Package 'anomalous'

Title: Anomaly Detection using the CAPA and PELT Algorithms
Description: Implimentations of the univariate CAPA <doi:10.1002/sam.11586> and PELT <doi:10.1080/01621459.2012.737745> algotithms along with various cost functions for different distributions and models. The modular design, using R6 classes, favour ease of extension (for example user written cost functions) over the performance of other implimentations (e.g. <doi:10.32614/CRAN.package.changepoint>, <doi:10.32614/CRAN.package.anomaly>).
Authors: Paul Smith [aut, cre]
Maintainer: Paul Smith <[email protected]>
License: GPL-3
Version: 0.0.4.2
Built: 2024-12-13 13:46:58 UTC
Source: https://github.com/waternumbers/anomalous

Help Index

An R implimentation of the segmented search algorithmpelt algorithm

Description

An R implimentation of the segmented search algorithmpelt algorithm

Usage

capa(part, fCost, prune = TRUE, verbose = FALSE)

Arguments

part

the starting partition
fCost

the cost function
prune

logical, should pruning be used
verbose

logical, print out progress

Details

Basic R implimentation of pelt - not efficent

Value

the optimal partition

R6 class for the categorical distribution

Description

Cost functions for the multinomial distribution

Details

Collective anomalies are represented as chnages to the expected proportions. Time varying expected proportions are currently not handled.

Methods

Public methods

Method length()

Get the length of time series

Usage
categoricalCost$length()

Method new()

Initialise the cost function

Usage
categoricalCost$new(x, m = rep(1/ncol(x), ncol(x)))
Arguments
x

integer matrix of observations of 0,1

m

numeric vector of expected proportions ## need to check row sums are 1 - possibly just use multinomial??

Method baseCost()

Compute the non-anomalous cost of a segment

Usage
categoricalCost$baseCost(a, b, pen = 0)
Arguments
a

start of period

b

end of period

pen

penalty cost

Method pointCost()

Compute the point anomaly cost of a time step

Usage
categoricalCost$pointCost(b, pen)
Arguments
b

time step

pen

penalty cost

Method collectiveCost()

Compute the anomalous cost of a segment

Usage
categoricalCost$collectiveCost(a, b, pen, len)
Arguments
a

start of period

b

end of period

pen

penalty cost

len

minimum number of observations

Method param()

Compute parameters of a segment if anomalous

Usage
categoricalCost$param(a, b)
Arguments
a

start of period

b

end of period

Method clone()

The objects of this class are cloneable with this method.

Usage
categoricalCost$clone(deep = FALSE)
Arguments
deep

Whether to make a deep clone.

Examples

set.seed(0)
m <- c(1:4)/sum(1:4)
X <- t(rmultinom(100, 1, m))

p <- categoricalCost$new(X,m)
p$baseCost(90,95) ## cost of non-anomalous distribution for x[90:95]
p$pointCost(90,0) ## point anomaly cost for x[90] with 0 penalty
## collective anomaly cost for x[90:95] with penalty of 57 and at least 3 observation
p$collectiveCost(90,95,57,3)

Coefficent method for an amomalous_partition

Description

Generates coefficents for the anomalous periods in an object with class amomalous_partition

Usage

## S3 method for class 'anomalous_partition'
coef(object, ...)

Arguments

object

the anomalous_partition
...

optional parameters see details

Details

Generates coefficents for all anomalous periods. Required input cost is a cost function. Optional input t is the time of the partitioning solution to use.

