Deviance Information Criterion

Description

Calculates the Deviance Information Criterion (DIC) for comparisons of georamps model fits.

Usage

   ## S3 method for class 'ramps'
DIC(object, ...)

Arguments

Value

An numeric vector with the following two elements:

Author(s)

Brian Smith brian-j-smith@uiowa.edu

References

Spiegelhalter, D.J., Best, N.G., Carlin, B.P., and van der Linde, A. (2002) “Bayesian Measures of Model Complexity and Fit”, Journal of the Royal Statistical Society - Series B, 64, 583-639.

See Also

georamps

Examples

## DIC calculation for georamps example results

## Not run: 
DIC(NURE.fit)

## End(Not run)

Dataset of USGS NURE Uranium Measurements

Description

Connecticut, USA, areal and point-source uranium measurements from the United States Geological Survey (USGS) National Uranium Resource Evaluation (NURE) project.

Usage

data(NURE)

Format

The following variables are provided in the NURE data frame:

ppm

uranium measurements in parts per million.

measurement

type of measurement: 1 = areal, 2 = point-source.

lon

longitude coordinates of point-source measurements.

lat

latitude coordinates of point-source measurements.

easting

Universal Transverse Mercator easting coordinates - projected distances from the central meridian.

northing

Universal Transverse Mercator northing coordinates - projected distances from the equator.

county

counties from which measurements were taken.

area

county land mass areas in square miles.

id

unique identifiers for measured counties or sites.

A grid of coordinates is provided by the NURE.grid data frame to facilitate Monte Carlo integration in geostatistical modeling of areal measurements. The included columns are

lon

longitude coordinates of grid sites.

lat

latitude coordinates of grid sites.

id

county identifiers.

Areal measurements in NURE can be matched to the grid coordinates in NURE.grid via the shared "id" variable.

References

Duval, J.S., Jones, W.J., Riggle, F.R., and Pitkin, J.A. (1989) “Equivalent uranium map of conterminous United States”, USGS Open-File Report 89-478.

Smith, S.M.(2006) “National Geochemical Database Reformatted Data from the National Uranium Resource Evaluation (NURE) Hydrogeochemical and Stream Sediment Reconnaissance (HSSR) Program”, USGS Open-File Report 97-492.

Examples

data(NURE)

## Map areal and point-source measurements
ppm1 <- NURE$ppm[NURE$measurement == 1]
level <- (max(ppm1) - ppm1) / diff(range(ppm1))
map("county", "connecticut", fill = TRUE, col = gray(level))
title("Connecticut Uranium Measurements")
points(NURE$lon, NURE$lat)

## Map grid sites
map("county", "connecticut")
title("Regular Grid of Coordinates")
points(NURE.grid$lon, NURE.grid$lat)

Cauchy Spatial Correlation Structure

Description

This function is a constructor for the 'corRCauchy' class, representing a Cauchy (rational quadratic) spatial correlation structure. Letting r denote the range, the correlation between two observations a distance d apart is 1/(1+(d/r)^2).

Usage

   corRCauchy(value = numeric(0), form = ~ 1,
             metric = c("euclidean", "maximum", "manhattan", "haversine"),
             radius = 3956)

Arguments

Value

Object of class 'corRCauchy', also inheriting from class 'corRSpatial', representing a rational quadratic spatial correlation structure.

Note

When "haversine" is used as the distance metric, longitude and latitude coordinates must be given as the first and second covariates, respectively, in the formula specification for the form argument.

Author(s)

Brian Smith brian-j-smith@uiowa.edu and Jose Pinheiro Jose.Pinheiro@pharma.novartis.com, and Douglas Bates bates@stat.wisc.edu

References

Cressie, N.A.C. (1993), “Statistics for Spatial Data”, J. Wiley & Sons.

Venables, W.N. and Ripley, B.D. (1997) “Modern Applied Statistics with S-plus”, 2nd Edition, Springer-Verlag.

See Also

corRClasses

Examples

sp1 <- corRCauchy(form = ~ x + y + z)

spatDat <- data.frame(x = (0:4)/4, y = (0:4)/4)

cs1Cauchy <- corRCauchy(1, form = ~ x + y)
cs1Cauchy <- Initialize(cs1Cauchy, spatDat)
corMatrix(cs1Cauchy)

cs2Cauchy <- corRCauchy(1, form = ~ x + y, metric = "man")
cs2Cauchy <- Initialize(cs2Cauchy, spatDat)
corMatrix(cs2Cauchy)

Spatial Correlation Structure Classes

Description

Standard classes of spatial correlation structures available for the georamps function.

Spatial Structures:

corRCauchy

Cauchy correlation.

corRExp

exponential correlation.

corRExpwr

powered exponential correlation.

corRGaus

Gaussian correlation.

corRGneit

Gneiting approximation to Gaussian correlation.

corRLin

linear correlation.

corRMatern

Matern correlation.

corRSpher

spherical correlation.

corRWave

sine wave correlation.

Spatio-Temporal Structures:

corRExp2

exponential correlation.

corRExpwr2

powered exponential correlation.

Temporally Integrated Spatial Structure:

corRExpwr2Dt

powered exponential correlation.

