Package 'plotMCMC' reference manual

Package 'plotMCMC'

Title:	MCMC Diagnostic Plots
Description:	Markov chain Monte Carlo diagnostic plots. The purpose of the package is to combine existing tools from the 'coda' and 'lattice' packages, and make it easy to adjust graphical details.
Authors:	Arni Magnusson [aut, cre], Ian Stewart [aut]
Maintainer:	Arni Magnusson <[email protected]>
License:	GPL-3
Version:	2.0.1
Built:	2024-11-15 04:21:25 UTC
Source:	https://github.com/arni-magnusson/plotmcmc

Title:

MCMC Diagnostic Plots

Description:

Markov chain Monte Carlo diagnostic plots. The purpose of the package is to combine existing tools from the 'coda' and 'lattice' packages, and make it easy to adjust graphical details.

Authors:

Arni Magnusson [aut, cre], Ian Stewart [aut]

Maintainer:

Arni Magnusson <[email protected]>

License:

GPL-3

Version:

2.0.1

Built:

2024-11-15 04:21:25 UTC

Source:

https://github.com/arni-magnusson/plotmcmc

MCMC Diagnostic Plots

Description

Markov chain Monte Carlo diagnostic plots. The purpose of the package is to combine existing tools from the coda and lattice packages, and make it easy to adjust graphical details.

Details

Diagnostic plots:

`plotTrace`	trends
`plotAuto`	thinning
`plotCumu`	convergence
`plotSplom`	confounding of parameters

Posterior plots:

`plotDens`	posterior(s)
`plotQuant`	multiple posteriors on a common y axis

Examples:

`xpar`	model parameters
`xrec`	recruitment
`xbio`	biomass
`xpro`	future projected biomass

Note

browseVignettes() shows a vignette with all the example plots.

The plot functions assume that MCMC results are stored either as a plain numeric vector (single chain) or in a data.frame (multiple chains). The mcmc class is also supported.

Author(s)

Arni Magnusson and Ian Stewart.

References

Fournier, D.A., Skaug, H.J., Ancheta, J., Ianelli, J., Magnusson, A., Maunder, M.N., Nielsen, A., and Sibert, J. (2012). AD Model Builder: using automatic differentiation for statistical inference of highly parameterized complex nonlinear models. Optimization Methods and Software, 27, 233–249. doi:10.1080/10556788.2011.597854

Magnusson, A., Punt, A.E., and Hilborn, R. (2013). Measuring uncertainty in fisheries stock assessment: the delta method, bootstrap, and MCMC. Fish and Fisheries, 14, 325–342. doi:10.1111/j.1467-2979.2012.00473.x

Plot MCMC Autocorrelation

Description

Plot Markov chain Monte Carlo autocorrelation over a range of lag values. This is a diagnostic plot for deciding whether a chain needs further thinning.

Usage

plotAuto(mcmc, thin=1, log=FALSE, base=10, main=NULL, xlab="Lag",
         ylab="Autocorrelation", lty=1, lwd=1, col="black", ...)
plotAuto(mcmc, thin=1, log=FALSE, base=10, main=NULL, xlab="Lag",
         ylab="Autocorrelation", lty=1, lwd=1, col="black", ...)

Arguments

`mcmc`	MCMC chain(s) as a vector, data frame or `mcmc` object.
`thin`	interval to subsample chain(s), or 1 to keep chain intact.
`log`	whether values should be log-transformed.
`base`	logarithm base.
`main`	main title.
`xlab`	x-axis label.
`ylab`	y-axis label.
`lty`	line type.
`lwd`	line width.
`col`	line color.
`...`	passed to `autocorr.plot`, `title`, and `axis`.

Value

Null, but a plot is drawn on the current graphics device.

Note

The Args function from the gdata package is recommended for reviewing the arguments, instead of args.

