R: Approximately near optimal survey scheme

approx_near_optimal_survey_scheme {surveyvoi}

R Documentation

Approximately near optimal survey scheme

Description

Find a near optimal survey scheme that maximizes value of information. This function uses the approximation method for calculating the expected value of the decision given a survey scheme, and a greedy heuristic algorithm to maximize this metric.

Usage

approx_near_optimal_survey_scheme(
  site_data,
  feature_data,
  site_detection_columns,
  site_n_surveys_columns,
  site_probability_columns,
  site_management_cost_column,
  site_survey_cost_column,
  feature_survey_column,
  feature_survey_sensitivity_column,
  feature_survey_specificity_column,
  feature_model_sensitivity_column,
  feature_model_specificity_column,
  feature_target_column,
  total_budget,
  survey_budget,
  site_management_locked_in_column = NULL,
  site_management_locked_out_column = NULL,
  site_survey_locked_out_column = NULL,
  prior_matrix = NULL,
  n_approx_replicates = 100,
  n_approx_outcomes_per_replicate = 10000,
  seed = 500,
  n_threads = 1,
  verbose = FALSE
)

Arguments

`site_data`	`sf::sf()` object with site data.
`feature_data`	`base::data.frame()` object with feature data.
`site_detection_columns`	`character` names of `numeric` columns in the argument to `site_data` that contain the proportion of surveys conducted within each site that detected each feature. Each column should correspond to a different feature, and contain a proportion value (between zero and one). If a site has not previously been surveyed, a value of zero should be used.
`site_n_surveys_columns`	`character` names of `numeric` columns in the argument to `site_data` that contain the total number of surveys conducted for each each feature within each site. Each column should correspond to a different feature, and contain a non-negative integer number (e.g. 0, 1, 2, 3). If a site has not previously been surveyed, a value of zero should be used.
`site_probability_columns`	`character` names of `numeric` columns in the argument to `site_data` that contain modeled probabilities of occupancy for each feature in each site. Each column should correspond to a different feature, and contain probability data (values between zero and one). No missing (`NA`) values are permitted in these columns.
`site_management_cost_column`	`character` name of column in the argument to `site_data` that contains costs for managing each site for conservation. This column should have `numeric` values that are equal to or greater than zero. No missing (`NA`) values are permitted in this column.
`site_survey_cost_column`	`character` name of column in the argument to `site_data` that contains costs for surveying each site. This column should have `numeric` values that are equal to or greater than zero. No missing (`NA`) values are permitted in this column.
`feature_survey_column`	`character` name of the column in the argument to `feature_data` that contains `logical` (`TRUE` / `FALSE`) values indicating if the feature will be surveyed in the planned surveys or not. Note that considering additional features will rapidly increase computational burden, and so it is only recommended to consider features that are of specific conservation interest. No missing (`NA`) values are permitted in this column.
`feature_survey_sensitivity_column`	`character` name of the column in the argument to `feature_data` that contains probability of future surveys correctly detecting a presence of each feature in a given site (i.e. the sensitivity of the survey methodology). This column should have `numeric` values that are between zero and one. No missing (`NA`) values are permitted in this column.
`feature_survey_specificity_column`	`character` name of the column in the argument to `feature_data` that contains probability of future surveys correctly detecting an absence of each feature in a given site (i.e. the specificity of the survey methodology). This column should have `numeric` values that are between zero and one. No missing (`NA`) values are permitted in this column.
`feature_model_sensitivity_column`	`character` name of the column in the argument to `feature_data` that contains probability of the initial models correctly predicting a presence of each feature in a given site (i.e. the sensitivity of the models). This column should have `numeric` values that are between zero and one. No missing (`NA`) values are permitted in this column. This should ideally be calculated using `fit_xgb_occupancy_models()` or `fit_hglm_occupancy_models()`.
`feature_model_specificity_column`	`character` name of the column in the argument to `feature_data` that contains probability of the initial models correctly predicting an absence of each feature in a given site (i.e. the specificity of the models). This column should have `numeric` values that are between zero and one. No missing (`NA`) values are permitted in this column. This should ideally be calculated using `fit_xgb_occupancy_models()` or `fit_hglm_occupancy_models()`.
`feature_target_column`	`character` name of the column in the argument to `feature_data` that contains the `target` values used to parametrize the conservation benefit of managing of each feature. This column should have `numeric` values that are equal to or greater than zero. No missing (`NA`) values are permitted in this column.
`total_budget`	`numeric` maximum expenditure permitted for conducting surveys and managing sites for conservation.
`survey_budget`	`numeric` maximum expenditure permitted for conducting surveys.
`site_management_locked_in_column`	`character` name of the column in the argument to `site_data` that contains `logical` (`TRUE` / `FALSE`) values indicating which sites should be locked in for (`TRUE`) being managed for conservation or (`FALSE`) not. No missing (`NA`) values are permitted in this column. This is useful if some sites have already been earmarked for conservation, or if some sites are already being managed for conservation. Defaults to `NULL` such that no sites are locked in.
`site_management_locked_out_column`	`character` name of the column in the argument to `site_data` that contains `logical` (`TRUE` / `FALSE`) values indicating which sites should be locked out for (`TRUE`) being managed for conservation or (`FALSE`) not. No missing (`NA`) values are permitted in this column. This is useful if some sites could potentially be surveyed to improve model predictions even if they cannot be managed for conservation. Defaults to `NULL` such that no sites are locked out.
`site_survey_locked_out_column`	`character` name of the column in the argument to `site_data` that contains `logical` (`TRUE` / `FALSE`) values indicating which sites should be locked out (`TRUE`) from being selected for future surveys or (`FALSE`) not. No missing (`NA`) values are permitted in this column. This is useful if some sites will never be considered for future surveys (e.g. because they are too costly to survey, or have a low chance of containing the target species). Defaults to `NULL` such that no sites are locked out.
`prior_matrix`	`numeric` `matrix` containing the prior probability of each feature occupying each site. Rows correspond to features, and columns correspond to sites. Defaults to `NULL` such that prior data is calculated automatically using `prior_probability_matrix()`.
`n_approx_replicates`	`integer` number of replicates to use for approximating the expected value calculations. Defaults to 100.
`n_approx_outcomes_per_replicate`	`integer` number of outcomes to use per replicate for approximation calculations. Defaults to 10000.
`seed`	`integer` state of the random number generator for simulating outcomes when conducting the value of information analyses. Defaults to 500.
`n_threads`	`integer` number of threads to use for computation.
`verbose`	`logical` indicating if information should be printed during processing. Defaults to `FALSE`.