Note

Users may define their own corRStruct classes by specifying a constructor function and, at a minimum, methods for the functions corMatrix and coef.

Author(s)

Brian Smith brian-j-smith@uiowa.edu and Jose Pinheiro Jose.Pinheiro@pharma.novartis.com, and Douglas Bates bates@stat.wisc.edu

See Also

corRCauchy, corRExp, corRExp2, corRExpwr, corRExpwr2, corRExpwr2Dt, corRGaus, corRGneit, corRLin, corRMatern, corRSpher corRWave

Exponential Spatial Correlation Structure

Description

This function is a constructor for the 'corRExp' class, representing an exponential spatial correlation structure. Letting r denote the range, the correlation between two observations a distance d apart is \exp(-d/r).

Usage

   corRExp(value = numeric(0), form = ~ 1,
           metric = c("euclidean", "maximum", "manhattan", "haversine"),
           radius = 3956)

Arguments

Value

Object of class 'corRExp', also inheriting from class 'corRSpatial', representing an exponential spatial correlation structure.

Note

When "haversine" is used as the distance metric, longitude and latitude coordinates must be given as the first and second covariates, respectively, in the formula specification for the form argument.

Author(s)

Brian Smith brian-j-smith@uiowa.edu and Jose Pinheiro Jose.Pinheiro@pharma.novartis.com, and Douglas Bates bates@stat.wisc.edu

References

Cressie, N.A.C. (1993), “Statistics for Spatial Data”, J. Wiley & Sons.

Venables, W.N. and Ripley, B.D. (1997) “Modern Applied Statistics with S-plus”, 2nd Edition, Springer-Verlag.

See Also

corRClasses

Examples

sp1 <- corRExp(form = ~ x + y + z)

spatDat <- data.frame(x = (0:4)/4, y = (0:4)/4)

cs1Exp <- corRExp(1, form = ~ x + y)
cs1Exp <- Initialize(cs1Exp, spatDat)
corMatrix(cs1Exp)

cs2Exp <- corRExp(1, form = ~ x + y, metric = "man")
cs2Exp <- Initialize(cs2Exp, spatDat)
corMatrix(cs2Exp)

Non-Separable Exponential Spatio-Temporal Correlation Structure

Description

This function is a constructor for the 'corRExp2' class, representing a non-separable spatial correlation structure. Letting rs denote the spatial range, rt the temporal range, and lambda the space-time interaction, the correlation between two observations a distance d apart in space and t in time is \exp(-d/rs - t/rt - \lambda (d/rs) (t/rt)).

Usage

   corRExp2(value = numeric(0), form = ~ 1,
            metric = c("euclidean", "maximum", "manhattan", "haversine"),
            radius = 3956)

Arguments

Value

Object of class 'corRExp2', inheriting from class 'corRSpatioTemporal', representing a non-separable spatial correlation structure.

Note

When "haversine" is used as the distance metric, longitude and latitude coordinates must be given as the first and second covariates, respectively, in the formula specification for the form argument.

Author(s)

Brian Smith brian-j-smith@uiowa.edu

References

Cressie, N. and Huang, H.-C. (1993) “Classes of Nonseperable, Spatio-Temporal Stationary Covariance Functions”, Journal of the American Statistical Association, 94, 1330-1340.

See Also

corRClasses

Examples

sp1 <- corRExp2(form = ~ x + y + t)

spatDat <- data.frame(x = (0:4)/4, y = (0:4)/4, t=(0:4)/4)

cs1Exp <- corRExp2(c(1, 1, 1), form = ~ x + y + t)
cs1Exp <- Initialize(cs1Exp, spatDat)
corMatrix(cs1Exp)

cs2Exp <- corRExp2(c(1, 1, 1), form = ~ x + y + t, metric = "man")
cs2Exp <- Initialize(cs2Exp, spatDat)
corMatrix(cs2Exp)

Powered Exponential Spatial Correlation Structure

Description

This function is a constructor for the 'corRExpwr' class, representing a powered exponential spatial correlation structure. Letting r denote the range and p the shape, the correlation between two observations a distance d apart is \exp(-(d/r)^p).

Usage

   corRExpwr(value = numeric(0), form = ~ 1,
             metric = c("euclidean", "maximum", "manhattan", "haversine"),
             radius = 3956)

Arguments

Value

Object of class 'corRExpwr', also inheriting from class 'corRSpatial', representing a powered exponential spatial correlation structure.

Note

When "haversine" is used as the distance metric, longitude and latitude coordinates must be given as the first and second covariates, respectively, in the formula specification for the form argument.

Author(s)

Brian Smith brian-j-smith@uiowa.edu

References

Cressie, N.A.C. (1993), “Statistics for Spatial Data”, J. Wiley & Sons.

Venables, W.N. and Ripley, B.D. (1997) “Modern Applied Statistics with S-plus”, 2nd Edition, Springer-Verlag.

