Package ‘boa’

June 23, 2016

Version 1.1.8-2
Date 2016-06-22
Title Bayesian Output Analysis Program (BOA) for MCMC
Maintainer Brian J. Smith <brian-j-smith@uiowa.edu>
Depends R (>= 2.7)
Imports graphics, grDevices, stats, utils
Description A menu-driven program and library of functions for carrying out
convergence diagnostics and statistical and graphical analysis of Markov
chain Monte Carlo sampling output.
License GPL-2

URL http://www.jstatsoft.org/v21/i11
NeedsCompilation no
Author Brian J. Smith [aut, cre]
Repository CRAN
Date/Publication 2016-06-23 01:29:05

R topics documented:
boa.acf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
boa.chain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
boa.chain.add . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
boa.chain.collapse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
boa.chain.del . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
boa.chain.eval . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
boa.chain.gandr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
boa.chain.import . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
boa.chain.info . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
boa.chain.reset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
boa.chain.subset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
boa.chain.support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
boa.geweke . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

1
2 boa.acf

boa.handw . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
boa.hpd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
boa.importASCII . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
boa.importBUGS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
boa.importMatrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
boa.init . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
boa.load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
boa.menu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
boa.par . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
boa.plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
boa.plot.acf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
boa.plot.bandg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
boa.plot.density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
boa.plot.gandr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
boa.plot.geweke . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
boa.plot.history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
boa.plot.par . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
boa.plot.title . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
boa.plot.trace . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
boa.print.acf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
boa.print.cor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
boa.print.gandr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
boa.print.geweke . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
boa.print.handw . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
boa.print.hpd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
boa.print.info . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
boa.print.par . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
boa.print.randl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
boa.print.stats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
boa.quit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
boa.randl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
boa.save . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
boa.stats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

Index 39

boa.acf Autocorrelation Function

Description
Computes lag autocorrelations for the parameters in an MCMC sequence.

Usage
boa.acf(link, lags)
boa.chain 3

Arguments
link Matrix whose columns and rows contain the monitored parameters and the MCMC
iterations, respectively. The iteration numbers and parameter names must be as-
signed to dimnames(link)
lags Vector of lags at which to estimate the autocorrelation function.

Value
A matrix whose columns and rows contain the estimated autocorrelation functions at the specified
lags and the monitored parameters, respectively.

Author(s)
Brian J. Smith

See Also
boa.plot, boa.plot.acf, boa.print.acf

boa.chain Session Lists of MCMC Sequences

Description
Extracts and sets the MCMC sequence(s) stored internally for use during a BOA session. Users
can safely use this function to extract data. However, it should not be called directly to modify the
stored MCMC sequence(s). Instead, data management should accomplished with the libboa.chain
functions.

Usage
boa.chain(...)

Arguments
... A list may be given as the only argument, or a character string given as the only
argument, or any number of arguments may be in the <name> = <value> form,
or no argument at all may be given. See the Value and Side Effects sections for
further details.

Value
If no arguments are supplied, a list of the current values is returned. If a character string is given,
the current value of the named variable is returned. Otherwise, no values are returned.
4 boa.chain.add

Parameter Names and Default Values

master = list() Master list containing all added MCMC sequences. Sequences may only be added
to or deleted from the master list. The sequences in this list are never modified or used in any
of the analyses. It serves as a template for the working list described below. The parameters
and iterations may differ between the sequences. Each element in the list is a matrix whose
columns and rows contain the monitored parameters and the MCMC iterations, respectively.
The iteration numbers and parameter names are stored in the dimnames.
master.support = list() List containing the support for each of the parameters in ’master’. Each
element in the list is a matrix whose columns and rows contain the monitored parameters and
the support (lower and upper limits), respectively. The default for each parameter is c(-Inf,
Inf).
work = master Working list used in all analyses. This list is essentially a modifiable copy of
’master’. All data management functions operate on the working list.
work.support = master.support List containing the support for each of the parameters in ’work’.
work.sync = TRUE Logical value indicating that the working list is an identical copy of the master
list. This variable is automatically set to F after a successful call to boa.chain.subset or
boa.chain.collapse. While work.sync = F, only the master list will be updated if MCMC
sequences are added or deleted. A call to boa.chain.reset will reset this variable to T and
copy the master list to the working list.

Side Effects

When variables are set, boa.chain() modifies the internal list .boa.chain. If boa.chain() is called
with either a list as the single argument, or with one or more arguments in the <name> = <value>
form, the variables specified by the names in the arguments are modified.

Author(s)

Brian J. Smith

boa.chain.add Add MCMC Sequence

Description

Adds an MCMC sequence to the session lists of sequences. Most users should not call this function
directly. Passing improperly formatted data to this function will most likely break the functions in
this library. The preferred method of adding a new sequence is to call the function boa.chain.import.

Usage

boa.chain.add(link, lname)
boa.chain.collapse 5

Arguments
link Matrix whose columns and rows contain the monitored parameters and the MCMC
iterations, respectively. The iteration numbers and parameter names must be as-
signed to dimnames(link).
lname Character string giving the list name to use for the newly added MCMC se-
quence.

Value
A logical value indicating that ’link’ has been successfully added.

Author(s)
Brian J. Smith

See Also
boa.chain.import

boa.chain.collapse Concatenate MCMC Sequences

Description
Concatenates together all of the MCMC sequences in the working session list of sequences. Only
those parameters common to all sequences are kept.

Usage
boa.chain.collapse()

Value
A logical value indicating that the MCMC sequences have been collapsed. If the sequences share
no common parameters, no modifications are made to the working list and FALSE is returned.

