rotations (version 1.5)

bayesCR: Bayes credible regions

Description

Find the radius of a $100(1-\alpha)$% credible region for the central orientation and concentration parameter using non-informative Bayesian methods.

Usage

bayesCR(x, type, S0, kappa0, tuneS, tuneK, burn_in, m = 5000, alp = 0.1)
  "bayesCR" (x, type, S0, kappa0, tuneS, tuneK, burn_in, m = 5000, alp = 0.1)
  "bayesCR" (x, type, S0, kappa0, tuneS, tuneK, burn_in, m = 5000, alp = 0.1)

Arguments

x

$n-by-p$ matrix where each row corresponds to a random rotation in matrix ($p=9$) or quaternion ($p=4$) form.

type

Angular distribution assumed on R. Options are Cayley, Fisher or Mises

S0

initial estimate of central orientation

kappa0

initial estimate of concentration parameter

tuneS

central orientation tuning parameter, concentration of proposal distribution

tuneK

concentration tuning parameter, standard deviation of proposal distribution

burn_in

number of draws to use as burn-in

m

number of draws to keep from posterior distribution

alp

alpha level desired, e.g. 0.05 or 0.10.

Value

list of

• Shat,Qhat Mode of the posterior distribution for the central orientation S
• Radius Radius of the credible region centered at the posterior mode

Details

Compute the radius of a $100(1-\alpha)$% credible region for the central orientation and concentration parameter as described in Bingham et al. (2009) and Bingham et al. (2010). The posterior mode is returned along with the radius of the credible region centered at the posterior mode.

References

Bingham MA, Vardeman SB and Nordman DJ (2009). "Bayes one-sample and one-way random effects analyses for 3-D orientations with application to materials science." Bayesian Analysis, 4(3), pp. 607-629.

Bingham MA, Nordman DJ and Vardeman SB (2010). "Finite-sample investigation of likelihood and Bayes inference for the symmetric von Mises-Fisher distribution." Computational Statistics & Data Analysis, 54(5), pp. 1317-1327.

See Also

fisheretal, prentice, chang, zhang

Examples

#Not run due to time constraints
## Not run: 
# Rs <- ruars(20, rvmises, kappa = 10)
# 
# #Compare the region size of the moment based theory mean estimator to the
# #Bayes region.
# 
# region(Rs, method = "direct", type = "theory", estimator = "mean", alp=0.1, m = 100)
# bayesCR <- region(Rs, type = "Mises", method = "Bayes", estimator = "mean", S0 = mean(Rs),
#                    kappa0 = 10, tuneS = 5000, tuneK = 1, burn_in = 1000, alp = .01, m = 5000)
# 
# bayesCR$Radius       #Region size is give by "Radius"
# bayesCR$Shat         #The Bayes region is centered around the posterior mode: "Shat"## End(Not run)