Examples

plotAuto(xpar$R0)
plotAuto(xpar$R0, thin=10)
plotAuto(xpar, lag.max=50, ann=FALSE, axes=FALSE)
plotAuto(xpar$R0)
plotAuto(xpar$R0, thin=10)
plotAuto(xpar, lag.max=50, ann=FALSE, axes=FALSE)

Plot MCMC Cumulative Quantiles

Description

Plot Markov chain Monte Carlo cumulative quantiles. This is a diagnostic plot for deciding whether the chain has converged.

Usage

plotCumu(mcmc, probs=c(0.025,0.975), div=1, log=FALSE, base=10,
         main=NULL, xlab="Iterations", ylab="Value", lty.median=1,
         lwd.median=2, col.median="black", lty.outer=2, lwd.outer=1,
         col.outer="black", ...)
plotCumu(mcmc, probs=c(0.025,0.975), div=1, log=FALSE, base=10,
         main=NULL, xlab="Iterations", ylab="Value", lty.median=1,
         lwd.median=2, col.median="black", lty.outer=2, lwd.outer=1,
         col.outer="black", ...)

Arguments

`mcmc`	MCMC chain(s) as a vector, data frame or `mcmc` object.
`probs`	vector of outer quantiles to draw, besides the median.
`div`	denominator to shorten values on the y axis.
`log`	whether values should be log-transformed.
`base`	logarithm base.
`main`	main title.
`xlab`	x-axis label.
`ylab`	y-axis label.
`lty.median`	line type of median.
`lwd.median`	line width of median.
`col.median`	color of median.
`lty.outer`	line type of outer quantiles.
`lwd.outer`	line width of outer quantiles.
`col.outer`	color of outer quantiles.
`...`	passed to `cumuplot`, `title`, and `axis`.

Value

Null, but a plot is drawn on the current graphics device.

Note

The Args function from the gdata package is recommended for reviewing the arguments, instead of args.

Examples

plotCumu(xpar$R0, main="R0")
plotCumu(xpar$cSfull, main="cSfull")
plotCumu(xpar, probs=c(0.25,0.75), ann=FALSE, axes=FALSE)
plotCumu(xpar$R0, main="R0")
plotCumu(xpar$cSfull, main="cSfull")
plotCumu(xpar, probs=c(0.25,0.75), ann=FALSE, axes=FALSE)

Plot MCMC Density

Description

Plot Markov chain Monte Carlo density. This is an approximation of the posterior probability density function.

Usage

plotDens(mcmc, probs=c(0.025,0.975), points=FALSE, axes=TRUE,
         same.limits=FALSE, between=list(x=axes,y=axes), div=1,
         log=FALSE, base=10, main=NULL, xlab=NULL, ylab=NULL,
         cex.main=1.2, cex.lab=1, cex.axis=0.8, cex.strip=0.8,
         col.strip="gray95", las=0, tck=0.5, tick.number=5,
         lty.density=1, lwd.density=3, col.density="black",
         lty.median=2, lwd.median=1, col.median="darkgray", lty.outer=3,
         lwd.outer=1, col.outer="darkgray", pch="|", cex.points=1,
         col.points="black", plot=TRUE, ...)
plotDens(mcmc, probs=c(0.025,0.975), points=FALSE, axes=TRUE,
         same.limits=FALSE, between=list(x=axes,y=axes), div=1,
         log=FALSE, base=10, main=NULL, xlab=NULL, ylab=NULL,
         cex.main=1.2, cex.lab=1, cex.axis=0.8, cex.strip=0.8,
         col.strip="gray95", las=0, tck=0.5, tick.number=5,
         lty.density=1, lwd.density=3, col.density="black",
         lty.median=2, lwd.median=1, col.median="darkgray", lty.outer=3,
         lwd.outer=1, col.outer="darkgray", pch="|", cex.points=1,
         col.points="black", plot=TRUE, ...)