See Also

corRClasses

Examples

sp1 <- corRExpwr(form = ~ x + y + z)

spatDat <- data.frame(x = (0:4)/4, y = (0:4)/4)

cs1Expwr <- corRExpwr(c(1, 1), form = ~ x + y)
cs1Expwr <- Initialize(cs1Expwr, spatDat)
corMatrix(cs1Expwr)

cs2Expwr <- corRExpwr(c(1, 1), form = ~ x + y, metric = "man")
cs2Expwr <- Initialize(cs2Expwr, spatDat)
corMatrix(cs2Expwr)

Non-Separable Powered Exponential Spatio-Temporal Correlation Structure

Description

This function is a constructor for the 'corRExpwr2' class, representing a non-separable spatial correlation structure. Letting rs denote the spatial range, ps the spatial shape, rt the temporal range, pt the temporal shape, and lambda the space-time interaction, the correlation between two observations a distance d apart in space and t in time is \exp(-(d/rs)^ps - (t/rt)^pt - \lambda (d/rs)^ps (t/rt)^pt).

Usage

   corRExpwr2(value = numeric(0), form = ~ 1,
              metric = c("euclidean", "maximum", "manhattan", "haversine"),
              radius = 3956)

Arguments

Value

Object of class 'corRExpwr2', inheriting from class 'corRSpatioTemporal', representing a non-separable spatial correlation structure.

Note

When "haversine" is used as the distance metric, longitude and latitude coordinates must be given as the first and second covariates, respectively, in the formula specification for the form argument.

Author(s)

Brian Smith brian-j-smith@uiowa.edu

References

Cressie, N. and Huang, H.-C. (1993) “Classes of Nonseperable, Spatio-Temporal Stationary Covariance Functions”, Journal of the American Statistical Association, 94, 1330-1340.

Gneiting, T. (2002) “Nonseparable, stationary covariance functions for space-time data”, Journal of the American Statistical Association, 97, 590-600.

See Also

corRClasses

Examples

sp1 <- corRExpwr2(form = ~ x + y + t)

spatDat <- data.frame(x = (0:4)/4, y = (0:4)/4, t=(0:4)/4)

cs1Expwr <- corRExpwr2(c(1, 1, 1, 1, 1), form = ~ x + y + t)
cs1Expwr <- Initialize(cs1Expwr, spatDat)
corMatrix(cs1Expwr)

cs2Expwr <- corRExpwr2(c(1, 1, 1, 1, 1), form = ~ x + y + t, metric = "man")
cs2Expwr <- Initialize(cs2Expwr, spatDat)
corMatrix(cs2Expwr)

Non-Separable Temporally Integrated Powered Exponential Spatial Correlation Structure

Description

This function is a constructor for the 'corRExpwr2Dt' class, representing a non-separable spatial correlation structure for temporally integrated measurements. Letting rs denote the spatial range, ps the spatial shape, rt the temporal range, and lambda the space-time interaction, the correlation between two observations a distance d apart in space and t in time is \exp(-(d/rs)^ps - t/rt - \lambda (d/rs)^ps (t/rt)).

Usage

   corRExpwr2Dt(value = numeric(0), form = ~ 1,
                metric = c("euclidean", "maximum", "manhattan", "haversine"),
                radius = 3956)

Arguments

Value

Object of class 'corRExpwr2Dt', also inheriting from class 'corRSpatial', representing a non-separable spatial correlation structure.

Note

When "haversine" is used as the distance metric, longitude and latitude coordinates must be given as the first and second covariates, respectively, in the formula specification for the form argument.

Author(s)

Brian Smith brian-j-smith@uiowa.edu

References

Cressie, N. and Huang, H.-C. (1993) “Classes of Nonseperable, Spatio-Temporal Stationary Covariance Functions”, Journal of the American Statistical Association, 94, 1330-1340.

Smith, B.J. and Oleson, J.J. (2007) “Geostatistical Hierarchical Model for Temporally Integrated Radon Measurements”, Jounal of Agricultural, Biological, and Environmental Statistics, in press.

See Also

corRClasses

Examples

sp1 <- corRExpwr2Dt(form = ~ x + y + t1 + t2)

spatDat <- data.frame(x = (0:4)/4, y = (0:4)/4, t1=(0:4)/4, t2=(1:5)/4)

cs1ExpwrDt <- corRExpwr2Dt(c(1, 1, 1, 1), form = ~ x + y + t1 + t2)
cs1ExpwrDt <- Initialize(cs1ExpwrDt, spatDat)
corMatrix(cs1ExpwrDt)

cs2ExpwrDt <- corRExpwr2Dt(c(1, 1, 1, 1), form = ~ x + y + t1 + t2, metric = "man")
cs2ExpwrDt <- Initialize(cs2ExpwrDt, spatDat)
corMatrix(cs2ExpwrDt)

Gaussian Spatial Correlation Structure

Description

This function is a constructor for the 'corRGaus' class, representing a Gaussian spatial correlation structure. Letting r denote the range, the correlation between two observations a distance d apart is \exp(-(d/r)^2).

Usage

   corRGaus(value = numeric(0), form = ~ 1,
            metric = c("euclidean", "maximum", "manhattan", "haversine"),
            radius = 3956)

Arguments

Value

Object of class 'corRGaus', also inheriting from class 'corRSpatial', representing a Gaussian spatial correlation structure.