Value

A matrix of parameters whose rows correspond to the rows in the summary output

Method for extracting collective anomalies

Description

Extracts the collective anomaly summaries from the object

Usage

collective_anomalies(p, t)

Arguments

p

object, such as a partition, from which to extract the point anomalies
t

the end time at which the partition is based

An implimentation of the CROPS algorithm in 1D

Description

An implimentation of the CROPS algorithm in 1D

Usage

crops(
  betaMin,
  betaMax,
  fCost,
  alg = pelt,
  betaP = Inf,
  min_length = 2,
  prune = TRUE,
  verbose = FALSE,
  maxIter = 100
)

Arguments

betaMin

lower bound of penalisation window
betaMax

upper bound of penalisation window
fCost

the cost function
alg

algorithm either capa of pelt
betaP

penalty for adding a point anomaly - only for use with capa
min_length

minimum number of values in a collective anomaly
prune

logical, should pruning be used
verbose

logical, print out progress
maxIter

maximum number of algorithm evaluations to perform

Details

This will only work for cost functions where the beta is additive!!!

Value

something...

R6 class for Univariate Gaussian Cost Functions

Description

Cost functions for differening types of univariate gaussion anomalies

Arguments

x

numeric vector or matrix of observations (see details)
m

numeric vector of mean values
s

numeric vector of standard deviation values
point_type

representation of point anomalies as either a change in mean or variance
a

start of period
b

end of period
pen

penalty cost
len

minimum number of obseervations

Details

Collective anomalies are represented either as changes in mean (gaussMean), variance (gaussVar) or mean and variance (gaussMeanvar). See vignettes for details. If x is a matrix then the values in each row are treated as IID replicate observations.

Methods

Public methods

Method length()

Get the length of time series

Usage
gaussCost$length()

Method new()

Initialise the cost function

Usage
gaussCost$new(x, m = 0, s = 1, point_type = c("var", "mean"))
Arguments
x

numeric vector of observations

m

numeric vector of mean values

s

numeric vector of standard deviation values

point_type

representation of point anomalies as either a change in mean or variance

Method baseCost()

Compute the non-anomalous cost of a segment

Usage
gaussCost$baseCost(a, b, pen = 0)
Arguments
a

start of period

b

end of period

pen

penalty cost

Method pointCost()

Compute the point anomaly cost of a time step

Usage
gaussCost$pointCost(b, pen)
Arguments
b

time step

pen

penalty cost

Method clone()

The objects of this class are cloneable with this method.

Usage
gaussCost$clone(deep = FALSE)
Arguments
deep

Whether to make a deep clone.

Super class

anomalous::gaussCost -> gaussMean

Methods

Public methods

Inherited methods

Method collectiveCost()

Compute the anomalous cost of a segment

Usage
gaussMean$collectiveCost(a, b, pen, len)
Arguments
a

start of period

b

end of period

pen

penalty cost

len

minimum number of observations

Method param()

Compute parameters of a segment if anomalous

Usage
gaussMean$param(a, b)
Arguments
a

start of period

b

end of period

Method clone()

The objects of this class are cloneable with this method.

Usage
gaussMean$clone(deep = FALSE)
Arguments
deep

Whether to make a deep clone.

Super class

anomalous::gaussCost -> gaussVar

Methods

Public methods

Inherited methods

Method collectiveCost()

Compute the anomalous cost of a segment

Usage
gaussVar$collectiveCost(a, b, pen, len)
Arguments
a

start of period

b

end of period

pen

penalty cost

len

minimum number of observations

Method param()

Compute parameters of a segment if anomalous

Usage
gaussVar$param(a, b)
Arguments
a

start of period

b

end of period

Method clone()

The objects of this class are cloneable with this method.

Usage
gaussVar$clone(deep = FALSE)
Arguments
deep

Whether to make a deep clone.

Super class

anomalous::gaussCost -> gaussMeanVar

Methods

Public methods

Inherited methods

Method collectiveCost()

Compute the non-anomalous cost of a segment

Usage
gaussMeanVar$collectiveCost(a, b, pen, len)
Arguments
a

start of period

b

end of period

pen

penalty cost

len

minimum number of observations

Method param()

Compute parameters of a segment if anomalous

Usage
gaussMeanVar$param(a, b)
Arguments
a

start of period

b

end of period

Method clone()

The objects of this class are cloneable with this method.

Usage
gaussMeanVar$clone(deep = FALSE)
Arguments
deep

Whether to make a deep clone.