Arguments

`mcmc`	MCMC chain(s) as a vector, data frame or `mcmc` object.
`probs`	vector of outer quantiles to draw, besides the median.
`points`	whether individual points should be plotted along the x axis.
`axes`	whether axis values should be plotted.
`same.limits`	whether panels should have same x-axis limits.
`between`	list with `x` and `y` indicating panel spacing.
`div`	denominator to shorten values on the x axis.
`log`	whether values should be log-transformed.
`base`	logarithm base.
`main`	main title.
`xlab`	x-axis label.
`ylab`	y-axis label.
`cex.main`	size of main title.
`cex.lab`	size of axis labels.
`cex.axis`	size of tick labels.
`cex.strip`	size of strip labels.
`col.strip`	color of strip labels.
`las`	orientation of tick labels: 0=parallel, 1=horizontal, 2=perpendicular, 3=vertical.
`tck`	tick mark length.
`tick.number`	number of tick marks.
`lty.density`	line type of density curve.
`lwd.density`	line width of density curve.
`col.density`	color of density curve.
`lty.median`	line type of median.
`lwd.median`	line width of median.
`col.median`	color of median.
`lty.outer`	line type of outer quantiles.
`lwd.outer`	line width of outer quantiles.
`col.outer`	color of outer quantiles.
`pch`	symbol for points.
`cex.points`	size of points.
`col.points`	color of points.
`plot`	whether to draw plot.
`...`	passed to `densityplot` and `panel.densityplot`.

Value

When plot=TRUE, a trellis plot is drawn and a data frame is returned, containing the data used for plotting. When plot=FALSE, a trellis object is returned.

Note

The Args function from the gdata package is recommended for reviewing the arguments, instead of args.

Examples

plotDens(xbio$"2004", points=TRUE, div=1000, main="2004\n",
         xlab="Biomass age 4+ (kt)", tick.number=6, strip=FALSE)
plotDens(xpar, xlab="Parameter value", ylab="Posterior density\n")
plotDens(xbio$"2004", points=TRUE, div=1000, main="2004\n",
         xlab="Biomass age 4+ (kt)", tick.number=6, strip=FALSE)
plotDens(xpar, xlab="Parameter value", ylab="Posterior density\n")

Plot MCMC Quantiles

Description

Plot quantiles of multiple Markov chain Monte Carlo chains, using bars, boxes, or lines.

Usage

plotQuant(mcmc, style="boxes", probs=c(0.025,0.975), axes=TRUE,
          names=NULL, ylim=NULL, yaxs="i", div=1, log=FALSE, base=10,
          main=NULL, xlab=NULL, ylab=NULL, cex.axis=0.8, las=1,
          tck=-0.015, tick.number=8, lty.median=1*(style!="bars"),
          lwd.median=1+1*(style!="boxes"), col.median="black",
          lty.outer=1+2*(style=="lines"), lwd.outer=1,
          col.outer="black", pch=16, cex=0.8, col="black",
          boxfill="darkgray", boxwex=0.5, staplewex=0.5, sfrac=0.005,
          mai=c(0.8,1,1,0.6),
          mgp=list(bottom=c(2,0.4,0),left=c(3,0.6,0),top=c(0,0.6,0),
          right=c(0,0.6,0)), ...)
plotQuant(mcmc, style="boxes", probs=c(0.025,0.975), axes=TRUE,
          names=NULL, ylim=NULL, yaxs="i", div=1, log=FALSE, base=10,
          main=NULL, xlab=NULL, ylab=NULL, cex.axis=0.8, las=1,
          tck=-0.015, tick.number=8, lty.median=1*(style!="bars"),
          lwd.median=1+1*(style!="boxes"), col.median="black",
          lty.outer=1+2*(style=="lines"), lwd.outer=1,
          col.outer="black", pch=16, cex=0.8, col="black",
          boxfill="darkgray", boxwex=0.5, staplewex=0.5, sfrac=0.005,
          mai=c(0.8,1,1,0.6),
          mgp=list(bottom=c(2,0.4,0),left=c(3,0.6,0),top=c(0,0.6,0),
          right=c(0,0.6,0)), ...)