Author(s)
Brian J. Smith

See Also
codeboa.chain.reset, codeboa.chain.subset
6 boa.chain.eval

boa.chain.del Delete MCMC Sequences

Description
Delete MCMC sequences from the session list of sequences.

Usage
boa.chain.del(lnames, pnames)

Arguments
lnames Character vector giving the names of the MCMC sequences in the session list of
sequences to be deleted. If omitted, no sequences are deleted.
pnames Character vector giving the names of the parameters in the MCMC sequences to
be deleted. If omitted, no parameters are deleted.

Side Effects
The specified MCMC sequences are deleted from the session lists of sequences.

Author(s)
Brian J. Smith

boa.chain.eval Formulate New Parameter

Description
Evaluates a user-specified expression to formulate a new parameter in each of the system lists of
MCMC sequences.

Usage
boa.chain.eval(expr, pname)

Arguments
expr S expression object used to formulate the new parameter. Typically, the new
parameter is a function of the existing parameters.
pname Name given to the new parameter.
boa.chain.gandr 7

Side Effects
The specified parameter is added to the session lists of MCMC sequences.

Author(s)
Brian J. Smith

boa.chain.gandr Gelman and Rubin Convergence Diagnostics

Description
Computes the Gelman and Rubin convergence diagnostics for a list of MCMC sequences. Estimates
are calculated from the second half of each sequence.

Usage
boa.chain.gandr(chain, chain.support, alpha, pnames, window, to)

Arguments
chain List of matrices whose columns and rows contain the monitored parameters and
the MCMC iterations, respectively. The iteration numbers and parameter names
must be assigned to the dimnames.
chain.support List of matrices whose columns and rows contain the monitored parameters and
the support (lower and upper limits), respectively.
alpha Quantile (1 - alpha / 2) at which to estimate the upper limit of the shrink factor.
pnames Character vector giving the names of the parameters to use in the analysis. If
omitted, all parameters are used.
window Proportion of interations to include in the analysis. If omitted, 50% are included.
to Largest iteration to include in the analysis. If omitted, no upper bound is set.

Value
psrf A vector containing the Gelman and Rubin (uncorrected) potential scale reduc-
tion factors for the monitored parameters.
csrf A matrix whose columns and rows are the Gelman and Rubin corrected scale
reduction factors (i.e. shrink factor estimates at the median and specified quan-
tile of the sampling distribution) and the monitored parameters, respectively. A
correction of (df + 3) / (df + 1) is applied to the scale reduction factors.
mpsrf A numeric value giving the multivariate potential scale reduction factor pro-
posed by Brooks and Gelman.
window A numeric vector with two elements giving the range of the iterations used in
the analysis.
8 boa.chain.import

Author(s)
Brian J. Smith, Nicky Best, Kate Cowles

References
1. Brooks, S. and Gelman, A. (1998). General methods for monitoring convergence of iterative
simulations. Journal of Computational and Graphical Statistics, 7(4), 434-55.
2. Gelman, A. and Rubin, D. B. (1992). Inference from iterative simulation using multiple se-
quences. Statistical Science, 7, 457-72.

See Also
boa.plot, boa.plot.bandg, boa.plot.gandr, boa.print.gandr

boa.chain.import Import MCMC Sequence

Description
Reads an MCMC sequence from an external file and adds it to the session lists of sequences.

Usage
boa.chain.import(prefix, path = boa.par("path"), type = "ASCII")

Arguments
prefix Character string giving the prefix for the file(s) in which the MCMC sequence
is stored.
path Character string giving the directory path in which the file(s) subsides.
type Character string specifying the type of data to be imported. Currently, the sup-
ported types are:
• "ASCII" : ASCII text file. Calls boa.importASCII to import data from
"prefix.txt".
• "BUGS" : BUGS output files. Calls boa.importBUGS to import data from
"prefix.ind" and "prefix.out".
• "S" : S data frame or matrix.

Value
A logical value indicating that the specified file(s) has been successfully imported.

Side Effects
The imported MCMC sequence is automatically added to the session lists of sequences via a call to
boa.chain.add.
boa.chain.info 9

Author(s)
Brian J. Smith

See Also
boa.chain.add, boa.importASCII, boa.importBUGS

boa.chain.info Information about MCMC Sequences

Description
Returns summary information from a list of MCMC sequences.

Usage
boa.chain.info(chain, chain.support)

Arguments
chain List of matrices whose columns and rows contain the monitored parameters and
the MCMC iterations, respectively. The iteration numbers and parameter names
must be assigned to the dimnames.
chain.support List of matrices whose columns and rows contain the monitored parameters and
the support (lower and upper limits), respectively.

Value
lnames Character vector giving the names of the MCMC sequences in the session list of
sequences.
pnames List of character vectors giving the parameter names in each of the MCMC
sequences.
iter List of numeric vectors giving the iterations from each MCMC sequence.
iter.range Matrix whose columns give the range of the iterations for the MCMC sequences
named in the rows.
support List of numeric vectors giving the support for the parameters in each of the
MCMC sequences.

Author(s)
Brian J. Smith

See Also
boa.print.info
10 boa.chain.subset

boa.chain.reset Reset MCMC Sequences

Description
Returns the data in the working list of MCMC sequences to the state it was in when originally im-
ported. This function undoes any subsetting or collapsing that was done via the boa.chain.collapse
or boa.chain.subset functions.

Usage
boa.chain.reset()

Side Effects
Returns the data in the working list of MCMC sequences to the state it was in when originally im-
ported. This function undoes any subsetting or collapsing that was done via the boa.chain.collapse
or boa.chain.subset functions.

Author(s)
Brian J. Smith

See Also
boa.chain.collapse, boa.chain.subset

boa.chain.subset Subset MCMC Sequences

Description
Selects a subset of the MCMC sequences stored in the working session list of sequences.

