Package 'beast' reference manual

Title:	Bayesian Estimation of Change-Points in the Slope of Multivariate Time-Series
Description:	Assume that a temporal process is composed of contiguous segments with differing slopes and replicated noise-corrupted time series measurements are observed. The unknown mean of the data generating process is modelled as a piecewise linear function of time with an unknown number of change-points. The package infers the joint posterior distribution of the number and position of change-points as well as the unknown mean parameters per time-series by MCMC sampling. A-priori, the proposed model uses an overfitting number of mean parameters but, conditionally on a set of change-points, only a subset of them influences the likelihood. An exponentially decreasing prior distribution on the number of change-points gives rise to a posterior distribution concentrating on sparse representations of the underlying sequence, but also available is the Poisson distribution. See Papastamoulis et al (2017) <arXiv:1709.06111> for a detailed presentation of the method.
Authors:	Panagiotis Papastamoulis
Maintainer:	Panagiotis Papastamoulis <[email protected]>
License:	GPL-2
Version:	1.1
Built:	2025-01-19 05:30:49 UTC
Source:	https://github.com/cran/beast

Bayesian Estimation of Change-Points in the Slope of Multivariate Time-Series

Description

Assume that a temporal process is composed of contiguous segments with differing slopes and replicated noise-corrupted time series measurements are observed. The unknown mean of the data generating process is modelled as a piecewise linear function of time with an unknown number of change-points. The package infers the joint posterior distribution of the number and position of change-points as well as the unknown mean parameters per time-series by MCMC sampling. A-priori, the proposed model uses an overfitting number of mean parameters but, conditionally on a set of change-points, only a subset of them influences the likelihood. An exponentially decreasing prior distribution on the number of change-points gives rise to a posterior distribution concentrating on sparse representations of the underlying sequence, but also available is the Poisson distribution. See Papastamoulis et al (2017) <arXiv:1709.06111> for a detailed presentation of the method.

Details

The beast package deals with Bayesian estimation of change-points in the slope of multivariate time-series, introduced by Papastamoulis et al (2017). For a given period $t = 1,\ldots,T$ we observe multiple time series which are assumed independent, each one consisting of multiple measurements (replicates). Each time series is assumed to have its own segmentation, which is common among its replicates. Thus, different time series have distinct mean parameters in the underlying normal distribution. The variance, which is assumed known, can be either shared between different time series or not and in practice it is estimated at a pre-processing stage.

Our model infers the joint posterior distribution of the number and location of change-points by MCMC sampling. For this purpose a Metropolis-Hastings MCMC sampler is used. The main function of the package is beast.

Assume that the observed data consists of $N$ time-series, each one consisting of $R$ variables (or replicates) measured at $T$ consecutive time-points. The input of the main function beast should be given in the form of a list myDataList with the following attributes:

length(myDataList) should be equal to $R$ , that is, the number of variables (or replicates)
dim(myDataList)[[1]], $\ldots$ , dim(myDataList)[[R]] should be all $T\times N$ , that is, rows and columns should correspond to time-points and different series, respectively.

Then, a basic usage of the package consists of the following commands:

beastRun <- beast( myDataList = myDataList )
print(beastRun)
plot(beastRun)

which correspond to running the MCMC sampler, printing and plotting output summaries, respectively.

Author(s)

Panagiotis Papastamoulis

Maintainer: Panagiotis Papastamoulis <[email protected]>

References

Papastamoulis P., Furukawa T., van Rhijn N., Bromley M., Bignell E. and Rattray M. (2017). Bayesian detection of piecewise linear trends in replicated time-series with application to growth data modelling. arXiv:1709.06111 [stat.AP]