Note

When "haversine" is used as the distance metric, longitude and latitude coordinates must be given as the first and second covariates, respectively, in the formula specification for the form argument.

Author(s)

Brian Smith brian-j-smith@uiowa.edu and Jose Pinheiro Jose.Pinheiro@pharma.novartis.com, and Douglas Bates bates@stat.wisc.edu

References

Cressie, N.A.C. (1993), “Statistics for Spatial Data”, J. Wiley & Sons.

Venables, W.N. and Ripley, B.D. (1997) “Modern Applied Statistics with S-plus”, 2nd Edition, Springer-Verlag.

See Also

corRClasses

Examples

sp1 <- corRGaus(form = ~ x + y + z)

spatDat <- data.frame(x = (0:4)/4, y = (0:4)/4)

cs1Gaus <- corRGaus(1, form = ~ x + y)
cs1Gaus <- Initialize(cs1Gaus, spatDat)
corMatrix(cs1Gaus)

cs2Gaus <- corRGaus(1, form = ~ x + y, metric = "man")
cs2Gaus <- Initialize(cs2Gaus, spatDat)
corMatrix(cs2Gaus)

Gneiting Spatial Correlation Structure

Description

This function is a constructor for the 'corRGneit' class, representing the Gneiting approximation to the Gaussian correlation structure. Letting r denote the range, the correlation between two observations a distance d < r / s apart is (1 + 8 s x + 25 (s x)^2 + 32 (s x)^3) (1 - s x)^8, where s = 0.301187465825. If d \geq r / s the correlation is zero.

Usage

   corRGneit(value = numeric(0), form = ~ 1,
             metric = c("euclidean", "maximum", "manhattan", "haversine"),
             radius = 3956)

Arguments

Value

Object of class 'corRGneit', also inheriting from class 'corRSpatial', representing the Gneiting spatial correlation structure.

Note

When "haversine" is used as the distance metric, longitude and latitude coordinates must be given as the first and second covariates, respectively, in the formula specification for the form argument.

Author(s)

Brian Smith brian-j-smith@uiowa.edu

References

Gneiting, T. (1999), “Correlation Functions for Atmospheric Data Analysis”, Quarterly Journal of the Royal Meteorological Society, 125(559), 2449-2464.

Venables, W.N. and Ripley, B.D. (1997) “Modern Applied Statistics with S-plus”, 2nd Edition, Springer-Verlag.

See Also

corRClasses

Examples

sp1 <- corRGneit(form = ~ x + y + z)

spatDat <- data.frame(x = (0:4)/4, y = (0:4)/4)

cs1Gneit <- corRGneit(1, form = ~ x + y)
cs1Gneit <- Initialize(cs1Gneit, spatDat)
corMatrix(cs1Gneit)

cs2Gneit <- corRGneit(1, form = ~ x + y, metric = "man")
cs2Gneit <- Initialize(cs2Gneit, spatDat)
corMatrix(cs2Gneit)

Linear Spatial Correlation Structure

Description

This function is a constructor for the 'corRLin' class, representing a linear spatial correlation structure. Letting r denote the range, the correlation between two observations a distance d < r apart is 1-(d/r). If d \geq r the correlation is zero.

Usage

   corRLin(value = numeric(0), form = ~ 1,
           metric = c("euclidean", "maximum", "manhattan", "haversine"),
           radius = 3956)

Arguments

Value

Object of class 'corRLin', also inheriting from class 'corRSpatial', representing a linear spatial correlation structure.

Note

When "haversine" is used as the distance metric, longitude and latitude coordinates must be given as the first and second covariates, respectively, in the formula specification for the form argument.

Author(s)

Brian Smith brian-j-smith@uiowa.edu and Jose Pinheiro Jose.Pinheiro@pharma.novartis.com, and Douglas Bates bates@stat.wisc.edu

References

Cressie, N.A.C. (1993), “Statistics for Spatial Data”, J. Wiley & Sons.

Venables, W.N. and Ripley, B.D. (1997) “Modern Applied Statistics with S-plus”, 2nd Edition, Springer-Verlag.

See Also

corRClasses

Examples

sp1 <- corRLin(form = ~ x + y + z)

spatDat <- data.frame(x = (0:4)/4, y = (0:4)/4)

cs1Lin <- corRLin(1, form = ~ x + y)
cs1Lin <- Initialize(cs1Lin, spatDat)
corMatrix(cs1Lin)

cs2Lin <- corRLin(1, form = ~ x + y, metric = "man")
cs2Lin <- Initialize(cs2Lin, spatDat)
corMatrix(cs2Lin)

Matern Spatial Correlation Structure

Description

This function is a constructor for the 'corRMatern' class, representing a Matern spatial correlation structure. Letting r denote the range, and s the scale, the correlation between two observations a distance d apart is 1/(2^{s-1} \Gamma(s)) (d/r)^s K_s(d/r).

Usage

   corRMatern(value = numeric(0), form = ~ 1,
              metric = c("euclidean", "maximum", "manhattan", "haversine"),
              radius = 3956)

Arguments

Value

Object of class 'corRMatern', also inheriting from class 'corRSpatial', representing a Matern spatial correlation structure.