Usage
boa.chain.subset(lnames, pnames, iter)

Arguments
lnames Character vector giving the names of the MCMC sequences to include in the
subset. If omitted, all sequences are included.
pnames Character vector giving the names of the parameters to include in the subset. If
omitted, all parameters are included.
iter Character vector giving the names of the parameters to include in the subset. If
omitted, all parameters are included.
boa.chain.support 11

Value
A logical value indicating that the data has been successfully subsetted. If the requested subset
contains no data, the working session list is not modified and FALSE is returned.

Side Effects
The subsetted data, if not an empty set, is copied to the working session list of MCMC sequences
used in all analyses.

Author(s)
Brian J. Smith

See Also
boa.chain.collapse, boa.chain.reset

boa.chain.support Set Support for Parameters

Description
Modifies the support (range of possible values) for the parameters in the session lists of MCMC
sequences.

Usage
boa.chain.support(lnames, pnames, limits)

Arguments
lnames Character vector giving the names of the MCMC sequences over which to apply
the changes. If omitted, changes are applied to all sequences.
pnames Character vector giving the names of the parameters whose support is to be
modified.
limits Numeric vector with two elements giving the lower and upper limits, respec-
tively, of the support for the specified parameters. Unbounded lower or upper
limits should be specified as -Inf or Inf, respectively.

Value
A logical vector with two elements indicating that the support has been changed for variables in the
master list and working list of MCMC sequences, respectively.

Side Effects
The support for each of the specified parameters is changed in the session lists of MCMC sequences.
12 boa.geweke

Author(s)

Brian J. Smith

boa.geweke Geweke Convergence Diagnostics

Description

Computes the Geweke convergence diagnostics for the parameters in an MCMC sequence.

Usage

boa.geweke(link, p.first, p.last)

Arguments

link Matrix whose columns and rows contain the monitored parameters and the MCMC
iterations, respectively. The iteration numbers and parameter names must be as-
signed to dimnames(link).
p.first Proportion of iterations to include in the first window.
p.last Proportion of iterations to include in the last window.

Value

A matrix whose columns contain the Z-Scores and associated p-values and whose rows contain the
monitored parameters.

Author(s)

Brian J. Smith

References

Geweke, J. (1992). Evaluating the accuracy of sampling-based approaches to calculating posterior

moments. In Bayesian Statistics 4, (ed. J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M.
Smith). Clarendon Press, Oxford, UK.

See Also

boa.plot, boa.plot.geweke, boa.print.geweke

boa.handw 13

boa.handw Heidelberger and Welch Convergence Diagnostics

Description

Computes the Heidleberger and Welch convergence diagnostics for the parameters in an MCMC
sequence.

Usage

boa.handw(link, error, alpha)

Arguments

link Matrix whose columns and rows contain the monitored parameters and the MCMC
iterations, respectively. The iteration numbers and parameter names must be as-
signed to dimnames(link).
error Accuracy of the posterior estimates for the parameters.
alpha Alpha level for the confidence in the sample mean of the retained iterations.

Value

A matrix whose columns and rows are the Heidleberger and Welch convergence diagnostics (i.e.
stationarity test, number of iterations to keep and to drop, Cramer-von-Mises statistic, halfwidth
test, mean, and halfwidth) and the monitored parameters, respectively.

Author(s)

Brian J. Smith, Nicky Best, Kate Cowles

References

Heidelberger, P. and Welch, P. (1983). Simulation run length control in the presence of an initial
transient. Operations Research, 31, 1109-44.

See Also

boa.print.handw
14 boa.importASCII

boa.hpd Highest Probability Density Interval

Description
Estimates the highest probability density (HPD) interval for the given parameter draws. Uses the
Chen and Shao algorithm assuming a unimodal marginal posterior distribution.

Usage
boa.hpd(x, alpha)

Arguments
x MCMC draws from the marginal posterior to use in computing the HPD.
alpha Specifies the 100*(1 - alpha)% interal to compute.

Value
A vector containing the lower and upper bound of the HPD interval, labeled "Lower Bound" and
"Upper Bound", respectively.

Author(s)
Brian J. Smith

References
Chen, M-H. and Shao, Q-M. (1999). Monte Carlo estimation of Bayesian credible and HPD inter-
vals. Journal of Computational and Graphical Statistics, 8(1), 69-92.

boa.importASCII Import ASCII Data

Description
Import data from an ASCII text file. The variables and iterations should appear in the columns and
rows, respectively, of the file. The variable names must be given in the first row. The iteration
numbers are taken from the the column entitled "iter" (case-sensitive), if it exists; otherwise, the
numbers 1..n are used, where n is the number of rows. The columns may be separated by white
space or tabs.

Usage
boa.importASCII(prefix, path = NULL)
boa.importBUGS 15

Arguments
prefix Character string giving the prefix for the files in which the ASCII data is stored.
boa.importASCII() looks for the file "prefix.txt".
path Character string giving the directory path in which the file subsides. This argu-
ment may be omitted if the file is located in the current working directory. The
specified path should not end with a slash(es).

Value
If the data is successfully imported, a matrix is returned whose columns and rows contain the
monitored parameters and the MCMC iterations, respectively. The iteration numbers and parameter
names are stored in the dimnames of the returned matrix. Otherwise, NULL is returned.

Author(s)
Brian J. Smith

See Also
boa.chain.import, boa.importBUGS, boa.importMatrix

boa.importBUGS Import BUGS Data

Description
Import data from BUGS output files.

