Type:	Package
Title:	Spatial Interpolation using Bayesian Maximum Entropy (BME)
Version:	1.0.0
Maintainer:	Kinspride Duah <kinspride2020@gmail.com>
Description:	Provides an accessible and robust implementation of core BME methodologies for spatial prediction. It enables the systematic integration of heterogeneous data sources including both hard data (precise measurements) and soft interval data (bounded or uncertain observations) while incorporating prior knowledge and supporting variogram-based spatial modeling. The BME methodology is described in Christakos (1990) <doi:10.1007/BF00890661> and Serre and Christakos (1999) <doi:10.1007/s004770050029>.
License:	MIT + file LICENSE
Encoding:	UTF-8
LazyData:	true
URL:	https://github.com/KinsprideDuah/BMEmapping
BugReports:	https://github.com/KinsprideDuah/BMEmapping/issues
RoxygenNote:	7.3.2
Suggests:	knitr, rmarkdown, testthat (≥ 3.0.0)
Config/testthat/edition:	3
Imports:	mvtnorm
Depends:	R (≥ 3.5)
VignetteBuilder:	knitr
NeedsCompilation:	no
Packaged:	2025-07-02 01:34:50 UTC; kwaku
Author:	Kinspride Duah [aut, cre, cph], Yan Sun [aut]
Repository:	CRAN
Date/Publication:	2025-07-02 02:40:02 UTC

Leave-one-out cross validation (LOOCV) at hard data locations.

Description

bme_cv performs LOOCV to evaluate the prediction performance of the Bayesian Maximum Entropy (BME) spatial interpolation method using both hard and soft (interval) data.

For each hard data location, the function removes the observed value and predicts it using all remaining hard and soft data points. This is repeated for every hard data location. The predictions are either posterior means or posterior modes, depending on the type argument.

The function returns prediction results at each location, including the residuals (differences between observed and predicted values), and computes three performance metrics:

• ME (Mean Error) – measures prediction bias.

• MAE (Mean Absolute Error) – measures average magnitude of prediction error.

• RMSE (Root Mean Squared Error) – emphasizes larger errors and reflects prediction accuracy.

This function is useful for validating the BME interpolation method and tuning variogram parameters.

Usage

bme_cv(ch, cs, zh, a, b,
       model, nugget, sill, range, nsmax = 5,
       nhmax = 5, n = 50, zk_range = extended_range(zh, a, b),
       type)

Arguments

Value

A list with two elements:

results

A data frame containing the coordinates, observed values, BME predictions (posterior mean or mode), posterior variance (if type = "mean"), residuals, and fold indices.

metrics

A one-row data frame reporting the mean error (ME), mean absolute error (MAE), and root mean squared error (RMSE) from the cross-validation.

Examples

data("utsnowload")
ch <- utsnowload[2:10, c("latitude", "longitude")]
cs <- utsnowload[68:232, c("latitude", "longitude")]
zh <- utsnowload[2:10, c("hard")]
a <- utsnowload[68:232, c("lower")]
b <- utsnowload[68:232, c("upper")]
bme_cv(ch, cs, zh, a, b, model = "exp", nugget = 0.0953, sill = 0.3639,
       range = 1.0787, type = "mean")

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, ch, cs, zh, a, b,
            model, nugget, sill, range, nsmax = 5,
            nhmax = 5, n = 50, zk_range = extended_range(zh, a, b),
            type)

Arguments

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.

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")]
bme_predict(x, ch, cs, zh, a, b,
  model = "exp", nugget = 0.0953,
  sill = 0.3639, range = 1.0787, type = "mean"
)

California Snow Load Data

Description

A subset of data from the 7964 measurement locations included in the 2020 National Snow Load Study. This data is basically on reliability-targeted snow loads (RTSL) in the state of California.

Usage

casnowload

Format

A data frame with 346 rows and 8 columns.

STATION

Name of the snow measuring station

LATITUDE

Latitude coordinate position

LONGITUDE

Longitude coordinate position

ELEVATION

Elevation of the measring station (measured in meters)

RTSL

The hard data RTSL value

LOWER

The lower endpoint RTSL

UPPER

The upper endpoint RTSL

TYPE

Type of snow measurement, WESD is direct and SNWD is indirect measurement. Direct measurements are hard data and have the lower, upper and center values are the same. Indirect measurements have LOWER < RTSL < UPPER.

Source

https://www1.ncdc.noaa.gov/pub/data/ghcn/daily/

Computes an extended numeric range that includes all elements from three numeric vectors: x, y, z. The range is extended by 10\ range on both sides

Description

Computes an extended numeric range that includes all elements from three numeric vectors: x, y, z. The range is extended by 10\ range on both sides

Usage

extended_range(zh, a, b)

Posterior Density Estimation at a Single Location

Description

Computes the posterior and plots probability density function (PDF) at a single unobserved spatial location using the Bayesian Maximum Entropy (BME) framework. This function integrates both hard data (precise measurements) and soft data (interval or uncertain observations), together with a specified variogram model, to numerically estimate the posterior density across a range of possible values. Optionally displays a plot of the posterior density function for the specified location.

Usage

prob_zk(x, ch, cs, zh, a, b,
        model, nugget, sill, range, nsmax = 5,
        nhmax = 5, n = 50, zk_range = extended_range(zh, a, b),
        plot = FALSE)

Arguments

Value

Two elements:

data frame

A data frame with two columns: zk_i (assumed zk values) and prob_zk_i (corresponding posterior densities).

plot

An optional plot of posterior density of the estimation location.

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, "hard"]
a <- utsnowload[68:232, "lower"]
b <- utsnowload[68:232, "upper"]
prob_zk(x, ch, cs, zh, a, b, model = "exp", nugget = 0.0953, sill = 0.3639,
        range = 1.0787, plot = TRUE)

A detrended reliability-targeted design ground snow loads in Utah

Description

This dataset contains detrended reliability-targeted design ground snow load measurements from 232 locations in state of Utah. Of these, 65 sites report precise measurements, treated as hard data, while the remaining 167 sites report imprecise measurements, represented as interval (soft) data. The dataset is structured such that the first 67 rows contain hard (point) measurements, and the remaining rows represent soft data using lower and upper interval bounds. For a detailed explanation of the dataset and its use, refer to the related version described in Duah et al. (2025) doi:10.1016/j.spasta.2025.100894

Usage

utsnowload

Format

A data frame with 232 rows and 5 variables:

latitude

Latitude coordinate position

longitude

Longitude coordinate position

hard

The hard data value

lower

The lower endpoint of the soft-interval

upper

The upper endpoint of the soft-interval

Source

doi:10.1016/j.spasta.2025.100894