[MGI33-P02] Bayesian statistical evaluation method for detrital zircon geochronology
Keywords:Bayesian statistics, detrital zircon geochronology, MCMC algorithm
The new method is based on Bayesian statistics, adapted a theory proposed by Riihimäki and Vehtari (2014) that provides a flexible modeling for density curve using the Logistic Gaussian Process (LGP)
For introducing non-negative consistency for density curve, the logistic density transformation is performed by p(x)=exp(f(x))/∫exp(f(s))ds; x is age, p(x) is density curve, and f(x) is Gaussian Process; f(x)∼GP(0,κ(x,x')). The covariance matrix κ(x,x') is calculated by Gaussian kernel with hyperparameters ρ and σ. For the actual computation, the logistic density transformation has integral difficulties, then, M discretized softmax function is used for approximation for it.
The likelihood function is L(p|ρ,σ)=yTp. p is M discretized p(x), and y is vector of yi, which is the number of observations that fall within the i'th M discretized age subregion.
We have used programming language R and Stan for the MCMC computation of the statistical model above. When the number of detrital zircon data is several hundred or less, the hyperparameters of Gaussian process ρ and σ do not converge, and Bayesian estimation can not be performed. For this reason, the author estimated most plausible ρ and σ by WAIC. Using zircon data from our own data and the literature, in this presentation, we will demonstrate powerfulness of our new statistical evaluation.