Examples

# toy-example (MCMC iterations not enough)
library('beast')	# load package
data("FungalGrowthDataset")	# load dataset
myIndex <- c(392, 62, 3, 117)	# run the sampler only for the 
#                                 specific subset of time-series
set.seed(1)	
# Run MCMC sampler with very small number of iterations (nIter):
run_mcmc <- beast(myDataList = FungalGrowthDataset, subsetIndex = myIndex, 
			zeroNormalization = TRUE, nIter = 40, burn = 20) 
# Print output:
print(run_mcmc)
# Plot output to file: "beast_plot.pdf"
plot(run_mcmc, fileName = "beast_plot_toy.pdf", timeScale=1/6, xlab = "hours", ylab = "growth")
# Run the following commands to obtain convergence:

## Not run: 
# This example illustrates the package using a subset of four 
#      time-series of the fungal dataset. 
library('beast')	# load package
data("FungalGrowthDataset")	# load dataset
myIndex <- c(392, 62, 3, 117)	# run the sampler only for the 
#                                 specific subset of time-series
set.seed(1)		# optional
# Run MCMC sampler with the default number of iterations (nIter =70000):
run_mcmc <- beast(myDataList = FungalGrowthDataset, subsetIndex = myIndex, 
			zeroNormalization = TRUE) 
# Print output:
print(run_mcmc)
# Plot output to file: "beast_plot.pdf"
plot(run_mcmc, fileName = "beast_plot.pdf", timeScale=1/6, xlab = "hours", ylab = "growth")
# NOTE 1: for a complete analysis remove the `subsetIndex = myIndex` argument.
# NOTE 2: `zeroNormalization = TRUE` is an optional argument that forces all 
#	   time-series to start from zero. It is not supposed to be used 
#	   for other applications.

## End(Not run)
# toy-example (MCMC iterations not enough)
library('beast')	# load package
data("FungalGrowthDataset")	# load dataset
myIndex <- c(392, 62, 3, 117)	# run the sampler only for the 
#                                 specific subset of time-series
set.seed(1)	
# Run MCMC sampler with very small number of iterations (nIter):
run_mcmc <- beast(myDataList = FungalGrowthDataset, subsetIndex = myIndex, 
			zeroNormalization = TRUE, nIter = 40, burn = 20) 
# Print output:
print(run_mcmc)
# Plot output to file: "beast_plot.pdf"
plot(run_mcmc, fileName = "beast_plot_toy.pdf", timeScale=1/6, xlab = "hours", ylab = "growth")
# Run the following commands to obtain convergence:

## Not run: 
# This example illustrates the package using a subset of four 
#      time-series of the fungal dataset. 
library('beast')	# load package
data("FungalGrowthDataset")	# load dataset
myIndex <- c(392, 62, 3, 117)	# run the sampler only for the 
#                                 specific subset of time-series
set.seed(1)		# optional
# Run MCMC sampler with the default number of iterations (nIter =70000):
run_mcmc <- beast(myDataList = FungalGrowthDataset, subsetIndex = myIndex, 
			zeroNormalization = TRUE) 
# Print output:
print(run_mcmc)
# Plot output to file: "beast_plot.pdf"
plot(run_mcmc, fileName = "beast_plot.pdf", timeScale=1/6, xlab = "hours", ylab = "growth")
# NOTE 1: for a complete analysis remove the `subsetIndex = myIndex` argument.
# NOTE 2: `zeroNormalization = TRUE` is an optional argument that forces all 
#	   time-series to start from zero. It is not supposed to be used 
#	   for other applications.

## End(Not run)

Main function

Description

This is the main function of the package, implementing the MCMC sampler described in Papastamoulis et al (2017).

Usage

beast(myDataList, burn, nIter, mhPropRange, mhSinglePropRange, startPoint,
    timeScale, savePlots, zeroNormalization, LRange, tau,
    gammaParameter, nu0, alpha0, beta0, subsetIndex, saveTheta, sameVariance,
    Prior
)
beast(myDataList, burn, nIter, mhPropRange, mhSinglePropRange, startPoint,
    timeScale, savePlots, zeroNormalization, LRange, tau,
    gammaParameter, nu0, alpha0, beta0, subsetIndex, saveTheta, sameVariance,
    Prior
)