Usage
boa.importBUGS(prefix, path = NULL)

Arguments
prefix Character string giving the prefix for the files in which the BUGS output is
stored. boa.importBUGS() looks for the two files "prefix.ind" and "prefix.out".
path Character string giving the directory path in which the file subsides. This argu-
ment may be omitted if the file is located in the current working directory. The
specified path should not end with a slash(es).

Value
If the data is successfully imported, a matrix is returned whose columns and rows contain the
monitored parameters and the MCMC iterations, respectively. The iteration numbers and parameter
names are stored in the dimnames of the returned matrix. Otherwise, NULL is returned.
16 boa.importMatrix

Author(s)

Brian J. Smith

See Also

boa.chain.import, boa.importASCII, boa.importMatrix

boa.importMatrix Import ASCII Data

Description

Import data from an S numeric matrix object. The variables and iterations should appear in the
columns and rows, respectively, of the matrix. The variable names and iteration numbers may
be optionally specified in the dimnames of the matrix object. Otherwise, the iterations will be
numbered 1..n, where n is the number of rows.

Usage

boa.importMatrix(prefix)

Arguments

prefix Character string giving the name of the S object.

Value

If the data is successfully imported, a matrix is returned whose columns and rows contain the
monitored parameters and the MCMC iterations, respectively. The iteration numbers and parameter
names are stored in the dimnames of the returned matrix. Otherwise, NULL is returned.

Author(s)

Brian J. Smith

See Also

boa.chain.import, boa.importASCII, boa.importBUGS

boa.init 17

boa.init Start Session

Description
boa.init() is the first function called to start a BOA session when using the command-line. It sets up
the internal data structures and initializes them with the appropriate default values.

Usage
boa.init(recover = FALSE)

Arguments
recover a logical value for use if the previous BOA menu session terminated unexpect-
edly. It may be possible to crash the menu system by supplying the wrong type
of data. In the event of a crash, recover = TRUE may be used to ensure that no
data is lost.

Author(s)
Brian J. Smith

See Also
boa.load, boa.quit

boa.load Load Session

Description
Loads the data and global parameter settings from a previously saved BOA session.

Usage
boa.load(name, envir = globalenv())

Arguments
name Character string giving the name of the object containing the session to be
loaded.
envir The ’environment’ from which the object should come. For more information,
consult the help documentation in R on the get function.
18 boa.menu

Value
A logical value indicating that the object was successfully loaded.

Author(s)
Brian J. Smith

boa.menu Interactive BOA Menu

Description
Starts the interactive menu for BOA. Provides a menu-driven interface to all of the convergence
diagnostics and statistical and graphical analysis tools.

Usage
boa.menu(recover = FALSE)

Arguments
recover a logical value for use if the previous BOA menu session terminated unexpect-
edly. It may be possible to crash the menu system by supplying the wrong type
of data. In the event of a crash, recover = TRUE may be used to ensure that no
data is lost.

Warning
Do not use the recover argument unless starting the menu immediately after a crash.

Note
boa.menu is the only function in the BOA library that need be called in order to use the menu-driven
interface.

Author(s)
Brian J. Smith

Examples
## Not run:
## Start the menu system
boa.menu()

## End(Not run)
boa.par 19

boa.par Global Parameters

Description
Displays and sets the global parameters stored internally for use during a BOA session.

Usage
boa.par(...)

Arguments
... A list may be given as the only argument, or a character string given as the only
argument, or any number of arguments may be in the <name> = <value> form,
or no argument at all may be given.

Value
If no arguments are supplied, a list of the current values is returned. If a character string is given,
the current value of the named variable is returned. Otherwise, a list of the named variables and
their old values is returned, but not printed.

Parameter Names and Default Values

acf.lags = c(1, 5, 10, 50) Numeric vector of lags at which to estimate the autocorrelation function.
alpha = 0.05 Type I error rate used for all statistical tests and confidence intervals.
ASCIIext = ".txt" Character string giving the filename extension used when importing ASCII
files.
bandwidth = function(x) 0.5 * diff(range(x)) / (log(length(x)) + 1) Function for computing the band-
width used in estimating the density functions for parameters. This should take one argument
which is a numeric vector of data on which density estimation is to be performed. A constant
bandwidth may be specified by having this function return the desired constant.
batch.size = 50 Number of iterations to include in each batch when computing batch means and
lag-1 batch autocorrelations. The batch size has the single largest impact on the time required
to compute summary statistics. The computation time is decreased dramatically as the batch
size increases. Consequently, users may want to increase the value of this variable for long
MCMC sequences.
dev = «see below» Character string giving the name of the function that creates graphics windows
on the current platform. For Unix systems this is either "motif", "openlook", or "X11". The
default is "motif" for the UNIX S-PLUS, "win.graph" for Windows S-PLUS, "X11" for UNIX
R, and "windows" for Windows R.
dev.list = numeric(0) Numeric vector containing the active graphics windows in use by the pro-
gram. This is automatically maintained by the program, user should not directly modify this
variable.
20 boa.par