Note

When "haversine" is used as the distance metric, longitude and latitude coordinates must be given as the first and second covariates, respectively, in the formula specification for the form argument.

Author(s)

Brian Smith brian-j-smith@uiowa.edu

References

Cressie, N.A.C. (1993), “Statistics for Spatial Data”, J. Wiley & Sons.

Venables, W.N. and Ripley, B.D. (1997) “Modern Applied Statistics with S-plus”, 2nd Edition, Springer-Verlag.

See Also

corRClasses

Examples

sp1 <- corRMatern(form = ~ x + y + z)

spatDat <- data.frame(x = (0:4)/4, y = (0:4)/4)

cs1Matern <- corRMatern(c(1, 1), form = ~ x + y)
cs1Matern <- Initialize(cs1Matern, spatDat)
corMatrix(cs1Matern)

cs2Matern <- corRMatern(c(1, 1), form = ~ x + y, metric = "man")
cs2Matern <- Initialize(cs2Matern, spatDat)
corMatrix(cs2Matern)

Spherical Spatial Correlation Structure

Description

This function is a constructor for the 'corRSpher' class, representing a spherical spatial correlation structure. Letting r denote the range, the correlation between two observations a distance d < r apart is 1-1.5(d/r)+0.5(d/r)^3. If d \geq r the correlation is zero.

Usage

   corRSpher(value = numeric(0), form = ~ 1,
             metric = c("euclidean", "maximum", "manhattan", "haversine"),
             radius = 3956)

Arguments

Value

An object of class 'corRSpher', also inheriting from class 'corRSpatial', representing a spherical spatial correlation structure.

Note

When "haversine" is used as the distance metric, longitude and latitude coordinates must be given as the first and second covariates, respectively, in the formula specification for the form argument.

Author(s)

Jose Pinheiro Jose.Pinheiro@pharma.novartis.com, Douglas Bates bates@stat.wisc.edu, and Brian Smith brian-j-smith@uiowa.edu

References

Cressie, N.A.C. (1993), “Statistics for Spatial Data”, J. Wiley & Sons.

Venables, W.N. and Ripley, B.D. (1997) “Modern Applied Statistics with S-plus”, 2nd Edition, Springer-Verlag.

See Also

corRClasses

Examples

sp1 <- corRSpher(form = ~ x + y + z)

spatDat <- data.frame(x = (0:4)/4, y = (0:4)/4)

cs1Spher <- corRSpher(1, form = ~ x + y)
cs1Spher <- Initialize(cs1Spher, spatDat)
corMatrix(cs1Spher)

cs2Spher <- corRSpher(1, form = ~ x + y, metric = "man")
cs2Spher <- Initialize(cs2Spher, spatDat)
corMatrix(cs2Spher)

Sine Wave Spatial Correlation Structure

Description

This function is a constructor for the 'corRWave' class, representing a sine wave spatial correlation structure. Letting r denote the range, the correlation between two observations a distance d apart is \sin(d/r)/(d/r).

Usage

   corRWave(value = numeric(0), form = ~ 1,
            metric = c("euclidean", "maximum", "manhattan", "haversine"),
            radius = 3956)

Arguments

Value

Object of class 'corRWave', also inheriting from class 'corRSpatial', representing a sine wave spatial correlation structure.

Note

When "haversine" is used as the distance metric, longitude and latitude coordinates must be given as the first and second covariates, respectively, in the formula specification for the form argument.

Author(s)

Brian Smith brian-j-smith@uiowa.edu

References

Cressie, N.A.C. (1993), “Statistics for Spatial Data”, J. Wiley & Sons.

Venables, W.N. and Ripley, B.D. (1997) “Modern Applied Statistics with S-plus”, 2nd Edition, Springer-Verlag.

See Also

corRClasses

Examples

sp1 <- corRWave(form = ~ x + y + z)

spatDat <- data.frame(x = (0:4)/4, y = (0:4)/4)

cs1Wave <- corRWave(1, form = ~ x + y)
cs1Wave <- Initialize(cs1Wave, spatDat)
corMatrix(cs1Wave)

cs2Wave <- corRWave(1, form = ~ x + y, metric = "man")
cs2Wave <- Initialize(cs2Wave, spatDat)
corMatrix(cs2Wave)

Expand MCMC Samples for georamps Model Fits

Description

Generates additional posterior samples for georamps model fits by restarting the MCMC sampler at the last set of sampled parameter values.

Usage

   expand.chain(object, n)

Arguments

Value

'ramps' object containing the previously and newly sampled parameter values.

Author(s)

Brian Smith brian-j-smith@uiowa.edu

See Also

georamps

Examples

## Generate 25 additional samples for the georamps example

## Not run: 
fit <- expand.chain(NURE.fit, 25)

## End(Not run)

Generating a Grid over a US State

Description

This function generate a grid of points over a US state with given increment size or resolution.