Arguments

`myDataList`	Observed data in the form of a `list` with length $R$ , denoting the dimensionality of the multivariate time-series data. For each $r = 1,\ldots,R$ , `myDataList[[r]]` should correspond to $T\times N$ array, with `myDataList[[r]][t, n]` corresponding to the observed data for time-series $n = 1,\ldots,N$ and time-point $t = 1,\ldots,T$ .
`burn`	Number of iterations that will be discarder as burn-in period. Default value: `burn = 20000`.
`nIter`	Number of MCMC iterations. Default value: `nIter = 70000`.
`mhPropRange`	Positive integer corresponding to the parameter $d_1$ of MCMC Move 3.a of Papastamoulis et al (2017). Default value: `mhPropRange = 1`.
`mhSinglePropRange`	Positive integer denoting the parameter $d_2$ of Papastamoulis et al (2017). Default value: `mhPropRange = 40`.
`startPoint`	An (optional) positive integer pointing at the minimum time-point where changes are allowed to occur. Default value: `startPoint = 2` (all possible values are taken into account).
`timeScale`	Null.
`savePlots`	Character denoting the name of the folder where various plots will be saved to.
`zeroNormalization`	Logical value denoting whether to normalize to zero all time time-series for $t=1$ . Default: `zeroNormalization = FALSE`.
`LRange`	Range of possible values for the number of change-points. Default value: `LRange = 0:30`.
`tau`	Positive real number corresponding to parameter $c$ in Move 2 of Papastamoulis et al (2017). Default value: `tau = 0.05`.
`gammaParameter`	Positive real number corresponding to parameter $\alpha$ of the exponential prior distribution. Default value: `gammaParameter = 2`.
`nu0`	Positive real number corresponding to prior parameter $\nu_0$ in Papastamoulis et al (2017). Default value: `nu0 = 0.1`.
`alpha0`	Positive real number corresponding to prior parameter $\alpha_0$ in Papastamoulis et al (2017). Default value: `alpha0 = 1`.
`beta0`	Positive real number corresponding to prior parameter $\beta_0$ in Papastamoulis et al (2017). Default value: `beta0 = 1`.
`subsetIndex`	Optional subset of integers corresponding to time-series indexes. If not null, the sampler will be applied only to the specified subset.
`saveTheta`	Logical value indicating whether to save the generated values of the mean per time-point across the MCMC trace. Default: FALSE.
`sameVariance`	Logical value indicating whether to assume the same variance per time-point across time-series. Default value: `sameVariance = TRUE`.
`Prior`	Character string specifying the prior distribution of the number of change-points. Allowed values: `Prior = "complexity"` (default) or `Prior = "Poisson"` (not suggested).

Value

The output of the sampler is returned as a list, with the following features:

`Cutpoint_posterior_median`	The estimated medians per change-point, conditionally on the most probable number of change-points per time-series.
`Cutpoint_posterior_variance`	The estimated variances per change-points, conditionally on the most probable number of change-points per time-series.
`NumberOfCutPoints_posterior_distribution`	Posterior distributions of number of change-points per time-series.
`NumberOfCutPoints_MAP`	The most probable number of change-points per time-series.
`Metropolis-Hastings_acceptance_rate`	Acceptance of the MCMC move-types.
`subject_ID`	the identifier of individual time-series.
`Cutpoint_mcmc_trace_map`	The sampled values of each change-point per time series, conditionally on the MAP values.
`theta`	The sampled values of the means per time-series, conditionally on the MAP values.
`nCutPointsTrace`	The sampled values of the number of change-points, per time-series.

Note

The complexity prior distribution with parameter gammaParameter = 2 is the default prior assumption imposed on the number of change-points. Smaller (larger) values of gammaParameter will a-priori support larger (respectively: smaller) number of change-points.

For completeness purposes, the Poisson distribution is also allowed in the Prior. In this latter case, the gammaParameter denotes the rate parameter of the Poisson distribution. Note that in this case the interpretation of gammaParameter is reversed: Smaller (larger) values of gammaParameter will a-priori support smaller (respectively: larger) number of change-points.