gandr.bins = 20 Number of line segments within the MCMC sequence at which to plot the Gelman
and Rubin shrink factors.
gandr.win = 0.50 Proportion of iterations to include in the Brooks, Gelman, and Rubin Statistics.
geweke.bins = 10 Number of line segments within the MCMC sequence at which to plot the
Geweke convergence diagnostics.
geweke.first = 0.1 Proportion of iterations to include in the first window when computing the
Geweke convergence diagnostics.
geweke.last = 0.5 Proportion of iterations to include in the last window when computing the Geweke
convergence diagnostics.
handw.error = 0.1 Accuracy of the posterior estimates when computing the Heidleberger and
Welch convergence diagnostics.
kernel = "gaussian" Character string giving the type of window used in estimating the density
functions for parameters. Other choices are "cosine", "rectangular", or "triangular".
legend = TRUE Logical value indicating that a legend be included in the plots.
path = "" Character string giving the directory path in which the raw data files are stored. The
default may be used if the files are located in the current working directory. The specified path
should not end with a slash(es).
par = list() List specifying graphics parameters passed to the par function for the construction of
new plots.
plot.mfdim = c(3, 2) Numeric vector giving the maximum number of rows and columns, respec-
tively, of plots to include in a single graphics window.
plot.new = F Logical value indicating that a new graphics window be automatically opened upon
successive calls to boa.plot(). Otherwise, previous graphics windows will be closed.
plot.onelink = FALSE Logical value indicating that each plot should include only one MCMC
sequence. Otherwise, all sequences are displayed on the same plot.
quantiles = c(0.025, 0.5, 0.975) Vector of probabilities at which to compute the quantiles. Values
must be between 0 and 1.
randl.error = 0.005 Desired amount of error in estimating the quantile specified in the Raftery and
Lewis convergence diagnostics.
randl.delta = 0.001 Delta valued used in computing the Raftery and Lewis convergence diagnos-
tics.
randl.q = 0.025 Quantile to be estimated in computing the Raftery and Lewis convergence diag-
nostics.
title = TRUE Logical value indicating that a title be added to the plots.

Side Effects
When variables are set, boa.par() modifies the internal list .boa.par. If boa.par() is called with either
a list as the single argument, or with one or more arguments in the <name> = <value> form, the
variables specified by the names in the arguments are modified.

Author(s)
Brian J. Smith
boa.plot 21

boa.plot Plot Parameters in MCMC Sequences

Description
Automatically generates the specified plot type for all parameters in the working session list of
MCMC sequences. This function takes care of all the plotting tasks - opening windows, setting the
number of plots per page, and adding titles.

Usage
boa.plot(type, dev = boa.par("dev"), mfdim = boa.par("plot.mfdim"),
newplot = boa.par("plot.new"), onelink = boa.par("plot.onelink"),
title = boa.par("title"))

Arguments
type The type of plots to generate. The supported types are:
• "acf" = autocorrelation functions
• "bandg" = Brooks and Gelman multivariate shrink factors
• "density" = density functions
• "gandr" = Gelman and Rubin shrink factors
• "geweke" = Geweke convergence diagnostics
• "history" = running means
• "trace" = trace histories
dev Character string giving the name of the function that creates graphics windows
on the current platform. For Unix systems this is either "motif", "openlook", or
"X11". For windows, this should be set to "win.graph"
mfdim Numeric vector giving the maximum number of rows and columns, respectively,
of plots to include in a single graphics window. If only one graphics window is
opened, ’mfdim’ is proportionately scaled down so as to minimize the number
of empty frames within that window.
newplot Logical value indicating that a new graphics window be automatically opened.
Otherwise, previous graphics windows will be closed.
onelink Logical value indicating that each plot should include only one MCMC se-
quence. Otherwise, all sequences are displayed on the same plot.
title Logical value indicating that a title be added to the plot.

Value
A logical value indicating that the plots were successfully created.

Author(s)
Brian J. Smith
22 boa.plot.acf

See Also

boa.plot.acf, boa.plot.bandg, boa.plot.density, boa.plot.gandr, boa.plot.geweke, boa.plot.history,

boa.plot.trace

boa.plot.acf Plot Autocorrelation Function

Description

Creates a single plot of the lag autocorrelations for a specified parameter.

Usage

boa.plot.acf(lname, pname, annotate = boa.par("legend"))

Arguments

lname Character string giving the name of the desired MCMC sequence in the working
session list of sequences.
pname Character string giving the name of the parameter to be plotted.
annotate Logical value indicating that a legend be included in the plot.

Value

A logical value indicating that the plot was successfully created.

Author(s)

Brian J. Smith

See Also

boa.acf, boa.print.acf
boa.plot.bandg 23

boa.plot.bandg Plot Brooks and Gelman Multivariate Shrink Factors

Description

Plots the Brooks and Gelman multivariate shrink factors within different line segments across the
MCMC sequences. This diagnostic is a multivariate extension to the Gelman and Rubin shrink
factors.

Usage

boa.plot.bandg(bins = boa.par("gandr.bins"), win = boa.par("gandr.win"),

annotate = boa.par("legend"))

Arguments

bins Number of line segments within the MCMC sequence at which to plot the Gel-
man and Rubin shrink factors. The first segment contains the first 50 iterations;
the remaining iterations are partitioned into equal bins and added incrementally
to construct the remaining line segments. The shrink factors are plotted against
the maximum iteration number for the segment. Cubic splines are used to inter-
polate through the point estimates for each segment.
win Proportion of iterations to include in the Brooks, Gelman, and Rubin Statistics.
annotate Logical value indicating that a legend be included in the plot.

Value

A logical value indicating that the plot was successfully created.

Author(s)

Brian J. Smith

See Also

boa.chain.gandr, boa.plot, boa.plot.gandr, boa.print.gandr

24 boa.plot.density

boa.plot.density Plot Density Functions

Description

Estimates and displays, in a single plot, the density function(s) for the specified parameter(s).

Usage

boa.plot.density(lnames, pname, bandwidth = boa.par("bandwidth"),

window = boa.par("kernel"), annotate = boa.par("legend"))

Arguments

lnames Character vector giving the names of the desired MCMC sequence in the work-
ing session list of sequences.
pname Character string giving the name of the parameter to be plotted.
bandwidth Function for computing the bandwidth used in estimating the density functions
for parameters. This should take one argument which is a numeric vector of data
on which density estimation is to be performed. A constant bandwidth may be
specified by having this function return the desired constant.
window Character string giving the type of window used in estimating the density func-
tions for the parameters. Available choices are "cosine", "gaussian", "rectangu-
lar", or "triangular".
annotate Logical value indicating that a legend be included in the plot.