Arguments

`mcmc`	MCMC chains as a data frame or `mcmc` object.
`style`	how quantiles should be drawn: `"bars"`, `"boxes"`, or `"lines"`.
`probs`	vector of outer quantiles to draw, besides the median.
`axes`	numeric vector indicating which axis labels should be drawn: 1=bottom, 2=left, 3=top, 4=right, or `TRUE` to display all (default).
`names`	x-axis labels.
`ylim`	y-axis limits.
`yaxs`	y-axis style: `"i"` to truncate exactly at limits (default) or `"r"` to extend the axis slightly beyond the limits.
`div`	denominator to shorten values on the y axis.
`log`	whether values should be log-transformed.
`base`	logarithm base.
`main`	main title.
`xlab`	x-axis label.
`ylab`	y-axis label.
`cex.axis`	size of tick labels.
`las`	orientation of tick labels: 0=parallel, 1=horizontal, 2=perpendicular, 3=vertical.
`tck`	tick mark length.
`tick.number`	number of tick marks.
`lty.median`	line type of median.
`lwd.median`	line width of median.
`col.median`	color of median.
`lty.outer`	line type of outer quantiles.
`lwd.outer`	line width of outer quantiles.
`col.outer`	color of outer quantiles.
`pch`	symbol for points.
`cex`	size of points.
`col`	color of points.
`boxfill`	color of boxes.
`boxwex`	width of boxes.
`staplewex`	width of error bar staples when `style="boxes"`, as a fraction of box width.
`sfrac`	width of error bar staples when `style="bars"`, as a fraction of plot region.
`mai`	margins around plot as a vector of four numbers (bottom, left, top, right).
`mgp`	margins around axis titles, labels, and lines as a list of four vectors (bottom, left, top, right).
`...`	passed to `plot`, `bxp`, `plotCI`, `lines`, `matplot`, `axis`, and `title`.

Value

List containing:

`x`	midpoint coordinates on the x axis.
`y`	quantile coordinates on the y axis.

Note

With style="boxes", the quartiles are shown as boxes.

The Args function from the gdata package is recommended for reviewing the arguments, instead of args.

Examples

plotQuant(xrec, names=substring(names(xrec),3), div=1000, xlab="Year",
          ylab="Recruitment (million one-year-olds)")
plotQuant(xbio, div=1000, xlab="Year", ylab="Biomass age 4+ (kt)")
plotQuant(xbio, style="bars", div=1000, sfrac=0, xlab="Year",
          ylab="Biomass age 4+ (kt)")
plotQuant(xbio, style="lines", div=1000, xlab="Year",
          ylab="Biomass age 4+ (kt)")
plotQuant(xpro, axes=1:2, div=1000, xlab="Year",
          ylab="Biomass age 4+ (kt)")
plotQuant(xrec, names=substring(names(xrec),3), div=1000, xlab="Year",
          ylab="Recruitment (million one-year-olds)")
plotQuant(xbio, div=1000, xlab="Year", ylab="Biomass age 4+ (kt)")
plotQuant(xbio, style="bars", div=1000, sfrac=0, xlab="Year",
          ylab="Biomass age 4+ (kt)")
plotQuant(xbio, style="lines", div=1000, xlab="Year",
          ylab="Biomass age 4+ (kt)")
plotQuant(xpro, axes=1:2, div=1000, xlab="Year",
          ylab="Biomass age 4+ (kt)")

Plot MCMC Scatterplot Matrix

Description

Plot scatterplots of multiple Markov chain Monte Carlo chains. This is a diagnostic plot for deciding whether parameters are confounded. When parameter estimates are highly dependent on each other, it may undermine conclusions based on MCMC results of that model.

Usage

plotSplom(mcmc, axes=FALSE, between=0, div=1, log=FALSE, base=10, ...)
plotSplom(mcmc, axes=FALSE, between=0, div=1, log=FALSE, base=10, ...)