Author(s)

Panagiotis Papastamoulis

References

Examples

# toy-example (MCMC iterations not enough)
library('beast')	# load package
data("FungalGrowthDataset")	# load dataset
myIndex <- c(392, 62, 3, 117)	# run the sampler only for the 
#                                 specific subset of time-series
set.seed(1)	
# Run MCMC sampler with very small number of iterations (nIter):
run_mcmc <- beast(myDataList = FungalGrowthDataset, subsetIndex = myIndex, 
			zeroNormalization = TRUE, nIter = 40, burn = 20) 
# Print output:
print(run_mcmc)
# Plot output to file: "beast_plot.pdf"
plot(run_mcmc, fileName = "beast_plot_toy.pdf", timeScale=1/6, xlab = "hours", ylab = "growth")
# Run the following commands to obtain convergence:

## Not run: 
# This example illustrates the package using a subset of four 
#      time-series of the fungal dataset. 
library('beast')	# load package
data("FungalGrowthDataset")	# load dataset
myIndex <- c(392, 62, 3, 117)	# run the sampler only for the 
#                                 specific subset of time-series
set.seed(1)		# optional
# Run MCMC sampler with the default number of iterations (nIter =70000):
run_mcmc <- beast(myDataList = FungalGrowthDataset, subsetIndex = myIndex, 
			zeroNormalization = TRUE) 
# Print output:
print(run_mcmc)
# Plot output to file: "beast_plot.pdf"
plot(run_mcmc, fileName = "beast_plot.pdf", timeScale=1/6, xlab = "hours", ylab = "growth")
# NOTE 1: for a complete analysis remove the `subsetIndex = myIndex` argument.
# NOTE 2: `zeroNormalization = TRUE` is an optional argument that forces all 
#	   time-series to start from zero. It is not supposed to be used 
#	   for other applications.

## End(Not run)
# toy-example (MCMC iterations not enough)
library('beast')	# load package
data("FungalGrowthDataset")	# load dataset
myIndex <- c(392, 62, 3, 117)	# run the sampler only for the 
#                                 specific subset of time-series
set.seed(1)	
# Run MCMC sampler with very small number of iterations (nIter):
run_mcmc <- beast(myDataList = FungalGrowthDataset, subsetIndex = myIndex, 
			zeroNormalization = TRUE, nIter = 40, burn = 20) 
# Print output:
print(run_mcmc)
# Plot output to file: "beast_plot.pdf"
plot(run_mcmc, fileName = "beast_plot_toy.pdf", timeScale=1/6, xlab = "hours", ylab = "growth")
# Run the following commands to obtain convergence:

## Not run: 
# This example illustrates the package using a subset of four 
#      time-series of the fungal dataset. 
library('beast')	# load package
data("FungalGrowthDataset")	# load dataset
myIndex <- c(392, 62, 3, 117)	# run the sampler only for the 
#                                 specific subset of time-series
set.seed(1)		# optional
# Run MCMC sampler with the default number of iterations (nIter =70000):
run_mcmc <- beast(myDataList = FungalGrowthDataset, subsetIndex = myIndex, 
			zeroNormalization = TRUE) 
# Print output:
print(run_mcmc)
# Plot output to file: "beast_plot.pdf"
plot(run_mcmc, fileName = "beast_plot.pdf", timeScale=1/6, xlab = "hours", ylab = "growth")
# NOTE 1: for a complete analysis remove the `subsetIndex = myIndex` argument.
# NOTE 2: `zeroNormalization = TRUE` is an optional argument that forces all 
#	   time-series to start from zero. It is not supposed to be used 
#	   for other applications.

## End(Not run)

Birth Probabilities

Description

This function defines the probability of proposing an addition of a change-point.

Usage

birthProbs(LRange)
birthProbs(LRange)

Arguments

LRange

The range of possible values for the number of change-points.