Examples

set.seed(0)
m <- runif(100)
s <- pmax(1e-4,runif(100))
x <- rnorm(100,m,s) ## example data

gM <- gaussMean$new(x,m,s) ## anomalies are changes in mean
gM$baseCost(90,95) ## cost of non-anomalous distribution for x[90:95]
gM$pointCost(90,0) ## point anomaly cost for x[90] with 0 penalty
## collective anomaly cost for x[90:95] with penalty of 57 and at least 3 observation
gM$collectiveCost(90,95,57,3)

gV <- gaussVar$new(x,m,s) ## anomalies are changes in variance
gV$baseCost(90,95) ## cost of non-anomalous distribution for x[90:95]
gV$pointCost(90,0) ## point anomaly cost for x[90] with 0 penalty
## collective anomaly cost for x[90:95] with penalty of 57 and at least 3 observation
gV$collectiveCost(90,95,57,3)

gMV <- gaussMeanVar$new(x,m,s) ## anomalies are changes in mean and variance
gMV$baseCost(90,95) ## cost of non-anomalous distribution for x[90:95]
gMV$pointCost(90,0) ## point anomaly cost for x[90] with 0 penalty
## collective anomaly cost for x[90:95] with penalty of 57 and at least 3 observation
gMV$collectiveCost(90,95,57,3)

R6 class for Univariate Gaussian Cost Functions

Description

Cost functions for differening types of univariate gaussion anomalies

Details

Collective anomalies are represented either as changes in parameters describing the mean (gaussRegMean), variance (gaussRegVar) or mean and variance (gaussRegMeanVar). Changes in variance are represented as a scaling parameter, not changes to the covariance. See vignettes for details.

Each element of the input x should be a list containing a vector of observations y and corresponding design matrix X. Optionally in can also include a vector of parameter m and covariance matrix S.

Methods

Public methods

Method length()

Get the length of time series

Usage
gaussRegCost$length()

Method new()

Initialise the cost function

Usage
gaussRegCost$new(x, non_neg = FALSE)
Arguments
x

a list of regressions (see details)

non_neg

should only non-negative paraemter solutions be considered

Method baseCost()

Compute the non-anomalous cost of a segment

Usage
gaussRegCost$baseCost(a, b, pen = 0)
Arguments
a

start of period

b

end of period

pen

penalty cost

Method pointCost()

Compute the point anomaly cost of a time step

Usage
gaussRegCost$pointCost(b, pen)
Arguments
b

time step

pen

penalty cost

Method clone()

The objects of this class are cloneable with this method.

Usage
gaussRegCost$clone(deep = FALSE)
Arguments
deep

Whether to make a deep clone.

Super class

anomalous::gaussRegCost -> gaussRegMean

Methods

Public methods

Inherited methods

Method collectiveCost()

Compute the anomalous cost of a segment

Usage
gaussRegMean$collectiveCost(a, b, pen, len)
Arguments
a

start of period

b

end of period

pen

penalty cost

len

minimum number of observations

Method param()

Compute parameters of a segment if anomalous

Usage
gaussRegMean$param(a, b)
Arguments
a

start of period

b

end of period

Method clone()

The objects of this class are cloneable with this method.

Usage
gaussRegMean$clone(deep = FALSE)
Arguments
deep

Whether to make a deep clone.

Super class

anomalous::gaussRegCost -> gaussRegVar

Methods

Public methods

Inherited methods

Method collectiveCost()

Compute the anomalous cost of a segment

Usage
gaussRegVar$collectiveCost(a, b, pen, len)
Arguments
a

start of period

b

end of period

pen

penalty cost

len

minimum number of observations

Method param()

Compute parameters of a segment if anomalous

Usage
gaussRegVar$param(a, b)
Arguments
a

start of period

b

end of period

Method clone()

The objects of this class are cloneable with this method.

Usage
gaussRegVar$clone(deep = FALSE)
Arguments
deep

Whether to make a deep clone.