Arguments

`mcmc`	MCMC chains as a data frame or `mcmc` object.
`axes`	whether axis values should be plotted.
`between`	space between panels.
`div`	denominator to shorten values on the y axis.
`log`	whether values should be log-transformed.
`base`	logarithm base.
`...`	passed to `pairs`.

Value

Null, but a plot is drawn on the current graphics device.

Note

The Args function from the gdata package is recommended for reviewing the arguments, instead of args.

Examples

plotSplom(xpar, pch=".")
plotSplom(xpro, axes=TRUE, between=1, div=1000, main="Future biomass",
          cex.labels=1.5, pch=".", cex=3)
plotSplom(xpar, pch=".")
plotSplom(xpro, axes=TRUE, between=1, div=1000, main="Future biomass",
          cex.labels=1.5, pch=".", cex=3)

Plot MCMC Traces

Description

Plot Markov chain Monte Carlo traces. This is a diagnostic plot for deciding whether a chain shows unwanted trends.

Usage

plotTrace(mcmc, axes=FALSE, same.limits=FALSE,
          between=list(x=axes,y=axes), div=1, span=1/4, log=FALSE,
          base=10, main=NULL, xlab=NULL, ylab=NULL, cex.main=1.2,
          cex.lab=1, cex.axis=0.8, cex.strip=0.8, col.strip="gray95",
          las=0, tck=0.5, tick.number=5, lty.trace=1, lwd.trace=1,
          col.trace="gray", lty.median=1, lwd.median=1,
          col.median="black", lty.loess=2, lwd.loess=1,
          col.loess="black", plot=TRUE, ...)
plotTrace(mcmc, axes=FALSE, same.limits=FALSE,
          between=list(x=axes,y=axes), div=1, span=1/4, log=FALSE,
          base=10, main=NULL, xlab=NULL, ylab=NULL, cex.main=1.2,
          cex.lab=1, cex.axis=0.8, cex.strip=0.8, col.strip="gray95",
          las=0, tck=0.5, tick.number=5, lty.trace=1, lwd.trace=1,
          col.trace="gray", lty.median=1, lwd.median=1,
          col.median="black", lty.loess=2, lwd.loess=1,
          col.loess="black", plot=TRUE, ...)

Arguments

`mcmc`	MCMC chain(s) as a vector, data frame or `mcmc` object.
`axes`	whether axis values should be plotted.
`same.limits`	whether panels should have same x-axis limits.
`between`	list with `x` and `y` indicating panel spacing.
`div`	denominator to shorten values on the y axis.
`span`	smoothness parameter, passed to `panel.loess`
`log`	whether values should be log-transformed.
`base`	logarithm base.
`main`	main title.
`xlab`	x-axis title.
`ylab`	y-axis title.
`cex.main`	size of main title.
`cex.lab`	size of axis labels.
`cex.axis`	size of tick labels.
`cex.strip`	size of strip labels.
`col.strip`	color of strip labels.
`las`	orientation of tick labels: 0=parallel, 1=horizontal, 2=perpendicular, 3=vertical.
`tck`	tick mark length.
`tick.number`	number of tick marks.
`lty.trace`	line type of trace.
`lwd.trace`	line width of trace.
`col.trace`	color of trace.
`lty.median`	line type of median.
`lwd.median`	line width of median.
`col.median`	color of median.
`lty.loess`	line type of loess.
`lwd.loess`	line width of loess.
`col.loess`	color of loess.
`plot`	whether to draw plot.
`...`	passed to `xyplot` and `panel.loess`.

Value

When plot=TRUE, a trellis plot is drawn and a data frame is returned, containing the data used for plotting. When plot=FALSE, a trellis object is returned.

Note

The Args function from the gdata package is recommended for reviewing the arguments, instead of args.