Value

probs

Vector of probabilities

Author(s)

Panagiotis Papastamoulis

Complexity prior distribution

Description

This function computes the complexity prior distribution on the number of change-points, defined as $f(\ell) = P(\ell_n = \ell)\propto e^{-\alpha\ell\log(bT/\ell)}, a, b > 0; \ell = 0,1,2,\ldots$ . Note that this distribution has exponential decrease (Castillo and van der Vaart, 2012) when $b>1+e$ , so we set $b=3.72$ .

Usage

complexityPrior(Lmax = 20, gammaParameter, nTime)
complexityPrior(Lmax = 20, gammaParameter, nTime)

Arguments

`Lmax`	maximum number of change-points (default = 20).
`gammaParameter`	positive real number, corresponding to $\alpha$ .
`nTime`	positive integer denoting the total number of time-points.

Value

logPrior

Prior distribution values in the log-scale.

Author(s)

Panagiotis Papastamoulis

References

Castillo I. and van der Vaart A (2012). Needles and Straw in a Haystack: Posterior concentration for possibly sparse sequences. The Annals of Statistics, 40(4), 2069–2101.

Compute the empirical mean.

Description

This function computes the empirical mean of the time-series.

Usage

computeEmpiricalPriorParameters(myDataList, nu0 = 1, alpha0 = 1, beta0 = 1)
computeEmpiricalPriorParameters(myDataList, nu0 = 1, alpha0 = 1, beta0 = 1)

Arguments

`myDataList`	Observed multivariate time-series.
`nu0`	positive real number.
`alpha0`	positive real number.
`beta0`	positive real number.

Value

mu0

Empirical mean

Author(s)

Panagiotis Papastamoulis

Compute empirical posterior parameters

Description

Compute empirical posterior parameters

Usage

computePosteriorParameters(myDataList, priorParameters)
computePosteriorParameters(myDataList, priorParameters)

Arguments

`myDataList`	Observed data.
`priorParameters`	Prior parameters.

Value

list of posterior parameters

Author(s)

Panagiotis Papastamoulis

Posterior parameters

Description

Posterior parameters

Usage

computePosteriorParametersFree(myDataList, priorParameters)
computePosteriorParametersFree(myDataList, priorParameters)

Arguments

`myDataList`	observed data.
`priorParameters`	list of prior parameters.

Value

list of posterior parameters.

Author(s)

Panagiotis Papastamoulis

Fungal Growth Dataset

Description

Time-series dataset with $N\times R \times T$ growth levels for $R = 3$ replicates of $N = 411$ objects (mutants) measured every 10 minutes for $T = 289$ time-points. See Papastamoulis et al (2017) for a detailed description.

Usage

FungalGrowthDatasetFungalGrowthDataset

Format

Time-series data.

References

Move 3.b

Description

Implements Move 3.b of the Metropolis-Hastings MCMC sampler.

Usage

localProposal(cutPoints, nTime, mhPropRange, startPoint)
localProposal(cutPoints, nTime, mhPropRange, startPoint)

Arguments

`cutPoints`	Current configuration of change-points.
`nTime`	Total number of time-points.
`mhPropRange`	Parameter $d_2$ .
`startPoint`	Integer, at least equal to 2.

Value

`newState`	Candidate state of the chain.
`propRatio`	Proposal ratio.

Author(s)

Panagiotis Papastamoulis

Log-likelihood function.

Description

Log-likelihood function.

Usage

logLikelihoodFullModel(myData, cutPoints, theta, startPoint)
logLikelihoodFullModel(myData, cutPoints, theta, startPoint)

Arguments

`myData`	data
`cutPoints`	change-points.
`theta`	means.
`startPoint`	optional integer at least equal to 2.

Value

log-likelihood value.

Author(s)

Panagiotis Papastamoulis

Log-prior.

Description

Logarithm of the prior distribution on the number of change-points.

Usage

logPrior(cutPoints, nTime, startPoint)
logPrior(cutPoints, nTime, startPoint)

Arguments

`cutPoints`	change-points.
`nTime`	number of time-points.
`startPoint`	optional integer, at least equal to 2.

Value

logarithm of the prior distribution.

