capturing prior-data conflict. Supports mixture and empirical Bayes power and commensurate priors. See Wiesenfarth and Calderazzo (2019).

Installation

To get the current development version from Github:

devtools::install_github("wiesenfa/ESS")

## load ESS package
library(ESS)
#> Lade nötiges Paket: RBesT
#> Lade nötiges Paket: Rcpp
#> This is RBesT version 1.3.7
#> 
#> ESS 0.4.4.3 loaded.
#> 
#> Attache Paket: 'ESS'
#> The following object is masked from 'package:RBesT':
#> 
#>     ess

Visualization of the impact of priors in terms of effective sample size

This section (same as vignette("vignettePlanning", package = "ESS")) visualizes how plotECSS() can be used to quantify the impact of a prior (including mixture priors and empirical Bayes power priors/commensurate priors) in terms of effective current sample sizes on a grid of true values of the data generating process.

The effective current sample size (ECSS) is defined as follows:

Let (\pi) be the prior of interest (specified by priorlist) with mean (\theta_\pi), (\pi_b) a baseline prior (an objective or reference prior) (specified by prior.base) and (f_n(y_{1:n} | \theta_0)) be the data distribution.

The ECSS at target sample size (k) (specified by n.target) is defined as the sample size (m) which minimizes [ECSS=argmin_{m} | D^{\theta_0}{MSE}({\pi}(\theta|y{1:(k-m)})) - D^{\theta_0}{MSE}(\pi_b(\theta|y{1:k})) |]

where (D^{\theta_0}{MSE}) is the mean squared error measure induced by the posterior mean estimate (\mbox{E}\pi(\theta|y_{1:k})), [D^{\theta_0}{MSE}({\pi}(\theta|y{1:k}))=E_{y|\theta_0 } (E_\pi(\theta|y_{1:k})-\theta_0 )^2] or a different target measure specified by D. The true parameter value (\theta_0) (specified by grid) is assumed to be known.

Normal Outcome

  # standard deviation
    sigma=1
  # baseline
    rob=c(0,10)
    vague <-mixnorm(vague=c(1, rob), sigma=sigma)
  # prior with nominal prior ESS=50
    inf=c(0,1/sqrt(50))
    info <-mixnorm(informative=c(1, inf), sigma=sigma)
  # robust mixture
    mix50 <-mixnorm(informative=c(.5, inf),vague=c(.5, rob), sigma=sigma)
  # emprirical Bayes power prior / emprirical Bayes commensurate prior
    pp <-as.powerprior(info)

    plotECSS(priorlist=list(informative=info,mixture=mix50,powerprior=pp), 
             grid=((0:100)/100), n.target=200, min.ecss=-150, sigma=sigma, 
             prior.base=vague, progress="none", D=MSE)

Binary outcome

# uniform baseline prior
  rob=c(1,1)
  vague <- mixbeta(rob=c(1.0, rob))
# prior with nominal EHSS=20
  inf=c(4, 16)
  info=mixbeta(inf=c(1, inf))
  prior.mean=inf[1]/sum(inf)

# robust mixture
  mix50 <-mixbeta(informative=c(.5, inf), vague=c(.5, rob))
# emprirical Bayes power prior 
  pp <-as.powerprior(info)
## emprirical Bayes commensurate prior (takes long) 
#  cp <-as.commensurateEB(info)

 plotECSS(priorlist=list(informative=info,mixture=mix50,powerprior=pp), 
          grid=((0:40)/40), n.target=40, min.ecss=-50,
          prior.base=vague, progress="none", D=MSE)

References

Wiesenfarth, M., Calderazzo, S. (2019). Quantification of Prior Impact in Terms of Effective Current Sample Size. Submitted.

wiesenfa/ESS documentation built on June 19, 2019, 4:19 p.m.