Usage

   genUSStateGrid(state, incr = NULL, resolution = NULL)

Arguments

Value

A data.frame:

Author(s)

Jun Yan jun.yan@uconn.edu

See Also

genUSStateSites

Examples

mygrid <- genUSStateGrid('iowa', resolution=c(8, 4))
map('state', 'iowa')
points(mygrid)

Generating Random Sites in a US State

Description

A completely spatial random set of point is generated for a US state.

Usage

   genUSStateSites(state, nsites)

Arguments

Value

A matrix of longitude and latitude....

See Also

genUSStateGrid

Bayesian Geostatistical Model Fitting with RAMPS

Description

General function for fitting Bayesian geostatistical models using the reparameterized and marginalized posterior sampling (RAMPS) algorithm of Yan et al. (2007).

Usage

   georamps(fixed, random, correlation, data, subset, weights,
            variance = list(fixed = ~ 1, random = ~ 1, spatial = ~ 1),
            aggregate = list(grid = NULL, blockid = ""), kmat = NULL,
            control = ramps.control(...), contrasts = NULL, ...)

Arguments

Value

An object of class 'ramps' containing the following elements:

Author(s)

Brian Smith brian-j-smith@uiowa.edu, Jun Yan jun.yan@uconn.edu, and Kate Cowles kate-cowles@uiowa.edu

References

Yan, J., Cowles, M.K., Wang, S., and Armstrong, M. (2007) “Parallelizing MCMC for Bayesian Spatiotemporal Geostatistical Models”, Statistics and Computing, 17(4), 323-335.

Smith, B. J., Yan, J., and Cowles, M. K. (2008) “Unified Geostatistical Modeling for Data Fusion and Spatial Heteroskedasticity with R Package ramps”, Journal of Statistical Software, 25(10), 1-21.

See Also

corRClasses, ramps.control, mcmc, DIC.ramps, plot.ramps, predict.ramps, summary.ramps, window.ramps

Examples

## Not run: 
## Load the included uranium datasets for use in this example
data(NURE)

## Geostatistical analysis of areal measurements
NURE.ctrl1 <- ramps.control(
   iter = 25,
   beta = param(0, "flat"),
   sigma2.e = param(1, "invgamma", shape = 2.0, scale = 0.1, tuning = 0.75),
   phi = param(10, "uniform", min = 0, max = 35, tuning = 0.50),
   sigma2.z = param(1, "invgamma", shape = 2.0, scale = 0.1)
)

NURE.fit1 <- georamps(log(ppm) ~ 1,
   correlation = corRExp(form = ~ lon + lat, metric = "haversine"),
   weights = area,
   data = NURE,
   subset = (measurement == 1),
   aggregate = list(grid = NURE.grid, blockid = "id"),
   control = NURE.ctrl1
)
print(NURE.fit1)
summary(NURE.fit1)


## Analysis of point-source measurements
NURE.ctrl2 <- ramps.control(
   iter = 25,
   beta = param(0, "flat"),
   sigma2.e = param(1, "invgamma", shape = 2.0, scale = 0.1, tuning = 0.75),
   phi = param(10, "uniform", min = 0, max = 35, tuning = 0.5),
   sigma2.z = param(1, "invgamma", shape = 2.0, scale = 0.1)
)

NURE.fit2 <- georamps(log(ppm) ~ 1,
   correlation = corRExp(form = ~ lon + lat, metric = "haversine"),
   data = NURE,
   subset = (measurement == 2),
   control = NURE.ctrl2
)
print(NURE.fit2)
summary(NURE.fit2)


## Joint analysis of areal and point-source measurements with
## prediction only at grid sites
NURE.ctrl <- ramps.control(
   iter = 25,
   beta = param(rep(0, 2), "flat"),
   sigma2.e = param(rep(1, 2), "invgamma", shape = 2.0, scale = 0.1, tuning = 0.75),
   phi = param(10, "uniform", min = 0, max = 35, tuning = 0.5),
   sigma2.z = param(1, "invgamma", shape = 2.0, scale = 0.1),
   z.monitor = NURE.grid
)

NURE.fit <- georamps(log(ppm) ~ factor(measurement) - 1,
   correlation = corRExp(form = ~ lon + lat, metric = "haversine"),
   variance = list(fixed = ~ measurement),
   weights = area * (measurement == 1) + (measurement == 2),
   data = NURE,
   aggregate = list(grid = NURE.grid, blockid = "id"),
   control = NURE.ctrl
)
print(NURE.fit)
summary(NURE.fit)


## Discard initial 5 MCMC samples as a burn-in sequence
fit <- window(NURE.fit, iter = 6:25)
print(fit)
summary(fit)

## Deviance Information Criterion
DIC(fit)

## Prediction at unmeasured sites
ct <- map("state", "connecticut", plot = FALSE)
lon <- seq(min(ct$x, na.rm = TRUE), max(ct$x, na.rm = TRUE), length = 20)
lat <- seq(min(ct$y, na.rm = TRUE), max(ct$y, na.rm = TRUE), length = 15)
grid <- expand.grid(lon, lat)

newsites <- data.frame(lon = grid[,1], lat = grid[,2],
                       measurement = 1)
pred <- predict(fit, newsites)

plot(pred, func = function(x) exp(mean(x)),
     database = "state", regions = "connecticut",
     resolution = c(200, 150), bw = 5,
     main = "Posterior Mean",
     legend.args = list(text = "ppm", side = 3, line = 1))

plot(pred, func = function(x) exp(sd(x)),
     database = "state", regions = "connecticut",
     resolution = c(200, 150), bw = 5,
     main = "Posterior Standard Deviation",
     legend.args = list(text = "ppm", side = 3, line = 1))

## End(Not run)

Initialization of georamps Model Parameters

Description

Function used in conjunction with ramps.control to specify the initial values and prior distributions used in calls to georamps.