Examples

plotTrace(xpar, xlab="Iterations", ylab="Parameter value",
          layout=c(2,4))
plotTrace(xpar$R0, axes=TRUE, div=1000)
plotTrace(xpar, xlab="Iterations", ylab="Parameter value",
          layout=c(2,4))
plotTrace(xpar$R0, axes=TRUE, div=1000)

MCMC Results for Biomass

Description

Markov chain Monte Carlo results from stock assessment of cod (Gadus morhua) in Icelandic waters, showing estimated biomass by year in tonnes.

Usage

xbioxbio

Format

Data frame containing 1000 rows and 34 columns (years 1971 to 2004).

Details

Each column contains the results of 1 million MCMC iterations, after thinning to every 1000th iteration.

The MCMC analysis started at the best fit, so no burn-in period was discarded.

Note

Biomass is the total weight of all individuals in a population, in this case ages 4 and older.

This data frame is a subset of the xmcmc list from the scape package, which contains further documentation about the data and model. Specifically, xbio <- xmcmc$B.

The MCMC analysis was run using the AD Model Builder software (https://www.admb-project.org).

References

Examples

plotDens(xbio$"2004", points=TRUE, div=1000, main="2004\n",
         xlab="Biomass age 4+ (1000 t)", tick.number=6, strip=FALSE)

plotQuant(xbio, div=1000, xlab="Year", ylab="Biomass age 4+ (kt)")
plotQuant(xbio, style="bars", div=1000, sfrac=0, xlab="Year",
          ylab="Biomass age 4+ (kt)")
plotQuant(xbio, style="lines", div=1000, xlab="Year",
          ylab="Biomass age 4+ (kt)")
plotDens(xbio$"2004", points=TRUE, div=1000, main="2004\n",
         xlab="Biomass age 4+ (1000 t)", tick.number=6, strip=FALSE)

plotQuant(xbio, div=1000, xlab="Year", ylab="Biomass age 4+ (kt)")
plotQuant(xbio, style="bars", div=1000, sfrac=0, xlab="Year",
          ylab="Biomass age 4+ (kt)")
plotQuant(xbio, style="lines", div=1000, xlab="Year",
          ylab="Biomass age 4+ (kt)")

MCMC Results for Model Parameters

Description

Markov chain Monte Carlo results from stock assessment of cod (Gadus morhua) in Icelandic waters, showing estimated model parameters.

Usage

xparxpar

Format

Data frame containing 1000 rows and 8 columns:

`R0`	average virgin recruitment
`Rinit`	initial recruitment scaler
`uinit`	initial harvest rate
`cSleft`	left-side slope of commercial selectivity curve
`cSfull`	age at full commercial selectivity
`sSleft`	left-side slope of survey selectivity curve
`sSfull`	age at full survey selectivity
`logq`	log-transformed survey catchability

Details

Each column contains the results of 1 million MCMC iterations, after thinning to every 1000th iteration.

The MCMC analysis started at the best fit, so no burn-in period was discarded.

Note

This data frame is a subset of the xmcmc list from the scape package, which contains further documentation about the data and model. Specifically, xpar <- xmcmc$P.

The MCMC analysis was run using the AD Model Builder software (https://www.admb-project.org).

References

Examples

plotTrace(xpar, xlab="Iterations", ylab="Parameter value",
          layout=c(2,4))
plotTrace(xpar$R0, axes=TRUE, div=1000)

plotAuto(xpar$R0)
plotAuto(xpar$R0, thin=10)
plotAuto(xpar, lag.max=50, ann=FALSE, axes=FALSE)

plotCumu(xpar$R0, main="R0")
plotCumu(xpar$cSfull, main="cSfull")
plotCumu(xpar, probs=c(0.25,0.75), ann=FALSE, axes=FALSE)

plotSplom(xpar, pch=".")

