make_priors_and_init: Elicit priors and initialization from background dataset

In lgaborini/bayessource: Bayesian approach to evaluate whether two datasets come from the same population

Description

Here we fix the hyperparameters for priors on theta_i and W_i, i.e., B, U, mu and n_w.

Usage

make_priors_and_init(
  df.background,
  col.variables,
  col.item,
  use.priors = c("ML", "vague"),
  use.init = c("random", "vague"),
  ...
)

Arguments

df.background	the background dataset
col.variables	columns with variables: names or positions
col.item	column with the id of the item (i): names or positions
use.priors	see details
use.init	see details
...	additional variables for priors and init (see the description)

Details

An appropriate initialization value for W^{-1}_i, i=1,2 ($h_p$ and $h_d$ chains respectively) is also generated.

Notice that we have three chains in the LR computations, the same initialization is used thrice.

Priors

use.priors:

• 'ML': maximum likelihood estimation as in \insertCiteBozza2008Probabilisticbayessource

• 'vague': low-information priors

  U is alpha*diag(p), B is beta*diag(p), mu is mu0.

  By default alpha = 1, beta = 1, mu0 = 0

The Wishart dofs nw are set as small as possible without losing full rank: n_w = 2*(p + 1) + 1

Initialization

Generate values for W^{-1}_1, W^{-1}_2 that will be used as starting values for the Gibbs chains. Two methods:

use.init:

• 'random': initialize according to the model

  • generate one W_i ~ IW_p(n_w, U)

  • then invert: W^{-1}_i = (W_i)^{-1}

• 'vague': low-information initialization

  • W_i = alpha_init + beta_init * diag(p)

Parameters

Some constants can be changed by passing the new values to ... :

• use.priors = 'vague': accepts parameters

  • alpha (default: 1)

  • beta (default: 1)

  • mu0 (default: 0)

• use.init = 'vague': accepts parameters

  • alpha_init (default: 1)

  • beta_init (default: 100)

Return values

A list of variables:

• mu: the global mean

• B.inv: the between-source prior covariance matrix, as the inverse

• U: the Inverted Wishart scale matrix

• nw: the Inverted Wishart dof n_w

• W.inv.1, W.inv.2: the initializations for the within-source covariance matrices, as their inverses

Value

a list of variables

See Also

Other core functions: bayessource-package, get_minimum_nw_IW(), marginalLikelihood_internal(), marginalLikelihood(), mcmc_postproc(), samesource_C(), two.level.multivariate.calculate.UC()

Examples

# Use the iris data
head(iris, 3)
col_variables <- c(1,3)
col_item <- 5

# Elicitation using MLE
priors_init <- make_priors_and_init(
   df.background = iris,
   col.variables = col_variables,
   col.item = col_item
)

priors_init

priors_init_2 <- make_priors_and_init(
   df.background = iris,
   col.variables = col_variables,
   col.item = col_item,
   use.priors = "vague",
   alpha_init = 100
)

priors_init_2

lgaborini/bayessource documentation built on Nov. 9, 2021, 2:10 p.m.