Details

Ideally, the brute-force algorithm would be used to identify the optimal survey scheme. Unfortunately, it is not feasible to apply the brute-force to large problems because it can take an incredibly long time to complete. In such cases, it may be desirable to obtain a "relatively good" survey scheme and the greedy heuristic algorithm is provided for such cases. The greedy heuristic algorithm – unlike the brute force algorithm – is not guaranteed to identify an optimal solution – or even a "relatively good solution" for that matter – though greedy heuristic algorithms tend to deliver solutions that are 15\ greedy algorithms is implemented as:

Initialize an empty list of survey scheme solutions, and an empty list of approximate expected values.
Calculate the expected value of current information.
Add a survey scheme with no sites selected for surveying to the list of survey scheme solutions, and add the expected value of current information to the list of approximate expected values.
Set the current survey solution as the survey scheme with no sites selected for surveying.
For each remaining candidate site that has not been selected for a survey, generate a new candidate survey scheme with each candidate site added to the current survey solution.
Calculate the approximate expected value of each new candidate survey scheme. If the cost of a given candidate survey scheme exceeds the survey budget, then store a missing ⁠NA value⁠ instead. Also if the the cost of a given candidate survey scheme plus the management costs of locked in planning units exceeds the total budget, then a store a missing value NA value too.
If all of the new candidate survey schemes are associated with missing NA values – because they all exceed the survey budget – then go to step 12.
Calculate the cost effectiveness of each new candidate survey scheme. This calculated as the difference between the approximate expected value of a given new candidate survey scheme and that of the current survey solution, and dividing this difference by the the cost of the newly selected candidate site.
Find the new candidate survey scheme that is associated with the highest cost-effectiveness value, ignoring any missing NA values. This new candidate survey scheme is now set as the current survey scheme.
Store the current survey scheme in the list of survey scheme solutions and store its approximate expected value in the list of approximate expected values.
Go to step 12.
Find the solution in the list of survey scheme solutions that has the highest expected value in the list of approximate expected values and return this solution.

Value

A matrix of logical (TRUE/ FALSE) values indicating if a site is selected in the scheme or not. Columns correspond to sites, and rows correspond to different schemes. If there are no ties for the best identified solution, then the the matrix will only contain a single row.

Examples

# set seeds for reproducibility
set.seed(123)

# load example site data
data(sim_sites)
print(sim_sites)

# load example feature data
data(sim_features)
print(sim_features)

# set total budget for managing sites for conservation
 # (i.e. 50% of the cost of managing all sites)
total_budget <- sum(sim_sites$management_cost) * 0.5

# set total budget for surveying sites for conservation
# (i.e. 40% of the cost of managing all sites)
survey_budget <- sum(sim_sites$survey_cost) * 0.4

# find survey scheme using approximate method and greedy heuristic algorithm
# (using 10 replicates so that this example completes relatively quickly)
approx_near_optimal_survey <- approx_near_optimal_survey_scheme(
  sim_sites, sim_features,
  c("f1", "f2", "f3"), c("n1", "n2", "n3"), c("p1", "p2", "p3"),
  "management_cost", "survey_cost",
  "survey", "survey_sensitivity", "survey_specificity",
  "model_sensitivity", "model_specificity",
  "target", total_budget, survey_budget)

# print result
print(approx_near_optimal_survey)

[Package surveyvoi version 1.0.6 Index]