BayesianNormal: Bayesian Estimation In Mixed Stochastic Differential...

In charlottedion/mixedsde: Estimation Methods for Stochastic Differential Mixed Effects Models

Description

Gibbs sampler for Bayesian estimation of the random effects (α_j, β_j) in the mixed SDE dX_j(t)= (α_j- β_j X_j(t))dt + σ a(X_j(t)) dW_j(t).

Usage

BayesianNormal(times, X, model = c("OU", "CIR"), prior, start, random,
  nMCMC = 1000, propSd = 0.2)

Arguments

times	vector of observation times
X	matrix of the M trajectories (each row is a trajectory with N= T/Δ column).
model	name of the SDE: 'OU' (Ornstein-Uhlenbeck) or 'CIR' (Cox-Ingersoll-Ross).
prior	list of prior parameters: mean and variance of the Gaussian prior on the mean mu, shape and scale of the inverse Gamma prior for the variances omega, shape and scale of the inverse Gamma prior for sigma
start	list of starting values: mu, sigma
random	random effects in the drift: 1 if one additive random effect, 2 if one multiplicative random effect or c(1,2) if 2 random effects.
nMCMC	number of iterations of the MCMC algorithm
propSd	proposal standard deviation of φ is |μ|*propSd/\log(N) at the beginning, is adjusted when acceptance rate is under 30% or over 60%

Value

alpha	posterior samples (Markov chain) of α
beta	posterior samples (Markov chain) of β
mu	posterior samples (Markov chain) of μ
omega	posterior samples (Markov chain) of Ω
sigma2	posterior samples (Markov chain) of σ^2

References

Hermann, S., Ickstadt, K. and C. Mueller (2016). Bayesian Prediction of Crack Growth Based on a Hierarchical Diffusion Model. Appearing in: Applied Stochastic Models in Business and Industry.

Rosenthal, J. S. (2011). 'Optimal proposal distributions and adaptive MCMC.' Handbook of Markov Chain Monte Carlo (2011): 93-112.

charlottedion/mixedsde documentation built on May 13, 2019, 3:35 p.m.