Value

A logical value indicating that the plot was successfully created.

Author(s)

Brian J. Smith

See Also

boa.plot
boa.plot.gandr 25

boa.plot.gandr Plot Gelman and Rubin Shrink Factors

Description

Creates a single plot of the Gelman and Rubin shrink factors within different line segments for a
parameter in an MCMC sequence.

Usage

boa.plot.gandr(pname, bins = boa.par("gandr.bins"), alpha = boa.par("alpha"),

win = boa.par("gandr.win"), annotate = boa.par("legend"))

Arguments

pname Character string giving the name of the parameter in the working session list of
MCMC sequences to be plotted.
bins Number of line segments within the MCMC sequence at which to plot the Gel-
man and Rubin shrink factors. The first segment contains the first 50 iterations;
the remaining iterations are partitioned into equal bins and added incrementally
to construct the remaining line segments. The shrink factors are plotted against
the maximum iteration number for the segment. Cubic splines are used to inter-
polate through the point estimates for each segment.
alpha Quantile (1 - alpha / 2) at which to estimate the upper limit of the shrink factor.
win Proportion of iterations to include in the Brooks, Gelman, and Rubin Statistics.
annotate Logical value indicating that a legend be included in the plot.

Value

A logical value indicating that the plot was successfully created.

Author(s)

Brian J. Smith

See Also

boa.chain.gandr, boa.plot, boa.plot.bandg, boa.print.gandr

26 boa.plot.geweke

boa.plot.geweke Plot Geweke Convergence Diagnostics

Description

Creates a single plot of the Geweke convergence diagnostics within different line segments for a
parameter in an MCMC sequence.

Usage

boa.plot.geweke(lname, pname, bins = boa.par("geweke.bins"),

p.first = boa.par("geweke.first"), p.last = boa.par("geweke.last"),
alpha = boa.par("alpha"), annotate = boa.par("legend"))

Arguments

lname Character string giving the name of the desired MCMC sequence in the working
session list of sequences.
pname Character string giving the name of the parameter to be plotted.
bins Number of line segments within the MCMC sequence at which to plot the
Geweke convergence diagnostics. The ith line segment contains the last ((bins
- i + 1) / bins)*100 bins. This may lead to segments in which there are too few
iterations to compute the convergence diagnostics. Such segments, if they exist,
are automatically omitted from the calculations.
p.first Proportion of iterations to include in the first window.
p.last Proportion of iterations to include in the last window.
alpha Alpha level for the rejection region lines drawn on the graph.
annotate Logical value indicating that a legend be included in the plot.

Value

A logical value indicating that the plot was successfully created.

Author(s)

Brian J. Smith, Nicky Best, Kate Cowles

See Also

boa.geweke, boa.plot, boa.print.geweke

boa.plot.history 27

boa.plot.history Plot Parameter Estimation Histories

Description
Computes and displays, in a single plot, the running mean(s) for the specified parameter(s).

Usage
boa.plot.history(lnames, pname, annotate = boa.par("legend"))

Arguments
lnames Character vector giving the name of the desired MCMC sequence in the working
session list of sequences.
pname Character vector giving the names of the parameters to be plotted.
annotate Logical value indicating that a legend be included in the plot.

Value
A logical value indicating that the plot was successfully created.

Author(s)
Brian J. Smith

See Also
boa.plot

boa.plot.par Set Plotting Parameters

Description
Set Plotting Parameters

Usage
boa.plot.par(mfdim = c(1, 1), title = TRUE)

Arguments
mfdim Numeric vector with two elements giving the number of rows and column, re-
spectively, of plots to display on the page. Plots will be drawn row-by-row.
title Logical value indicating that a title be added to the plot.
28 boa.plot.trace

Author(s)
Brian J. Smith

boa.plot.title Add Plot Title

Description
Adds a title to the graphics window. This function should be called after all plots have been added
to the target graphics window.

Usage
boa.plot.title(text)

Arguments
text Character string giving the title to be centered and displayed across the top of
the graphics window.

Author(s)
Brian J. Smith

boa.plot.trace Plot Trace Histories

Description
Displays, in a single plot, the trace histories for the specified parameter(s).

Usage
boa.plot.trace(lnames, pname, annotate = boa.par("legend"))

Arguments
lnames Character vector giving the name of the desired MCMC sequence in the working
session list of sequences.
pname Character string giving the name of the parameters to be plotted.
annotate Logical value indicating that a legend be included in the plot.

Value
A logical value indicating that the plot was successfully created.
boa.print.acf 29

Author(s)
Brian J. Smith

See Also
boa.plot

boa.print.acf Print Autocorrelation Functions

Description
Iteratively calls boa.acf() to display the lag autocorrelations for the parameters in each of the MCMC
sequences in the working session list of sequences.

Usage
boa.print.acf(lags = boa.par("acf.lags"))

Arguments
lags Numeric vector of lags at which to estimate the autocorrelation functions.

Author(s)
Brian J. Smith

See Also
boa.acf, boa.plot, boa.plot.acf

boa.print.cor Print Correlation Matrices

Description
Iteratively computes and displays the correlation matrices for the parameters in each of the MCMC
sequences in the working session list of sequences.

Usage
boa.print.cor()

Author(s)
Brian J. Smith
30 boa.print.geweke

boa.print.gandr Print Gelman and Rubin Convergence Diagnostics

Description
Calls boa.chain.gandr() and displays the Gelman and Rubin convergence diagnostics for the MCMC
sequences in the working session list of sequences.