Super class

anomalous::gaussRegCost -> gaussRegMeanVar

Methods

Public methods

Inherited methods

Method collectiveCost()

Compute the anomalous cost of a segment

Usage
gaussRegMeanVar$collectiveCost(a, b, pen, len)
Arguments
a

start of period

b

end of period

pen

penalty cost

len

minimum number of observations

Method param()

Compute parameters of a segment if anomalous

Usage
gaussRegMeanVar$param(a, b)
Arguments
a

start of period

b

end of period

Method clone()

The objects of this class are cloneable with this method.

Usage
gaussRegMeanVar$clone(deep = FALSE)
Arguments
deep

Whether to make a deep clone.

Examples

## simple test
set.seed(10)
x <- list()
n <- 120
for(ii in 1:48){
    
    if(ii < 10){ theta = c(1,0); sigma <- 0.1 }
    if(ii >= 10 & ii <12){ theta <- c(10,0); sigma <- 2}
    if(ii >= 12 & ii < 44){ theta <- c(5,1); sigma <- 2}
    if(ii >= 44 ){ theta <- c(1,0); sigma <- 0.1}
    
    X <- cbind(rep(1,n),runif(n,ii-1,ii))
    y <- rnorm(n, X%*%theta, sigma)
    x[[ii]] <- list(y=y,X=X)
}

fCost <- gaussRegMeanVar$new(x)
p <- partition(4*log(sum(sapply(y,length))),NA,2)
res <- pelt(p,fCost)

R6 class for LAD Cost Functions

Description

Cost functions for the Least Absolution Deviation from a given quantile

Details

this is a very niaive and slow implimentation

Methods

Public methods

Method length()

Get the length of time series

Usage
ladCost$length()

Method new()

Initialise the cost function

Usage
ladCost$new(x, m = 0, tau = 0.5)
Arguments
x

numeric vector of observations

m

expected value of x

tau

the quantile

Method baseCost()

Compute the non-anomalous cost of a segment

Usage
ladCost$baseCost(a, b, pen = 0)
Arguments
a

start of period

b

end of period

pen

penalty cost

Method pointCost()

Compute the point anomaly cost of a time step

Usage
ladCost$pointCost(a, pen)
Arguments
a

time step

pen

penalty cost

Method collectiveCost()

Compute the anomalous cost of a segment

Usage
ladCost$collectiveCost(a, b, pen, len)
Arguments
a

start of period

b

end of period

pen

penalty cost

len

minimum number of observations

Method param()

Compute parameters of a segment if anomalous

Usage
ladCost$param(a, b)
Arguments
a

start of period

b

end of period

Method clone()

The objects of this class are cloneable with this method.

Usage
ladCost$clone(deep = FALSE)
Arguments
deep

Whether to make a deep clone.

Examples

set.seed(0)
m <- runif(100)
x <- rnorm(100,m)

p <- ladCost$new(x,m,0.5)
p$baseCost(90,95) ## cost of non-anomalous distribution for x[90:95]
p$pointCost(90,0) ## point anomaly cost for x[90] with 0 penalty
## collective anomaly cost for x[90:95] with penalty of 57 and at least 3 observation
p$collectiveCost(90,95,57,3)

Normalized glioblastoma profile for an excerpt of chromosome 7, the EGFR locus.

Description

This dataset is taken from Lai W, Johnson MJ, Kucherlapati R, Park PJ, Bioinformatics , 2005. The paper states that the original source of the data is from Bredel et al. (2005). The data is an excerpt of chromosome 7 in GBM29 from 40 to 65 Mb.

This version of the data is a copy of that in the changepoint package.

Usage

data(Lai2005fig4)

Format

A matrix of dimensions 193 x 5. The columns are Spot, CH, POS.start, POS.end, GBM31.

