rotations (version 0.2)

MCMCSO3: MCMC for rotation data

Description

Use non-informative Bayes to infer about the central orientation and concentration parameter for a sample of rotations.

Usage

MCMCSO3(x, type, S0, kappa0, tuneS, tuneK, burn_in,
    m = 5000)
  ## S3 method for class 'SO3':
MCMCSO3(x, type, S0, kappa0, tuneS, tuneK,
    burn_in, m = 5000)
  ## S3 method for class 'Q4':
MCMCSO3(x, type, S0, kappa0, tuneS, tuneK,
    burn_in, m = 5000)

Arguments

x

$n\times p$ 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

Value

• list of
• S
  Draws from the posterior distribution for central orientation S
• kappa
  Draws from the posterior distribution for concentration parameter kappa
• Saccept
  Acceptance rate for cenral orientaion draws
• Kaccept
  Acceptance rate for concentration draws

Details

The procedures detailed in Bingham et al. (2009) and Bingham et al. (2010) are implemented to get draws from the posterior distribution for the central orientation and concentration parameters for a sample of 3D rotations. A uniform prior on SO(3) is used for the central orientation and the appropriate Jeffreys prior is used for the concentration parameter.

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.

Examples

Rs<-ruars(20,rcayley,kappa=4)
draws<-MCMCSO3(Rs,type='Cayley',S0=mean(Rs),kappa0=2,tuneS=39,tuneK=.8,burn_in=100,m=5000)