ciPhase function

Mean and Confidence Interval for Circular Phase

Calculates the mean and confidence interval for the phase based on a chain of MCMC samples.

ciPhase(theta, alpha = 0.05)

Arguments

• theta: chain of Markov chain Monte Carlo (MCMC) samples of the phase.
• alpha: the confidence level (default = 0.05 for a 95% confidence interval).

Returns

• mean: the estimated mean phase. - lower: the estimated lower limit of the confidence interval. - upper: the estimated upper limit of the confidence interval.

Details

The estimates of the phase are rotated to have a centre of $\pi$, the point on the circumference of a unit radius circle that is furthest from zero. The mean and confidence interval are calculated on the rotated values, then the estimates are rotated back.

Examples

theta = rnorm(n=2000, mean=0, sd=pi/50) # 2000 normal samples, centred on zero
hist(theta, breaks=seq(-pi/8, pi/8, pi/30))
ciPhase(theta)

References

Fisher, N. (1993) Statistical Analysis of Circular Data. Cambridge University Press. Page 36.

Barnett, A.G., Dobson, A.J. (2010) Analysing Seasonal Health Data. Springer.

Author(s)

Adrian Barnett a.barnett@qut.edu.au