Source

http://compbio.med.harvard.edu/Supplements/Bioinformatics05b/Profiles/Chrom_7_from40_to65Mb_GBM29.xls

R6 class for local regression Cost Functions

Description

VERY experimental - do not use

Methods

Public methods

Method length()

Get the length of time series

Usage
localRegCost$length()

Method new()

Initialise the cost function

Usage
localRegCost$new(x, family = c("gaussian", "symmetric"))
Arguments
x

observations as for gauss_reg

family

for fitting

Method baseCost()

Compute the non-anomalous cost of a segment

Usage
localRegCost$baseCost(a, b, pen = 0)
Arguments
a

start of period

b

end of period

pen

penalty cost

Method pointCost()

Compute the point anomaly cost of a time step

Usage
localRegCost$pointCost(b, pen)
Arguments
b

time step

pen

penalty cost

Method collectiveCost()

Compute the non-anomalous cost of a segment

Usage
localRegCost$collectiveCost(a, b, pen, len)
Arguments
a

start of period

b

end of period

pen

penalty cost

len

minimum number of observations

Method param()

Compute parameters of a segment if anomalous

Usage
localRegCost$param(a, b)
Arguments
a

start of period

b

end of period

Method clone()

The objects of this class are cloneable with this method.

Usage
localRegCost$clone(deep = FALSE)
Arguments
deep

Whether to make a deep clone.

Machine temperature data.

Description

Temperature sensor data of an internal component of a large, industrial machine. The data contains three known anomalies. The first anomaly is a planned shutdown of the machine. The second anomaly is difficult to detect and directly led to the third anomaly, a catastrophic failure of the machine. The data consists of 22695 observations of machine temperature recorded at 5 minute intervals along with the date and time of the measurement. The data was obtained from the Numenta Anomaly Benchmark, which can be found at https://github.com/numenta/NAB.

Usage

data(machinetemp)

Format

A dataframe with 22695 rows and 2 columns. The first column contains the date and time of the temperature measurement. The second column contains the machine temperature.

R6 class for the multinomial distribution

Description

Cost functions for the multinomial distribution

Details

Collective anomalies are represented as chnages to the expected proportions. Time varying expected proportions are currently not handled.

Methods

Public methods

Method length()

Get the length of time series

Usage
multinomialCost$length()

Method new()

Initialise the cost function

Usage
multinomialCost$new(x, m = rep(1/ncol(x), ncol(x)))
Arguments
x

integer matrix of observations

m

numeric vector of expected proportions

Method baseCost()

Compute the non-anomalous cost of a segment

Usage
multinomialCost$baseCost(a, b, pen = 0)
Arguments
a

start of period

b

end of period

pen

penalty cost

Method pointCost()

Compute the point anomaly cost of a time step

Usage
multinomialCost$pointCost(b, pen)
Arguments
b

time step

pen

penalty cost

Method collectiveCost()

Compute the anomalous cost of a segment

Usage
multinomialCost$collectiveCost(a, b, pen, len)
Arguments
a

start of period

b

end of period

pen

penalty cost

len

minimum number of observations

Method param()

Compute parameters of a segment if anomalous

Usage
multinomialCost$param(a, b)
Arguments
a

start of period

b

end of period

Method clone()

The objects of this class are cloneable with this method.

Usage
multinomialCost$clone(deep = FALSE)
Arguments
deep

Whether to make a deep clone.

Examples

set.seed(0)
m <- c(1:4)/sum(1:4)
X <- t(rmultinom(100, 144, m))

p <- multinomialCost$new(X,m)
p$baseCost(90,95) ## cost of non-anomalous distribution for x[90:95]
p$pointCost(90,0) ## point anomaly cost for x[90] with 0 penalty
## collective anomaly cost for x[90:95] with penalty of 57 and at least 3 observation
p$collectiveCost(90,95,57,3)

Get the parameters for a partitioning result

Description

Get the parameters for a partitioning result

Usage

param(res, fCost)

Arguments

res

the result of a partitioning algorithm
fCost

the cost function

Details

Not yet implimented for all cost functions

Value

list of parameters

Partion record for the data

Description

A partition records the seperation of the data generated by the pelt or capa methods