Usage

   param(init, prior = c("flat", "invgamma", "normal", "uniform", "user"), tuning,
         ...)

Arguments

Details

The supported prior distributions and associated hyperparameters are:

"flat"

Flat prior with no hyperparameters.

"invgamma"

Inverse-gamma with hyperparameters shape > 0 and scale > 0 such that f(x) = scale^{shape} / \Gamma(shape) x^{-shape - 1} \exp(-scale / x).

"normal"

Normal with hyperparameters mean and variance such that f(x) = (2 \pi)^{-n/2} |\Sigma|^{-1/2} \exp(-1/2 (x - \mu)' \Sigma^{-1} (x - \mu)). The variance hyperparameter must be positive definite and may be supplied either as a vector (independence) or a matrix.

"uniform"

Uniform with hyperparameters min and max > min such that f(x) = 1 / (max - min).

"user"

Use-defined function supplied as hyperparameter f which takes a single numeric vector of length and order equal to the associated model parameters and whose returns values are proportional to the prior distribution.

The number of model parameters to be initialized is determined by length(init). Missing values occurring in the supplied init vector will be replaced with draws from the prior distribution, for all but the "flat" specification.

Value

A list of class 'param' containing the following components:

Author(s)

Brian Smith brian-j-smith@uiowa.edu

See Also

georamps, ramps.control

Examples

## Initial values for a flat prior
param(rep(0, 2), "flat")

## Random generation of initial values for an inverse-gamma prior
param(rep(NA, 2), "invgamma", shape = 2.0, scale = 0.1)

## Independent normal priors
param(rep(0, 2), "normal", mean = c(0, 0), variance = c(100, 100))

## Correlated normal priors
npv <- rbind(c(100, 25), c(25, 100))
param(rep(0, 2), "normal", mean = c(0, 0), variance = npv)

## Uniform prior and MCMC tuning parameter specification
param(10, "uniform", min = 0, max = 100, tuning = 0.5)

Posterior Spatial Distribution Plots

Description

Creates surface maps of posterior spatial distributions from georamps or predict.ramps.

Usage

   ## S3 method for class 'ramps'
plot(x, type = c("i", "c", "w"), col = tim.colors(64), func = mean,
        sites = FALSE, database = NULL, regions = ".", resolution = c(64, 64),
        bw = 1, ...)

   ## S3 method for class 'predict.ramps'
plot(x, type = c("i", "c", "w"), col = tim.colors(64), func = mean,
        database = NULL, regions = ".", resolution = c(64, 64), bw = 1, ...)

Arguments

Author(s)

Brian Smith brian-j-smith@uiowa.edu

See Also

georamps predict.ramps contour drape.plot image image.plot map

Examples

## Surface maps of the georamps example results

## Not run: 
plot(NURE.fit, database = "state", regions = "connecticut",
     resolution = c(200, 150), bw = 5,
     main = "Spatial Process Posterior Mean")

## End(Not run)

Prediction Method for georamps Model Fits

Description

Obtains prediction of main effects plus spatial variability from a georamps model fit.

Usage

   ## S3 method for class 'ramps'
predict(object, newdata, type = c("response", "spatial", "error", "random"), ...)

Arguments

Details

Prediction will be performed only at the coordinates in newdata that differ from those used in the initial georamps model fitting. In particular, overlapping coordinates will be excluded automatically in the prediction.

Value

'predict.ramps' object, inheriting from class 'matrix', of samples from the posterior predictive distribution. Labels for the samples at each new coordinate are supplied in the returned column names and MCMC iteration numbers in the row names. A matrix containing the new coordinates is supplied in the coords attribute of the object.

Author(s)

Brian Smith brian-j-smith@uiowa.edu

See Also

georamps plot.predict.ramps, window.predict.ramps,

Examples

## Prediction for georamps example results

## Not run: 
ct <- map("state", "connecticut", plot = FALSE)
lon <- seq(min(ct$x, na.rm = TRUE), max(ct$x, na.rm = TRUE), length = 20)
lat <- seq(min(ct$y, na.rm = TRUE), max(ct$y, na.rm = TRUE), length = 15)
grid <- expand.grid(lon, lat)

newsites <- data.frame(lon = grid[,1], lat = grid[,2],
                       measurement = 1)
NURE.pred <- predict(NURE.fit, newsites)

par(mfrow=c(2,1))
plot(NURE.pred, func = function(x) exp(mean(x)),
     database = "state", regions = "connecticut",
     resolution = c(200, 150), bw = 5,
     main = "Posterior Mean",
     legend.args = list(text = "ppm", side = 3, line = 1))
plot(NURE.pred, func = function(x) exp(sd(x)),
     database = "state", regions = "connecticut",
     resolution = c(200, 150), bw = 5,
     main = "Posterior Standard Deviation",
     legend.args = list(text = "ppm", side = 3, line = 1))

## End(Not run)

Auxiliary for Controlling georamps Model Fitting

Description

Auxiliary function that provides a user interface to control the georamps model fitting algorithm.

