BaSAR.post: Normalized posterior
In JIC-CSB/BaSAR: Bayesian Spectrum Analysis in R

Description Usage Arguments Details Value Author(s) References Examples

View source: R/BaSAR.R

A normalised posterior of the frequency in the chosen range.

1	BaSAR.post(data, start, stop, nsamples, nbackg, tpoints)

`data`	data as a 1-dimensional vector
`start`	lower limit of period of interest, in seconds
`stop`	upper limit of period of interest, in seconds
`nsamples`	number of samples within the interval start-stop
`nbackg`	number of background functions to be added to the model
`tpoints`	vector of time points, in seconds

This function calculates the posterior probability distribution over a chosen range of omega (angular frequency), following Bretthorst (1988). It is based on a signal model of sines and cosines, and assumes uniform priors for model parameters such as amplitudes and noise models. The resulting distribution is then normalized over the range of omega.

If there is a background trend in the data, background functions can be added to the signal model to account for this. The Legendre polynomials are used for these background functions, and nbackg is the number of Legendre extension orders to be used.

To plot the output over period instead of omega, see BaSAR.plotperiod.

A list containing:

`normp`	1D normalized posterior distribution over omega
`omega`	1D vector of the omega sampled
`stats`	list of statistics from the probability distribution

Emma Granqvist, Matthew Hartley and Richard J Morris.

Granqvist, E., Oldroyd, G. E. and Morris, R. J. (2011) Automated Bayesian model development for frequency detection in biological time series. BMC Syst Biol 5, 97.
http://dx.doi.org/10.1186/1752-0509-5-97

Bretthorst, G. L. (1988) Bayesian spectrum analysis and parameter estimation. Lecture notes in statistics. New York: Springer-Verlag.

# Create time series omega = 0.5
tpoints = seq(from=1, to=200, length=200)
dpoints = sin(0.5 * tpoints) + 0.1 * rnorm(200, 0, 1)
# Plot time series
plot(dpoints, type="l", col="blue", xlab="t", ylab="d(t)")
# Run BaSAR to get normalized posterior distirbution
r <- BaSAR.post(dpoints, 6, 600, 100, 0, tpoints)
# Plot the resulting posterior density function
plot(r$omega, r$normp, xlim=c(0:1), type="h", col="red", ylab="PDF",
xlab=expression(omega))