pair_align_functions_expomap: Align two functions using geometric properties of warping...

In fdasrvf: Elastic Functional Data Analysis

Align two functions using geometric properties of warping functions

Description

This function aligns two functions using Bayesian framework. It will align f2 to f1. It is based on mapping warping functions to a hypersphere, and a subsequent exponential mapping to a tangent space. In the tangent space, the Z-mixture pCN algorithm is used to explore both local and global structure in the posterior distribution.

Usage

pair_align_functions_expomap(
  f1,
  f2,
  timet,
  iter = 20000,
  burnin = min(5000, iter/2),
  alpha0 = 0.1,
  beta0 = 0.1,
  zpcn = list(betas = c(0.5, 0.05, 0.005, 1e-04), probs = c(0.1, 0.1, 0.7, 0.1)),
  propvar = 1,
  init.coef = rep(0, 2 * 10),
  npoints = 200,
  extrainfo = FALSE
)

Arguments

f1	observed data, numeric vector
f2	observed data, numeric vector
timet	sample points of functions
iter	length of the chain
burnin	number of burnin MCMC iterations
alpha0, beta0	IG parameters for the prior of sigma1
zpcn	list of mixture coefficients and prior probabilities for Z-mixture pCN algorithm of the form list(betas, probs), where betas and probs are numeric vectors of equal length
propvar	variance of proposal distribution
init.coef	initial coefficients of warping function in exponential map; length must be even
npoints	number of sample points to use during alignment
extrainfo	T/F whether additional information is returned

Details

The Z-mixture pCN algorithm uses a mixture distribution for the proposal distribution, controlled by input parameter zpcn. The zpcn$betas must be between 0 and 1, and are the coefficients of the mixture components, with larger coefficients corresponding to larger shifts in parameter space. The zpcn$probs give the probability of each shift size.

Value

Returns a list containing

f2_warped	f2 aligned to f1
gamma	Posterior mean gamma function
g.coef	matrix with iter columns, posterior draws of g.coef
psi	Posterior mean psi function
sigma1	numeric vector of length iter, posterior draws of sigma1
accept	Boolean acceptance for each sample (if extrainfo=TRUE)
betas.ind	Index of zpcn mixture component for each sample (if extrainfo=TRUE)
logl	numeric vector of length iter, posterior loglikelihood (if extrainfo=TRUE)
gamma_mat	Matrix of all posterior draws of gamma (if extrainfo=TRUE)
gamma_q025	Lower 0.025 quantile of gamma (if extrainfo=TRUE)
gamma_q975	Upper 0.975 quantile of gamma (if extrainfo=TRUE)
sigma_eff_size	Effective sample size of sigma (if extrainfo=TRUE)
psi_eff_size	Vector of effective sample sizes of psi (if extrainfo=TRUE)
xdist	Vector of posterior draws from xdist between registered functions (if extrainfo=TRUE)
ydist	Vector of posterior draws from ydist between registered functions (if extrainfo=TRUE)

References

Lu, Y., Herbei, R., and Kurtek, S. (2017). Bayesian registration of functions with a Gaussian process prior. Journal of Computational and Graphical Statistics, DOI: 10.1080/10618600.2017.1336444.

Examples

## Not run: 
  # This is an MCMC algorithm and takes a long time to run
  myzpcn <- list(
    betas = c(0.1, 0.01, 0.005, 0.0001),
    probs = c(0.2, 0.2, 0.4, 0.2)
  )
  out <- pair_align_functions_expomap(
    f1 = simu_data$f[, 1],
    f2 = simu_data$f[, 2],
    timet = simu_data$time,
    zpcn = myzpcn,
    extrainfo = TRUE
  )
  # overall acceptance ratio
  mean(out$accept)
  # acceptance ratio by zpcn coefficient
  with(out, tapply(accept, myzpcn$betas[betas.ind], mean))

## End(Not run)

fdasrvf documentation built on Oct. 5, 2024, 1:08 a.m.