Usage

   ramps.control(iter = 1000, beta, sigma2.e, phi, sigma2.z, sigma2.re,
                 z.monitor = TRUE, mpdfun = c("mpdbeta", "mpdbetaz"), file)

Arguments

Details

Tuning parameters may be set for the sigma2 and phi arguments via the param function. If a user-defined prior is specified, then tuning parameters must be supplied and are taken to be the initial widths of the slice sampling windows. Otherwise, tuning parameters are taken to be factors by which the initial widths are multiplied. Separate tuning parameters may be set for each of the arguments. However, only the minimum of all sigma2 tuning parameters is used in the sampling of those parameters.

Value

A list containing the following components:

Author(s)

Brian Smith brian-j-smith@uiowa.edu

See Also

georamps, param

Examples

ctrl <- ramps.control(
   iter = seq(1, 100, by = 2),
   beta = param(rep(0, 2), "flat"),
   sigma2.e = param(rep(1, 2), "invgamma", shape = 2.0, scale = 0.1),
   phi = param(10, "uniform", min = 0, max = 100, tuning = 0.5),
   sigma2.z = param(1, "invgamma", shape = 2.0, scale = 0.1),
   file = c("params.txt", "z.txt")
)

Dataset of Simulated Measurements from JSS Publication

Description

Simulated Iowa, USA, areal and point-source measurements analyzed in the Working Example of the ramps package paper published in Journal of Statistical Software.

Usage

data(simJSS)

Format

The following variables are provided in the simIowa data frame:

areal

type of measurement: 1 = areal, 0 = point-source.

y

simulated measurement.

id

unique identifiers for measurements.

siteId

unique identifiers for point-source measurement sites.

lon

longitude coordinates of point-source measurements.

lat

latitude coordinates of point-source measurements.

weights

number of sites per measurement.

A grid of coordinates is provided by the simGrid data frame to facilitate Monte Carlo integration in geostatistical modeling of areal measurements. The included columns are

lon

longitude coordinates of grid sites.

lat

latitude coordinates of grid sites.

id

county identifiers.

county

county names.

Areal measurements in simIowa can be matched to the grid coordinates in simGrid via the shared "id" variable.

Details

Areal and point-source observations were generated from from a geostatistical model using the county structure in the state of Iowa, USA. There are 99 counties in the state. Areal observations were generated from each as county averages from a uniform grid of 391 sites - approximately 4 sites per county. An additional 600 point-source observations were generated from a set of 300 unique sites sampled from a uniform distribution in Iowa.

An exponential correlation structure with a range parameter of 10 was used for the underlying Gaussian spatial structure. Measurement errors were generated with variances of 0.25 for point-source data and 0.09 for areal data. Site-specific non-spatial random effects were generated with a variance 0.16. One fixed effects covariate with coefficient equal to 0.5 was included as an indicator for areal observations.

References

Smith, B. J., Yan, J., and Cowles, M. K. (2008) “Unified Geostatistical Modeling for Data Fusion and Spatial Heteroskedasticity with R Package ramps”, Journal of Statistical Software, 25(10), 1-21.

Examples

data(simJSS)

## Map areal and point-source measurements
y <- simIowa$y[simIowa$areal == 1]
level <- (max(y) - y) / diff(range(y))
map("county", "iowa", fill = TRUE, col = gray(level))
title("Simulated Iowa Measurements")
points(simIowa$lon, simIowa$lat)

## Map grid sites
map("county", "iowa")
title("Regular Grid of Coordinates")
points(simGrid$lon, simGrid$lat)

Posterior Summaries of georamps Model Fits

Description

Posterior summaries of georamps model parameters.

Usage

   ## S3 method for class 'ramps'
summary(object, ...)

Arguments

Value

Two sets of summary statistics for each model parameter. Sample mean, standard deviation, naive standard error of the mean, and time-series-based standard error are included in the first set. Quantiles are included in the second.

Author(s)

Brian Smith brian-j-smith@uiowa.edu

See Also

georamps summary.mcmc

Examples

## Posterior summaries for georamps example results

## Not run: 
summary(NURE.fit)

## End(Not run)

Subsetting of MCMC Sampler Results

Description

Post-processing function to subset the MCMC iterations in georamps or predict.ramps results.

Usage

   ## S3 method for class 'ramps'
window(x, iter, ...)

   ## S3 method for class 'predict.ramps'
window(x, iter, ...)

Arguments

Value

Subsetted object of the same class as the one supplied.

Author(s)

Brian Smith brian-j-smith@uiowa.edu

See Also

georamps predict.ramps

Examples

## Exclude first five iterations of the georamps example results

## Not run: 
fit <- window(NURE.fit, iter = 6:25)
print(fit)
summary(fit)

## End(Not run)