Author(s)

Panagiotis Papastamoulis

MCMC sampler

Description

This function implements the Metropolis-Hastings MCMC sampler for individual time-series.

Usage

mcmcSampler(myData, nIter, finalIterationPdf, modelVariance, mhPropRange, 
mhSinglePropRange, movesRange, startPoint, postPar, dName, timeScale, 
burn, iterPerPlotPrefix, priorParameters, L = 3, LRange, tau, 
gammaParameter, saveTheta, Prior = "complexity")
mcmcSampler(myData, nIter, finalIterationPdf, modelVariance, mhPropRange, 
mhSinglePropRange, movesRange, startPoint, postPar, dName, timeScale, 
burn, iterPerPlotPrefix, priorParameters, L = 3, LRange, tau, 
gammaParameter, saveTheta, Prior = "complexity")

Arguments

`myData`	observed data.
`nIter`	number of mcmc iterations
`finalIterationPdf`	output folder
`modelVariance`	null
`mhPropRange`	positive integer
`mhSinglePropRange`	positive integer
`movesRange`	null
`startPoint`	positive integer
`postPar`	list of emprirically estimated parameters
`dName`	subject ID
`timeScale`	null
`burn`	burn-in period.
`iterPerPlotPrefix`	null
`priorParameters`	prior parameters.
`L`	null
`LRange`	range of possible values of the number of change-points.
`tau`	real.
`gammaParameter`	real.
`saveTheta`	TRUE.
`Prior`	character.

Value

MCMC output.

Author(s)

Panagiotis Papastamoulis

Printing

Description

Printing various unicode symbols.

Usage

myUnicodeCharacters()
myUnicodeCharacters()

Value

printed symbol

Zero normalization

Description

Zero normalization at 1st time-point

Usage

normalizeTime0(myDataList)
normalizeTime0(myDataList)

Arguments

myDataList

data

Value

null

Author(s)

Panagiotis Papastamoulis

Plot function

Description

This function plots objects returned by the beast function. All output is diverted to a pdf file provided in the fileName argument.

Usage

## S3 method for class 'beast.object'
plot(x, fileName, width, height, pointsize, ylab, xlab, timeScale, myPal, boxwex, ...)
## S3 method for class 'beast.object'
plot(x, fileName, width, height, pointsize, ylab, xlab, timeScale, myPal, boxwex, ...)

Arguments

`x`	An object of class `beast.object`, which is returned by the `beast` function.
`fileName`	Name of the output pdf file.
`width`	Width of pdf file. Default: 9
`height`	Height pdf file. Default: 6
`pointsize`	Pointsize. Default: 12
`ylab`	$y$ -axis label. Default: x.
`xlab`	$x$ -axis label. Default: t.
`timeScale`	A multiplicative-factor which will be used to scale the $x$ -axis labels. For example, if time-points correspond to 10-minute periods, then setting `timeScale = 1/6` will make the $x$ -axis labels correspond to hours. Default: `timeScale = 1`.
`myPal`	Vector of colors that will be used to produce the plot with all time-series overlayed. If the distinct values of the inferred numbers of change-points is less than 10, the `Set1` pallete of the `RColorBrewer` library is used. Otherwise, the user has to manually define the colors.
`boxwex`	A scale factor to be applied to all boxes. The appearance of the plot can be improved by making the boxes narrower or wider. Default: 0.2.
`...`	ignored.

Details

The function will produce a plot with all time-series coloured according to the corresponding number of change-points. In addition, it will generate individual plots per time-series displaying the observed data with boxplots which summarize the posterior distribution of change-points locations, conditionally on the most probable number of change-points.

Author(s)

Panagiotis Papastamoulis

Print function

Description

This function prints a summary of objects returned by the beast function.

Usage

## S3 method for class 'beast.object'
print(x, ...)
## S3 method for class 'beast.object'
print(x, ...)

Arguments

`x`	An object of class `beast.object`, which is returned by the `beast` function.
`...`	ignored.

