Quantifying dating uncertainties in layer-counted paleoclimate proxy archives

Paleoclimate proxy records have non-negligible uncertainties that arise from both the proxy measurement and the dating processes. Knowledge of the dating uncertainties is important for a rigorous propagation to further analyses; for example for identification and dating of stadial-interstadial transitions in Greenland ice core records during glacial intervals, for comparing the variability in different proxy archives, and for model-data comparisons in general. In this study we develop a statistical framework to quantify and propagate dating uncertainties in layer-counted proxy archives using the example of the Greenland Ice Core Chronology 2005 (GICC05). We express the number of layers per depth interval as the sum of a structured component that represents both underlying physical processes and biases in layer counting, described by a regression model, and a noise component that represents the fluctuations of the underlying physical processes, as well as unbiased counting errors. The age-depth relationship of the joint dating uncertainties can then be described by a multivariate Gaussian process from which realizations of the chronology can be sampled. We show how the effect of an unknown counting bias can be incorporated in our framework and present refined estimates of the occurrence times of Dansgaard-Oeschger events evidenced in Greenland ice cores together with a complete uncertainty quantification of these timings.

A statistical model for dating uncertainties in Greenland ice core records

<p>Most layer-counting based paleoclimate proxy records have non-negligible uncertainties that arise from both the proxy measurement and the dating processes. Proper knowledge of the dating uncertainties in paleoclimatic ice core records is important for a rigorous propagation to further analyses; for example for identification and dating of stadial-interstadial transitions during glacial intervals, for model-data comparisons in general, or to provide a complete uncertainty quantification of early warning signals. We develop a statistical model that incorporates the dating uncertainties of the Greenland Ice Core Chronology 2005 (GICC05), which includes the uncertainty associated with layer counting. We express the number of layers per depth interval as the sum of a structural component that represents both underlying physical processes and biases in layer counting, described by a linear regression model, and a noise component that represents the internal variation of the underlying physical processes, as well as residual counting errors. We find the residual components to be described well by a Gaussian white noise process that appear to be largely uncorrelated, allowing us to represent the dating uncertainties using a multivariate Gaussian process. This means that we can easily produce simulations as well as incorporate tie-points from other proxy records to match the GICC05 time scale to other chronologies. Moreover, this multivariate Gaussian process exhibits Markov properties which grants a substantial gain in computational efficiency.</p>

A generalization of functional clustering for discrete multivariate longitudinal data

This paper presents a new model-based generalized functional clustering method for discrete longitudinal data, such as multivariate binomial and Poisson distributed data. For this purpose, we propose a multivariate functional principal component analysis (MFPCA)-based clustering procedure for a latent multivariate Gaussian process instead of the original functional data directly. The main contribution of this study is two-fold: modeling of discrete longitudinal data with the latent multivariate Gaussian process and developing of a clustering algorithm based on MFPCA coupled with the latent multivariate Gaussian process. Numerical experiments, including real data analysis and a simulation study, demonstrate the promising empirical properties of the proposed approach.

System Reliability Analysis Using Hybrid Gaussian Process Model

This paper proposes a system reliability analysis method based on the hybrid of multivariate Gaussian process (MGP) and univariate Gaussian process (UGP) models, named as hybrid Gaussian process-based system reliability analysis (HGP-SRA). MGP and UGP models are selectively constructed for the components of a complex engineered system: MGP models are constructed over the groups of highly interdependent components and the individual UGP models are built over the components which are relatively independent of one another. A nonlinear-dependence measure, namely the randomized dependence coefficient, is adopted to adaptively learn and quantify the pairwise dependencies of the components with both linear and nonlinear dependency patterns. In the proposed HGP-SRA method, initial hybrid Gaussian process (HGP) models are first constructed with a set of near-random samples and these surrogate models are then updated with new samples that are sequentially identified based on the acquisition function named as multivariate probability of improvement (MPI). The results of two mathematical and a real-world engineering case studies suggest that the proposed method can achieve better accuracy and efficiency in system reliability estimation than the benchmark surrogate-based methods.