Package 'yodel'

Posterior Weights and Model Averaging Setup

Description

Calculate posterior weights of each model and optionally supply MCMC samples and functions (through the bma_model() function) to calculate a quantity of interest from each model using the posterior() function.

Usage

bma(..., seed = sample(.Machine$integer.max, 1))

model_bma_predictive(
  log_post_pred,
  adjustment = 0,
  w_prior = 1,
  mcmc = NULL,
  fun = NULL
)

model_bma_marginal(log_marginal, w_prior = 1, mcmc = NULL, fun = NULL)

Arguments

...	Named calls to the bma_model() function.
seed	an integer which is used to specify the seed when sampling from the different models (e.g. in posterior()).
log_post_pred	a matrix containing the log likelihood for each observation on each iteration of the MCMC. The matrix should have dimensions (number-of-MCMC-iteration) by (number of observations).
adjustment	an adjustment to be applied to the posterior log-predictive likelihood. A simple bias correction in Ando & Tsay (2010) is: - (number of parameters in the model) / 2.
w_prior	the prior weight for the model.
mcmc	a named list (or dataframe) of MCMC samples of model parameters.
fun	a function which takes the MCMC samples and returns a value of interest.
log_marginal	The log marginal likelihood of the model.

Details

It is required that if MCMC samples are supplied, that each MCMC run must have the same number of collected samples.

Value

bma: A list containing the prior and posterior weights for each model, the sampled model (model_index) at each MCMC iteration and the arguments supplied to each bma_model() call.

model_bma: A named list of the arguments, with a "yodel_bma_candidate" class attached.

model_bma: A named list of the arguments, with a "yodel_bma_candidate" class attached.

References

Ando, T., & Tsay, R. (2010). Predictive likelihood for Bayesian model selection and averaging. International Journal of Forecasting, 26(4), 744-763.

Examples

# Minimal example
fit <- bma(
  linear = model_bma_predictive(
    # mcmc = data.frame(b1 = 1:5, b2 = 11:15, sigma = seq(.1, .5, .1)),
    log_post_pred = matrix(log(1:100), 5, 20),
    adjustment = - 3 / 2,
    w_prior = .5
  ),
  quad = model_bma_predictive(
    # mcmc = data.frame(b1 = 1:5 / 2, b2 = 11:15 / 2, b3 = 5:1, sigma = seq(.1, .5, .1)),
    log_post_pred = matrix(log(2:101), 5, 20),
    adjustment = - 4 / 2,
    w_prior = .5
  )
)

fit$w_prior
fit$w_post

---

Calculate Posterior Quantities

Description

Calculate posterior quantities specifically of interest for a given model.

Usage

posterior(x, ...)

Arguments

x	MCMC output.
...	additional arguments passed to S3 methods.

Value

a dataframe or tibble with the posterior probabilities.

Examples

# functions which caclulate the dose response for a linear and quadratic model
fun_linear <- function(x, dose) {
  mean_response <- x$b1 + x$b2 * dose
  data.frame(iter = 1:nrow(x), dose = dose, mean = mean_response)
}
fun_quad <- function(x, dose) {
  mean_response <- x$b1 + x$b2 * dose + x$b3 * dose ^ 2
  data.frame(iter = 1:nrow(x), dose = dose, mean = mean_response)
}

# Bayesian model averaging
fit <- bma(
  linear = model_bma_predictive(
    mcmc = data.frame(b1 = 1:5, b2 = 11:15, sigma = seq(.1, .5, .1)),
    log_post_pred = matrix(log(1:100), 5, 20),
    adjustment = - 3 / 2,
    w_prior = .5,
    fun = fun_linear
  ),
  quad = model_bma_predictive(
    mcmc = data.frame(b1 = 1:5 / 2, b2 = 11:15 / 2, b3 = 5:1, sigma = seq(.1, .5, .1)),
    log_post_pred = matrix(log(2:101), 5, 20),
    adjustment = - 4 / 2,
    w_prior = .5,
    fun = fun_quad
  )
)

# posterior samples using Bayesian model averaging
posterior(fit, dose = 1)
posterior(fit, dose = 2)

---

Posterior Samples from Bayesian Model Averaging

Description

Calculate posterior quantities of interest using Bayesian model averaging.

Usage

## S3 method for class 'yodel_bma'
posterior(x, ...)

Arguments

x	output from a call to bma().
...	additional arguments to be passed to each of the functions used to calculate the quantity of interest.

Value

A dataframe with the posterior samples for each iteration of the MCMC. The dataframe will have, at a minimum, the columns "iter" and "model" indicating the MCMC iteration and the model that was used in the calculations. The functions used for each model are defined within the model_bma() function and used in the bma() function. See the example below.

Examples

# functions which caclulate the dose response for a linear and quadratic model
fun_linear <- function(x, dose) {
  mean_response <- x$b1 + x$b2 * dose
  data.frame(iter = 1:nrow(x), dose = dose, mean = mean_response)
}
fun_quad <- function(x, dose) {
  mean_response <- x$b1 + x$b2 * dose + x$b3 * dose ^ 2
  data.frame(iter = 1:nrow(x), dose = dose, mean = mean_response)
}

# Bayesian model averaging
fit <- bma(
  linear = model_bma_predictive(
    mcmc = data.frame(b1 = 1:5, b2 = 11:15, sigma = seq(.1, .5, .1)),
    log_post_pred = matrix(log(1:100), 5, 20),
    adjustment = - 3 / 2,
    w_prior = .5,
    fun = fun_linear
  ),
  quad = model_bma_predictive(
    mcmc = data.frame(b1 = 1:5 / 2, b2 = 11:15 / 2, b3 = 5:1, sigma = seq(.1, .5, .1)),
    log_post_pred = matrix(log(2:101), 5, 20),
    adjustment = - 4 / 2,
    w_prior = .5,
    fun = fun_quad
  )
)

# posterior samples using Bayesian model averaging
posterior(fit, dose = 1)
posterior(fit, dose = 2)

---