BMEmapping (version 1.2.2)

bme_predict: Bayesian Maximum Entropy (BME) Spatial Interpolation

Description

bme_predict performs BME spatial interpolation at user-specified estimation locations. It uses both hard data (precise measurements) and soft data (interval or uncertain measurements), along with a specified variogram model, to compute either the posterior mean or mode and associated variance for each location. This function enables spatial prediction in settings where uncertainty in data must be explicitly accounted for, improving estimation accuracy when soft data is available.

Usage

bme_predict(x, data_object, model, nugget, sill, range,
                   nsmax = 5, nhmax = 5, n = 50,
                   zk_range = extended_range(data_object), type)

Value

A data frame with either 3 or 4 columns, depending on the prediction type. The first two columns contain the geographic coordinates. If type = "mean", the third and fourth columns represent the posterior mean and its associated variance, respectively. If type = "mode", only a third column is returned for the posterior mode.

Arguments

x

A two-column matrix of spatial coordinates for the estimation locations.

data_object

A list containing the hard and soft data.

model

A string specifying the variogram or covariance model to use (e.g., "exp", "sph", etc.).

nugget

A non-negative numeric value for the nugget effect in the variogram model.

sill

A numeric value representing the sill (total variance) in the variogram model.

range

A positive numeric value for the range (or effective range) parameter of the variogram model.

nsmax

An integer specifying the maximum number of nearby soft data points to include for estimation (default is 5).

nhmax

An integer specifying the maximum number of nearby hard data points to include for estimation (default is 5).

n

An integer indicating the number of points at which to evaluate the posterior density over zk_range (default is 50).

zk_range

A numeric vector specifying the range over which to evaluate the unobserved value at the estimation location (zk). Although zk is unknown, it is assumed to lie within a range similar to the observed data (zh, a, and b). It is advisable to explore the posterior distribution at a few locations using prob_zk() before finalizing this range.

type

A string indicating the type of BME prediction to compute: either "mean" for the posterior mean or "mode" for the posterior mode.

Examples

data("utsnowload")
x <- utsnowload[1, c("latitude", "longitude")]
ch <- utsnowload[2:67, c("latitude", "longitude")]
cs <- utsnowload[68:232, c("latitude", "longitude")]
zh <- utsnowload[2:67, c("hard")]
a <- utsnowload[68:232, c("lower")]
b <- utsnowload[68:232, c("upper")]
data_object <- bme_map(ch, cs, zh, a , b)
bme_predict(x, data_object,
  model = "exp", nugget = 0.0953,
  sill = 0.3639, range = 1.0787, type = "mean"
)