Usage

partition(beta, betaP, min_length)

Arguments

beta

penalty for a new collective anomaly
betaP

penalty for a new point anomaly
min_length

shortest length of a collective anomaly

Examples

p <- partition(3,4,2)

An R implimentation of the segmented search algorithmpelt algorithm

Description

An R implimentation of the segmented search algorithmpelt algorithm

Usage

pelt(part, fCost, prune = TRUE, verbose = FALSE)

Arguments

part

the starting partition
fCost

the cost function
prune

logical, should pruning be used
verbose

logical, print out progress

Details

Basic R implimentation of pelt - not efficent

Value

the optimal partition

Plot method for an amomalous_partition

Description

Provides a summary plot of an object with class amomalous_partition

Usage

## S3 method for class 'anomalous_partition'
plot(x, ...)

Arguments

x

the anomalous_partition
...

optional parameters see details

Details

If providing t a time the results prodiced are as though the analysis was stopped then. The optional inputs xx and yy allow for data to be displayed under the shaded anomaly/changepoint areas. If no data is provided xx = 1:t and yy is the cost of the periods the timestep is in.

Value

Produces a plot

Method for extracting point anomalies

Description

Extracts the point anomaly summaries from the object

Usage

point_anomalies(p, t)

Arguments

p

object, such as a partition, from which to extract the point anomalies
t

the end time at which the partition is based

R6 class for Univariate Poisson Cost Functions

Description

Cost functions for the univariate Poission distribution

Details

Collective anomalies are represented as multiplicative changes in rate

Methods

Public methods

Method length()

Get the length of time series

Usage
poisCost$length()

Method new()

Initialise the cost function

Usage
poisCost$new(x, rate = 1)
Arguments
x

numeric vector of observations

rate

numeric vector of rate parameters

Method baseCost()

Compute the non-anomalous cost of a segment

Usage
poisCost$baseCost(a, b, pen = 0)
Arguments
a

start of period

b

end of period

pen

penalty cost

Method pointCost()

Compute the point anomaly cost of a time step

Usage
poisCost$pointCost(b, pen)
Arguments
b

time step

pen

penalty cost

Method collectiveCost()

Compute the anomalous cost of a segment

Usage
poisCost$collectiveCost(a, b, pen, len)
Arguments
a

start of period

b

end of period

pen

penalty cost

len

minimum number of observations

Method param()

Compute parameters of a segment if anomalous

Usage
poisCost$param(a, b)
Arguments
a

start of period

b

end of period

Method clone()

The objects of this class are cloneable with this method.

Usage
poisCost$clone(deep = FALSE)
Arguments
deep

Whether to make a deep clone.

Examples

set.seed(0)
r <- 8 + runif(100)*2
x <- rpois(100,lambda = r)

p <- poisCost$new(x,r)
p$baseCost(90,95) ## cost of non-anomalous distribution for x[90:95]
p$pointCost(90,0) ## point anomaly cost for x[90] with 0 penalty
## collective anomaly cost for x[90:95] with penalty of 57 and at least 3 observation
p$collectiveCost(90,95,57,3)

R6 class for rank based anomalies

Description

This is VERY developmental - do not use

Methods

Public methods

Method length()

Get the length of time series

Usage
rankCost$length()

Method new()

Initialise the cost function

Usage
rankCost$new(x, m = 0)
Arguments
x

numeric matrix of observations

m

numeric vector or matrix of mean values

Method baseCost()

Compute the non-anomalous cost of a segment

Usage
rankCost$baseCost(a, b, pen = 0)
Arguments
a

start of period

b

end of period

pen

penalty cost

Method pointCost()

Compute the point anomaly cost of a time step

Usage
rankCost$pointCost(b, pen)
Arguments
b

time step

pen

penalty cost

Method collectiveCost()

Compute the non-anomalous cost of a segment

Usage
rankCost$collectiveCost(a, b, pen, len)
Arguments
a

start of period

b

end of period

pen

penalty cost

len

minimum number of observations

Method param()

Compute parameters of a segment if anomalous

Usage
rankCost$param(a, b)
Arguments
a

start of period

b

end of period

Method clone()

The objects of this class are cloneable with this method.