Usage
boa.print.gandr(alpha = boa.par("alpha"), win = boa.par("gandr.win"))

Arguments
alpha Quantile (1 - alpha / 2) at which to estimate the upper limit of the corrected
shrink factor.
win Proportion of iterations to include in the Brooks, Gelman, and Rubin Statistics.

Author(s)
Brian J. Smith

See Also
boa.chain.gandr, boa.plot, boa.plot.bandg, boa.plot.gandr

boa.print.geweke Print Geweke Convergence Diagnostics

Description
Iteratively calls boa.geweke() to display the Geweke convergence diagnostics for the parameters in
each of the MCMC sequences in the working session list of sequences.

Usage
boa.print.geweke(p.first = boa.par("geweke.first"), p.last = boa.par("geweke.last"))

Arguments
p.first Proportion of iterations to include in the first window.
p.last Proportion of iterations to include in the last window.

Author(s)
Brian J. Smiht
boa.print.handw 31

See Also
boa.geweke, boa.plot, boa.plot.geweke

boa.print.handw Print Heidelberger and Welch Convergence Diagnostics

Description
Iteratively calls boa.handw() to display the Heidelberger and Welch convergence diagnostics for the
parameters in each of the MCMC sequences in the working session list of sequences.

Usage
boa.print.handw(error = boa.par("handw.error"), alpha = boa.par("alpha"))

Arguments
error Accuracy of the posterior estimates for the monitored parameters.
alpha Alpha level for the confidence in the sample mean of the retained iterations.

Author(s)
Brian J. Smith

See Also
boa.handw

boa.print.hpd Print Highest Probability Density Intervals

Description
Iteratively calls boa.hpd() to display the highest probability density (HPD) intervals for the param-
eters in each of the MCMC sequences in the working session list of sequences.

Usage
boa.print.hpd(alpha = boa.par("alpha"))

Arguments
alpha Specifies the 100*(1-alpha)% HPD intervals to be computed.
32 boa.print.info

Author(s)

Brian J. Smith

See Also

boa.hpd

boa.print.info Print Information about MCMC Sequences

Description

Iteratively calls boa.chain.info() to display information from the MCMC sequences in the specified
session list of sequences.

Usage

boa.print.info(which = "work")

Arguments

which Character string specifying which session list of MCMC sequences for which to
print information. The two choices are "work" (used in all analyses) or "data"
(the template for "work").

Value

The full list obtained from boa.chain.info() is returned, but not printed.

Author(s)

Brian J. Smith

See Also

boa.chain.info
boa.print.par 33

boa.print.par Print Global Parameters’ Descriptions and Current Values

Description

Displays a description of and the current value for all global parameters.

Usage

boa.print.par(group)

Arguments

group Character string specifying which parameter group to display. The groups are
"Analysis", "Data", and "Plot". If omitted, information on all global parameters
is displayed.

Value

The character matrix obtained from boa.pardesc() is returned, but not printed.

Author(s)

Brian J. Smith

See Also

boa.pardesc

boa.print.randl Print Raftery and Lewis Convergence Diagnostics

Description

Iteratively calls boa.randl() to display the Raftery and Lewis convergence diagnostics for the pa-
rameters in each of the MCMC sequences in the working session list of sequences.

Usage

boa.print.randl(q = boa.par("randl.q"), error = boa.par("randl.error"),

prob = 1 - boa.par("alpha"), delta = boa.par("randl.delta"))
34 boa.print.stats

Arguments
q Quantile to be estimated.
error Desired amount of error in estimating the specified quantile ’q’.
prob Probability of attaining the desired degree of ’error’.
delta Delta value used in computing the convergence diagnostic.

Author(s)
Brian J. Smith

See Also
boa.randl

boa.print.stats Print Summary Statistics

Description
Iteratively calls boa.stats() to display summary statistics for the parameters in each of the MCMC
sequences in the working session list of sequences.

Usage
boa.print.stats(probs = boa.par("quantiles"), batch.size = boa.par("batch.size"))

Arguments
probs Vector of probabilities at which to compute the quantiles. Values must be be-
tween 0 and 1.
batch.size Number of iterations to include in each batch when computing batch means and
lag-1 batch autocorrelation function.

Author(s)
Brian J. Smith

See Also
boa.stats
boa.quit 35

boa.quit Quit Session

Description
boa.quit() is called to end a BOA session. It removes the objects used to store the session lists of
MCMC sequences and the global parameters. Failure to do this may result in lost or lingering data.

Usage
boa.quit()

Author(s)
Brian J. Smith

See Also
boa.save, boa.init

boa.randl Raftery and Lewis Convergence Diagnostics

Description
Computes the Raftery and Lewis convergence diagnostics for the parameters in an MCMC se-
quence.

Usage
boa.randl(link, q, error, prob, delta)

Arguments
link Matrix whose columns and rows contain the monitored parameters and the MCMC
iterations, respectively. The iteration numbers and parameter names must be as-
signed to dimnames(link).
q Quantile to be estimated.
error Desired amount of error in estimating the specified quantile ’q’.
prob Probability of attaining the desired degree of error - ’error’.
delta Delta value used in computing the convergence diagnostics.

Value
A matrix whose columns and rows are the Raftery and Lewis convergence diagnostics (i.e. thin,
burn-in, total, lower bound, and dependence factor) and the monitored parameters, respectively.
36 boa.save

Author(s)
Brian J. Smith, Nicky Best, Kate Cowles

References
1. Raftery, A. L. and Lewis, S. (1992a). Comment: One long run with diagnostics: Implementa-
tion strategies for Markov chain Monte Carlo. Statistical Science, 7, 493-7.
2. Raftery, A. L. and Lewis, S. (1992b). How many iterations in the Gibbs sampler? In Bayesian
Statistics 4, (ed. J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Smith), pp. 763-74.
Oxford University Press.