Details

The function prints a summary of the most probable number (MAP) of change-points per time-series in the form of a table, as well as a list containing the MAP number of change-points and the corresponding locations (posterior medians) per time-series.

Author(s)

Panagiotis Papastamoulis

Move 2

Description

Proposes an update of $\theta$ according to Metropolis-Hastings move 2.

Usage

proposeTheta(thetaOld, tau, alpha, beta)
proposeTheta(thetaOld, tau, alpha, beta)

Arguments

`thetaOld`	Current values
`tau`	Parameter $c$ .
`alpha`	null
`beta`	null

Value

mean

proposed values.

Author(s)

Panagiotis Papastamoulis

Prior random numbers

Description

Generation of mean values according to the prior

Usage

simMultiIndNormInvGamma(mu, nu, alpha, beta)
simMultiIndNormInvGamma(mu, nu, alpha, beta)

Arguments

`mu`	means
`nu`	precision parameter
`alpha`	prior parameter
`beta`	prior parameter

Value

null

Author(s)

Panagiotis Papastamoulis

Generate change-points according to the prior

Description

Generate change-points according to the prior distribution conditionally on a given number of change-points.

Usage

simulateFromPrior(nTime, startPoint, L = 3)
simulateFromPrior(nTime, startPoint, L = 3)

Arguments

`nTime`	Number of time-points
`startPoint`	At least equal to 2.
`L`	null

Value

cutPoints

Change-point locations

Author(s)

Panagiotis Papastamoulis

Move 3.b

Description

Implement Metropolis-Hastings Move 3.b.

Usage

singleLocalProposal(cutPoints, nTime, mhSinglePropRange, startPoint)
singleLocalProposal(cutPoints, nTime, mhSinglePropRange, startPoint)

Arguments

`cutPoints`	Current state
`nTime`	Number of time-points
`mhSinglePropRange`	Prior parameter.
`startPoint`	Optional.

Value

`newState`	Candidate state
`propRatio`	Proposal ratio

Author(s)

Panagiotis Papastamoulis

Truncated Poisson pdf

Description

Probability density function of the truncated Poisson distribution.

Usage

truncatedPoisson(Lmax = 20, gammaParameter = 1)
truncatedPoisson(Lmax = 20, gammaParameter = 1)

Arguments

`Lmax`	Max number
`gammaParameter`	Location parameter.

Value

logPrior

Log-pdf values

Author(s)

Panagiotis Papastamoulis

Move 1

Description

Update the number of change-points according to Metropolis-Hastings move 1.

Usage

updateNumberOfCutpoints(cutPoints, nTime, startPoint, LRange, birthProbs)
updateNumberOfCutpoints(cutPoints, nTime, startPoint, LRange, birthProbs)

Arguments

`cutPoints`	Current configuration
`nTime`	Number of time-points
`startPoint`	Optional integer
`LRange`	Range of possible values
`birthProbs`	Birth probabilities

Value

`newState`	Candidate state
`propRatio`	Proposal ratio

Author(s)

Panagiotis Papastamoulis

Package 'beast'

Help Index

Bayesian Estimation of Change-Points in the Slope of Multivariate Time-Series

Description

Details

Author(s)

References

See Also

Examples

Main function

Description

Usage

Arguments

Value

Note

Author(s)

References

Examples

Birth Probabilities

Description

Usage

Arguments

Value

Author(s)

Complexity prior distribution

Description

Usage

Arguments

Value

Author(s)

References

Compute the empirical mean.

Description

Usage

Arguments

Value

Author(s)

Compute empirical posterior parameters

Description

Usage

Arguments

Value

Author(s)

Posterior parameters

Description

Usage

Arguments

Value

Author(s)

Fungal Growth Dataset

Description

Usage

Format

References

Move 3.b

Description

Usage

Arguments

Value

Author(s)

Log-likelihood function.

Description

Usage

Arguments

Value

Author(s)

Log-prior.

Description

Usage

Arguments

Value

Author(s)

MCMC sampler

Description

Usage

Arguments

Value

Author(s)

Printing

Description