fitOrderStat: Restricted likelihood Bayesian model using a middle set of...
In jrlewi/brlm: Bayesian Restricted Likelihood Methods

Description Usage Arguments Details Value See Also

Conditioning on a set of order statistics under a Guassian location and scale model. The full model is:

μ\sim N(η, τ^2), σ^2 \sim IG(α, β), y_i~N(μ, σ^2)

Conditioning is on a middle set of order statistics (Y_{(k+1)}, … Y_{(n-k)}). That is, the likelihood used in the Bayesian update is the likelihood of these order statistics. When k=0, the model is the full normal theory model written above.

fitOrderStat(
  y,
  k,
  mu_lims,
  length_mu,
  sigma2_lims,
  length_sigma2,
  eta,
  tau,
  alpha,
  beta
)

`y`	vector of data
`k`	numeric: choice of k determining the set of order statistics on which to condition.
`mu_lims, sigma2_lims`	vectors of length 2 specifying the lower and upper limits for the numerical integration. Should span region of non-negligble posterior probability, otherwise the posterior will be incorrect
`length_mu, length_sigma2`	Number of grid points for each parameter used in the numerical integration
`eta, tau`	mean and standard deviation of the normal prior distribution on μ
`alpha, beta`	prior shape and scale of inverse gamma prior on σ^2

Fit is done a grid of μ and σ^2 using Riemann sum numerical integration to find the marginal distribution of the data. This is rather naive but is relatively quick - it only works well if the choice of grid on which the Riemann sum is done is chosen carefully. The grid is specified by mu_lims, sigma2_lims, length_mu, and length_sigma2. The grid should cover the region of non-negligble posterior mass. The number of grid points (length_mu/length_sigma2) etast be large enough for good precision. However, larger values increase computation time.

A list of length 4: the joint posterior, the two marginals, and the posterior means

fitMixture

jrlewi/brlm documentation built on March 17, 2021, 1:10 a.m.