See Also
boa.print.randl

boa.save Save Session

Description
Save the current state of the session lists of MCMC sequences and the global parameters to a
database object.

Usage
boa.save(name, envir = globalenv(), replace = FALSE)

Arguments
name Character string giving the name of the object to which the current session
should be saved.
envir The ’environment’ to which the object should be saved. For more information,
consult the help documentation in R on the assign() function.
replace Logical value indicating whether object name should be replaced if it already
exists.

Value
A logical value indicating that the session was successfully saved to the specified object.

Author(s)
Brian J. Smith
boa.stats 37

boa.stats Summary Statistics

Description

Computes summary statistics for the parameters in an MCMC sequence.

Usage

boa.stats(link, probs, batch.size)

Arguments

link Matrix whose columns and rows contain the monitored parameters and the MCMC
iterations, respectively. The iteration numbers and parameter names must be as-
signed to dimnames(link).
probs Vector of probabilities at which to compute the quantiles. Values must be be-
tween 0 and 1.
batch.size Number of iterations to include in each batch when computing batch means and
lag-1 batch autocorrelations.

Value

A matrix whose columns and rows contain the summary statistics (i.e. sample mean, standard
deviation, naive standard error, MC error, batch standard error, lag-1 batch autocorrelation, specified
quantiles, minimum and maximum iteration numbers, and total iterations in the sample) and the
monitored parameters, respectively.

Author(s)

Brian J. Smith

See Also

boa.print.stats
38 line

line BUGS Line Example

Description
The Line example involves a linear regression analysis of the data points (1,1), (2,3), (3,3), (4,3),
and (5,5). The proposed Bayesian model is

y[i] N (mu[i], tau)

mu[i] = alpha + beta ∗ (x[i] − mean(x[]))

with the following priors:
alpha N (0, 0.0001)
beta N (0, 0.0001)
tau Gamma(0.001, 0.001)
Two parallel chains from the MCMC sampler were generated and the output saved in the S data
frames line1 and line2.

Usage
data(line)

Format
The data frames line1 and line2 each containing 200 observations.

References
Spiegelhalter, D., Thomas, A. and Best, N., (2000). WinBugs Version 1.4 User Manual.
Index

∗Topic datasets boa.chain.info, 9

line, 38 boa.chain.reset, 10
∗Topic hplot boa.chain.subset, 10
boa.plot, 21 boa.chain.support, 11
boa.plot.acf, 22 boa.importASCII, 14
boa.plot.bandg, 23 boa.importBUGS, 15
boa.plot.density, 24 boa.importMatrix, 16
boa.plot.gandr, 25 boa.init, 17
boa.plot.geweke, 26 boa.load, 17
boa.plot.history, 27 boa.par, 19
boa.plot.trace, 28 boa.plot.par, 27
∗Topic interface boa.plot.title, 28
boa.menu, 18 boa.quit, 35
∗Topic print boa.save, 36
boa.print.acf, 29
boa.acf, 2, 22, 29
boa.print.cor, 29
boa.chain, 3
boa.print.gandr, 30
boa.chain.add, 4, 8, 9
boa.print.geweke, 30
boa.chain.collapse, 4, 5, 10, 11
boa.print.handw, 31
boa.chain.del, 6
boa.print.hpd, 31
boa.chain.eval, 6
boa.print.info, 32 boa.chain.gandr, 7, 23, 25, 30
boa.print.par, 33 boa.chain.import, 4, 5, 8, 15, 16
boa.print.randl, 33 boa.chain.info, 9, 32
boa.print.stats, 34 boa.chain.reset, 4, 5, 10, 11
∗Topic univar boa.chain.subset, 4, 5, 10, 10
boa.acf, 2 boa.chain.support, 11
boa.chain.gandr, 7 boa.geweke, 12, 26, 31
boa.geweke, 12 boa.handw, 13, 31
boa.handw, 13 boa.hpd, 14, 32
boa.hpd, 14 boa.importASCII, 8, 9, 14, 16
boa.randl, 35 boa.importBUGS, 8, 9, 15, 15, 16
boa.stats, 37 boa.importMatrix, 15, 16, 16
∗Topic utilities boa.init, 17, 35
boa.chain, 3 boa.load, 17, 17
boa.chain.add, 4 boa.menu, 18
boa.chain.collapse, 5 boa.par, 19
boa.chain.del, 6 boa.pardesc, 33
boa.chain.eval, 6 boa.plot, 3, 8, 12, 21, 23–27, 29–31
boa.chain.import, 8 boa.plot.acf, 3, 22, 22, 29

39
40 INDEX

boa.plot.bandg, 8, 22, 23, 25, 30

boa.plot.density, 22, 24
boa.plot.gandr, 8, 22, 23, 25, 30
boa.plot.geweke, 12, 22, 26, 31
boa.plot.history, 22, 27
boa.plot.par, 27
boa.plot.title, 28
boa.plot.trace, 22, 28
boa.print.acf, 3, 22, 29
boa.print.cor, 29
boa.print.gandr, 8, 23, 25, 30
boa.print.geweke, 12, 26, 30
boa.print.handw, 13, 31
boa.print.hpd, 31
boa.print.info, 9, 32
boa.print.par, 33
boa.print.randl, 33, 36
boa.print.stats, 34, 37
boa.quit, 17, 35
boa.randl, 34, 35
boa.save, 35, 36
boa.stats, 34, 37

line, 38
line1 (line), 38
line2 (line), 38