plotDens(xpar, xlab="Parameter value", ylab="Posterior density\n")
plotTrace(xpar, xlab="Iterations", ylab="Parameter value",
          layout=c(2,4))
plotTrace(xpar$R0, axes=TRUE, div=1000)

plotAuto(xpar$R0)
plotAuto(xpar$R0, thin=10)
plotAuto(xpar, lag.max=50, ann=FALSE, axes=FALSE)

plotCumu(xpar$R0, main="R0")
plotCumu(xpar$cSfull, main="cSfull")
plotCumu(xpar, probs=c(0.25,0.75), ann=FALSE, axes=FALSE)

plotSplom(xpar, pch=".")

plotDens(xpar, xlab="Parameter value", ylab="Posterior density\n")

MCMC Results for Future Projections

Description

Markov chain Monte Carlo results from stock assessment of cod (Gadus morhua) in Icelandic waters, showing future projected biomass in tonnes.

Usage

xproxpro

Format

Data frame containing 1000 rows and 4 columns (years 2004 to 2007).

Details

Each column contains the results of 1 million MCMC iterations, after thinning to every 1000th iteration.

The MCMC analysis started at the best fit, so no burn-in period was discarded.

Note

The projections are based on a fixed harvest rate, where 25% of the biomass (ages 4 and older) is caught every year.

This data frame is a subset of the xproj list from the scape package, which contains further documentation about the data and model. Specifically, xpro <- xproj$"0.25".

The MCMC analysis was run using the AD Model Builder software (https://www.admb-project.org).

References

Examples

plotQuant(xpro, axes=1:2, div=1000, xlab="Year",
          ylab="Biomass age 4+ (kt)")

plotSplom(xpro, axes=TRUE, between=1, div=1000, main="Future biomass",
          cex.labels=1.5, pch=".", cex=3)
plotQuant(xpro, axes=1:2, div=1000, xlab="Year",
          ylab="Biomass age 4+ (kt)")

plotSplom(xpro, axes=TRUE, between=1, div=1000, main="Future biomass",
          cex.labels=1.5, pch=".", cex=3)

MCMC Results for Recruitment

Description

Markov chain Monte Carlo results from stock assessment of cod (Gadus morhua) in Icelandic waters, showing estimated recruitment by year.

Usage

xrecxrec

Format

Data frame containing 1000 rows and 33 columns (years 1970 to 2002).

Details

Each column contains the results of 1 million MCMC iterations, after thinning to every 1000th iteration.

The MCMC analysis started at the best fit, so no burn-in period was discarded.

Note

Recruitment is the size of a cohort (year class), in this case thousands of one-year-olds.

For example, xrec$"1980" is the estimated number of one-year-olds in 1981, the cohort that hatched in 1980.

This data frame is a subset of the xmcmc list from the scape package, which contains further documentation about the data and model. Specifically, xrec <- xmcmc$R.

The MCMC analysis was run using the AD Model Builder software (https://www.admb-project.org).

References

Examples

plotQuant(xrec, names=substring(names(xrec),3), div=1000, xlab="Year",
          ylab="Recruitment (million one-year-olds)")
plotQuant(xrec, names=substring(names(xrec),3), div=1000, xlab="Year",
          ylab="Recruitment (million one-year-olds)")

Package 'plotMCMC'

Help Index

MCMC Diagnostic Plots

Description

Details

Note

Author(s)

References

See Also

Plot MCMC Autocorrelation

Description

Usage

Arguments

Value

Note

See Also

Examples

Plot MCMC Cumulative Quantiles

Description

Usage

Arguments

Value

Note

See Also

Examples

Plot MCMC Density

Description

Usage

Arguments

Value

Note

See Also

Examples

Plot MCMC Quantiles

Description

Usage

Arguments

Value

Note

See Also

Examples

Plot MCMC Scatterplot Matrix

Description

Usage

Arguments

Value

Note

See Also

Examples

Plot MCMC Traces

Description

Usage

Arguments

Value

Note

See Also

Examples

MCMC Results for Biomass

Description

Usage

Format

Details

Note

References

See Also

Examples

MCMC Results for Model Parameters

Description

Usage

Format

Details

Note

References

See Also

Examples

MCMC Results for Future Projections

Description

Usage

Format

Details