Usage
rankCost$clone(deep = FALSE)
Arguments
deep

Whether to make a deep clone.

Examples

set.seed(0)
m <- runif(100)
s <- pmax(1e-4,runif(100))
x <- rnorm(100,m,s) ## example data

Simulated data.

Description

A simulated data set for use in the examples and vignettes. The data consists of 500 observations on 20 variates drawn from the standard normal distribution. Within the data there are three multivariate anomalies of length 15 located at t=100, t=200, and t=300 for which the mean changes from 0 to 2. The anomalies affect variates 1 to 8, 1 to 12 and 1 to 16 respectively.

Usage

data(simulated)

Format

A matrix with 500 rows and 40 columns.

Summmary method for an amomalous_partition

Description

Provides a summary of an object with class amomalous_partition

Usage

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

Arguments

object

the anomalous_partition
...

optional parameters see details

Details

If providing t a time the results prodiced are as though the analysis was stopped then.

Value

A data.frame summarising the partitions

Ireland wind data, 1961-1978

Description

Daily average wind speeds for 1961-1978 at 12 synoptic meteorological stations in the Republic of Ireland (Haslett and raftery 1989). Wind speeds are in knots (1 knot = 0.5418 m/s), at each of the stations in the order given in Fig.4 of Haslett and Raftery (1989, see below)

This data is a copy of that contained within the gstat package

Usage

data(wind)

Format

data.frame wind contains the following columns:

year

year, minus 1900

month

month (number) of the year

day

day

RPT

average wind speed in knots at station RPT

VAL

average wind speed in knots at station VAL

ROS

average wind speed in knots at station ROS

KIL

average wind speed in knots at station KIL

SHA

average wind speed in knots at station SHA

BIR

average wind speed in knots at station BIR

DUB

average wind speed in knots at station DUB

CLA

average wind speed in knots at station CLA

MUL

average wind speed in knots at station MUL

CLO

average wind speed in knots at station CLO

BEL

average wind speed in knots at station BEL

MAL

average wind speed in knots at station MAL

data.frame wind.loc contains the following columns:

Station

Station name

Code

Station code

Latitude

Latitude, in DMS, see examples below

Longitude

Longitude, in DMS, see examples below

MeanWind

mean wind for each station, metres per second

Note

This data set comes with the following message: “Be aware that the dataset is 532494 bytes long (thats over half a Megabyte). Please be sure you want the data before you request it.” The data were obtained on Oct 12, 2008, from: http://www.stat.washington.edu/raftery/software.html The data are also available from statlib. Locations of 11 of the stations (ROS, Rosslare has been thrown out because it fits poorly the spatial correlations of the other stations) were obtained from: http://www.stat.washington.edu/research/reports/2005/tr475.pdf Roslare lat/lon was obtained from google maps, location Roslare. The mean wind value for Roslare comes from Fig. 1 in the original paper. Haslett and Raftery proposed to use a sqrt-transform to stabilize the variance.

Author(s)

Adrian Raftery; imported to R by Edzer Pebesma

References

These data were analyzed in detail in the following article:

Haslett, J. and Raftery, A. E. (1989). Space-time Modelling with Long-memory Dependence: Assessing Ireland's Wind Power Resource (with Discussion). Applied Statistics 38, 1-50. and in many later papers on space-time analysis, for example: Tilmann Gneiting, Marc G. Genton, Peter Guttorp: Geostatistical Space-Time Models, Stationarity, Separability and Full symmetry. Ch. 4 in: B. Finkenstaedt, L. Held, V. Isham, Statistical Methods for Spatio-Temporal Systems.

Examples

data(wind)
summary(wind)