Bayesian_UPL() wraps setup_likelihood(), run_likelihood(), output_likelihood(), converge_likelihood(), and fit_likelihood()

For each distribution in distr_list, Bayesian_UPL() will setup_likelihood(), run_likelihood(), organize mcmc results in output_likelihood(), test for convergence of likelihood parameters using converge_likelihood(), and calculate goodness of fit metrics using fit_likelihood(). Results include $fit_table: a tibble with the UPL, pdf_integral, SSE, and count of observations within 95 percent CI for each distribution in 'distr_list', $conv_output: a tibble with the parameters, Gelman-Rubin diagnostics, and if the converged for distribution in distr_list, $obs_pdf_dat: a tibble with the emissions observations, corresponding observation densities, median, upper, and lower 95 percent CI around predicted densities for the distribution in distr_list, and a 1 if the observation is within the 95 percent CI, a 0 otherwise, and $pred_pdf_dat:a tibble with the predicted probability density pdf_hat, the observation density ydens for each value in the range of emissions in x_hat. The maximum emission value of distributions, maxY, the ordered range emissions to predict to xvals, and the prior distributions and initial values are all automatically supplied from the emissions data to be fully encompassing and uninformative by default. They can be supplied manually instead however by supplying maxY, xvals, or setting manual_prior = TRUE with corresponding lower and upper limits in prior_list. If manual priors are used, only a single distribution can be run at a time in distr_list.

Usage

Bayesian_UPL(
  distr_list = c("Normal", "Skewed", "Lognormal", "Gamma", "Beta"),
  data,
  future_runs = 3,
  significance = 0.99,
  xvals = NULL,
  maxY = NULL,
  convergence_report = FALSE,
  manual_prior = FALSE,
  prior_list = NULL
)

Arguments

distr_list: A list including one or more of c('Normal','Skewed','Lognormal','Gamma','Beta'). Note that if prior bounds are supplied manually, only one distribution can be used.
data: Emissions data from either the best source or top performers, must have a column named 'emissions'.
future_runs: Integer of future runs to use in prediction, the default is 3 since compliance uses 1 test average of 3 runs.
significance: Level of significance from 0 to 1, the default is 0.99.
xvals: Ordered sequence of emissions at which to predict probability density. Default is NULL, in which case x_hat is a 1024 length sequence between 0 and 3*max(data$emissions).
maxY: The maximum emission value possible, used to truncate likelihood distributions and set upper ranges on prior distributions, not specified manually. Default is NULL, in which case is is calculated as 3*max(data$emissions).
convergence_report: Default is FALSE, if a report containing convergence figures should be generated with results. If TRUE, a document Bayesian_UPL_convergence_MMDDYYY_HHMM.pdf will be written to the current working directory.
manual_prior: Default is FALSE, if priors should be specified manually or be uninformative calculated from range of emissions data. Note that if you are supplying priors manually than you can only run one type of distribution at a time.
prior_list: Optional list of stats::dunif() upper and lower bounds for prior distributions. For 'Normal' they are ordered c(sd_low, sd_high, mean_low,mean_high'). For 'Lognormal' they are ordered c(log_sd_low, log_sd_high, log_mean_low, log_mean_high). For 'Skewed' they are ordered c(omega_low, omega_high, xi_low, xi_high, alpha_low, alpha_high). For 'Gamma' they are ordered c(rate_low, rate_high, shape_low, shape_high). For 'Beta' they are ordered c(alpha_low, alpha_high, beta_low, beta_high).

Value

A list of tibble results from setup_likelihood(), run_likelihood(), output_likelihood(), obs_density(), fit_likelihood(), and converge_likelihood() for each distribution in distr_list.