bound_frequency_exceeding_bp: This function uses the Nelder-Mead algorithm for the...

In Iraices/PrecisePvsBoundedP: A suggestion for the quantification of precise and bounded probability to express epistemic uncertainty in scientific assessments

Description

This function uses the Nelder-Mead algorithm for the optimization procedure. This algorithm is implemented in the 'nmkb' function from the dfoptim package.

Usage

bound_frequency_exceeding_bp(
  obj_func_bp,
  maximize = FALSE,
  lower_parameters = c(1, -5, -20),
  upper_parameters = c(6, 1, -10),
  niter_ale = 1000,
  niter_epi = 1000,
  threshold = 1,
  exposure_scenario = "av",
  suff_stat_concentration,
  suff_stat_consumption,
  consumption_change_vals_EKE = c(-15, 7.5),
  consumption_change_probs_EKE = c(0.25, 0.75),
  consumers_info_sample_size,
  concentration_mu0 = 2.75,
  concentration_v0 = 5,
  concentration_alpha0 = 1,
  concentration_beta0 = 1,
  sufficient_statistics_concentration = TRUE,
  consumption_mu0 = -2.5,
  consumption_v0 = 5,
  consumption_alpha0 = 1,
  consumption_beta0 = 1,
  sufficient_statistics_consumption = TRUE,
  consumption_event_alpha0 = 1,
  consumption_event_beta0 = 1,
  percentile = NULL
)

Arguments

obj_func_bp	The objective function to optimize.
maximize	A logical variable indicating whether the objective function should be maximized. Default is FALSE.
lower_parameters	Lower bounds on the parameters. A vector of the same length as the parameters.
upper_parameters	Upper bounds on the parameters. A vector of the same length as the parameters.
niter_ale	number of generated samples
niter_epi	number of generated parameters from the posterior distrbutions (it indicates the number of repetitions the assessment will be done)
threshold	safety threshold
exposure_scenario	a value that indicates if the assessment is done on average consumption scenario by 'av' or on high consumption scenario by 'perc_95'. Default is 'av'
suff_stat_concentration	a vector of sufficient statistics: sample_size, sample_mean and sample_sd corresponding to concentration. If sufficient_statistics_concentration = FALSE, then it is vector of observed data
suff_stat_consumption	a vector of sufficient statistics: sample_size, sample_mean and sample_sd corresponding to consumption. If sufficient_statistics_consumption = FALSE, then it is vector of observed data
consumption_change_vals_EKE	a vector of elicited values from experts
consumption_change_probs_EKE	a vector of elicited probabilities from experts
consumers_info_sample_size	a vector with the sample size of non_consumer_sample_size and consumer_sample_size
concentration_mu0	prior hyperparameter mu0 for the normal-gamma distribution corresponding to concentration
concentration_v0	prior hyperparameter v0 for the normal-gamma distribution corresponding to concentration
concentration_alpha0	prior hyperparameter alpha0 for the normal-gamma distribution corresponding to concentration
concentration_beta0	prior hyperparameter beta0 for the normal-gamma distribution corresponding to concentration
sufficient_statistics_concentration	logical; if TRUE, sufficient statistics (sample_size, sample_mean, sample_variance) corresponding to concentration are given as input data, otherwise sufficient_statistics_concentration is given as observed data. Default is TRUE
consumption_mu0	prior hyperparameter mu0 for the normal-gamma distribution corresponding to consumption
consumption_v0	prior hyperparameter v0 for the normal-gamma distribution corresponding to consumption
consumption_alpha0	prior hyperparameter alpha0 for the normal-gamma distribution corresponding to consumption
consumption_beta0	prior hyperparameter beta0 for the normal-gamma distribution corresponding to consumption
sufficient_statistics_consumption	logical; if TRUE, sufficient statistics (sample_size, sample_mean, sample_variance) corresponding to consumption are given as input data, otherwise sufficient_statistics_consumption is given as observed data. Default is TRUE
consumption_event_alpha0	prior hyperparameter alpha0 for the beta distribution corresponding to consumption event
consumption_event_beta0	prior hyperparameter beta0 for the beta distribution corresponding to consumption event
percentile	a value between 1 and 100 which indicates a percentile. By default is NULL

Value

## Two lists

1. opt_value

2. opt_freq

The components of the first list (opt_value) are

par

Best estimate of the parameter vector found by the algorithm

value

The value of the objective function at termination

feval

The number of times the objective function was evaluated

restarts

The number of times the algorithm had to be restarted when it stagnated

convergence

An integer code indicating type of convergence. 0 indicates successful convergence. Positive integer codes indicate failure to converge

message

Text message indicating the type of convergence or failure

The components of the second list (opt_freq) are

prob_consumption_event

The estimated probability of consumption events

parameters_concentration

A list with the values of the prior and posterior parameters of concentration

parameters_consumption

A list with the prior and posterior parameters of consumption

frequency_exceeding

A vector with the estimated frequency of exceeding the threshold (the lenght is niter_epi)

expected_frequency_exceeding

The expected value of the frequency of exceeding the threshold

hdi_frequency_exceeding

The highest posterior density interval of the frequency of exceeding the threshold

Examples

## Not run: 
lower_bound_average_consumption <-
  bound_frequency_exceeding_bp(obj_func_bp = obj_func_bp, maximize = FALSE,
           lower_parameters  = c(1, -5, -20),
           upper_parameters  = c(6, 1, -10),
           niter_ale = 2000, niter_epi = 2000, threshold = 1, exposure_scenario = 'av',
           suff_stat_concentration = data_assessment$log_concentration_ss_data,
           suff_stat_consumption = data_assessment$log_consumption_ss_data,
           consumption_change_vals_EKE = c(-15, 7.5),
           consumption_change_probs_EKE = c(0.25, 0.75),
           consumers_info_sample_size = data_assessment$consumers_info_sample_size,
           concentration_mu0 = 2.75,
           concentration_v0 = 5, concentration_alpha0 = 1, concentration_beta0 = 1,
           sufficient_statistics_concentration = TRUE,
           consumption_mu0 = -2.5,
           consumption_v0 = 5, consumption_alpha0 = 1, consumption_beta0 = 1,
           sufficient_statistics_consumption = TRUE,
           consumption_event_alpha0 = 1, consumption_event_beta0 = 1, percentile = NULL)

upper_bound_average_consumption <-
 bound_frequency_exceeding_bp(obj_func_bp = obj_func_bp, maximize = TRUE,
           lower_parameters  = c(1, -5, -20),
           upper_parameters  = c(6, 1, -10),
           niter_ale = 2000, niter_epi = 2000, threshold = 1, exposure_scenario = 'av',
           suff_stat_concentration = data_assessment$log_concentration_ss_data,
           suff_stat_consumption = data_assessment$log_consumption_ss_data,
           consumption_change_vals_EKE = c(-15, 7.5),
           consumption_change_probs_EKE = c(0.25, 0.75),
           consumers_info_sample_size = data_assessment$consumers_info_sample_size,
           concentration_mu0 = 2.75,
           concentration_v0 = 5, concentration_alpha0 = 1, concentration_beta0 = 1,
           sufficient_statistics_concentration = TRUE,
           consumption_mu0 = -2.5,
           consumption_v0 = 5, consumption_alpha0 = 1, consumption_beta0 = 1,
           sufficient_statistics_consumption = TRUE,
           consumption_event_alpha0 = 1, consumption_event_beta0 = 1, percentile = NULL)


## End(Not run)

Iraices/PrecisePvsBoundedP documentation built on Jan. 18, 2021, 11:32 p.m.