CMG Collaborative Research: Probabilistic stratigraphic alignment and dating of paleoclimate data

学术价值：地层排列是将长期海洋气候记录(105-107年)放置在共同的年龄模型上的主要方法。然而，目前还没有技术来量化与这些比对相关的不确定性。该项目将为古气候记录建立自动地层排列算法的概率模型，作为表征这种不确定性的一种手段。这种不确定性分析的发展很重要，因为气候响应的相对时间(根据地层排列得出)经常被用来评估气候系统内的因果关系。因此，本研究还将评估对齐不确定性对这些评估的影响。此外，还将通过轨道调整为年龄模型的开发创建一个概率算法。这项工作提高了古气候年龄模型的精度和误差估计，将改善对气候系统S对辐射强迫变化的敏感性的估计。由PiL.Lisiecki开发的原始软件使用动态编程，根据用户定义的参数设置找到古气候记录的最佳比对，并生成一个最佳比对，而不进行不确定性分析。新版本将为用户提供按其概率比例采样的比对，并将为比对中每个点的估计相对年龄提供误差条。具体地说，该项目将开发(成对和横向)隐马尔可夫模型(HMM)形式的配对算法的两个概率版本(成对和多个)，并开发一个概率HMM，用于为古气候数据创建轨道调整的年龄模型。年龄模型开发的算法将结合从Pair和Profile HMM算法中获得的关于沉降率可变性的知识。所有这三种算法都将被应用于创建一个新的海底记录堆叠模型(代表全球气候)，其不确定性估计包括数据噪声、对齐不确定性和年龄模型不确定性。这一“概率堆叠”具有重要的科学意义，因为它将为一项广泛使用的过去气候变化衡量标准提供不确定性估计。该项目还旨在开发统计方法，以描述地层排列和轨道调整的后验分布的形状。这种对齐问题属于一大类离散的高维问题，往往具有复杂的多峰解空间，难以刻画。到目前为止，对这些空间的描述仅限于点估计(S)和围绕这些高D估计的贝叶斯置信限。在这个项目中，将开发新的方法来识别这些高维空间中的多个模式，并将它们表征为特定的概率模型，使用来自后验分布的直接样本和每个采样值的概率。由于点估计和置信度在这类高维空间中的效用有限，这些后验空间的概率刻画将极大地提高描述这类后验空间的能力。更广泛的影响：由Pi Lisiecki开发的当前版本的比对软件已被许多不同国家的用户下载，并适用于许多出版物中的各种数据。新的软件和带有不确定度分析的18O堆将发布在NOAA NCDC的网站上，Lisiecki的个人网站，Brown CCMB网络服务器。新软件将改进地层对比和对其不确定性的估计，这最终将导致对气候系统的更好理解和更好的气候变化预测。比对问题是离散高维推理中的许多问题之一，包括：RNA二级结构的预测；灵长类基因组中片段复制的表征；语言学中的随机上下文无关文法。这项关于离散高维后方空间特征的工作将对所有这些其他领域和更远的领域产生直接影响。这项提议将培训本科生和研究生以及地层学和数理统计方面的博士后。这项提议还将扩大任职人数不足群体的参与，在职业生涯开始时支持一名女性PI。

Intellectual Merit: Stratigraphic alignment is the primary way in which long marine climate records (105-107years) are placed on a common age model. However, currently there are no techniques for quantifying the uncertainty associated with these alignments. This project will build probabilistic models of an automated stratigraphic alignment algorithm for paleoclimate records as a means of characterizing this uncertainty. The development of this uncertainty analysis is important because the relative timing of climate responses (derived from stratigraphic alignment) is frequently used to evaluate causal relationships within the climate system. Therefore, this study will also assess the effects of alignment uncertainty on these evaluations. Additionally, a probabilistic algorithm will be created for age model development through orbital tuning. The improved accuracy and error estimates for paleoclimate age models that result from this work will improve estimates of the climate system?s sensitivity to changes in radiative forcing. The original software developed by PI L. Lisiecki uses dynamic programming to find the optimal alignment of paleoclimate records based on user-defined parameter settings and produces one best-fit alignment with no uncertainty analysis. The new version will provide users with alignments sampled in proportion to their probability and will provide error bars for the estimated relative ages at each point in the alignment. Specifically, this project will develop two probabilistic versions of the alignment algorithm (pairwise and multiple) in the form of (pair and profile) Hidden Markov models (HMM) and develop a probabilistic HMM for creating orbitally tuned age models for paleoclimate data. The algorithm for age model development will incorporate knowledge gained about sedimentation rate variability from the pair and profile HMM algorithms. All three algorithms will be applied to create a new stack model of benthic δ18O records (a proxy for global climate) with uncertainty estimates which include data noise, alignment uncertainty and age model uncertainty. This "probabilistic stack" is scientifically important because it will yield uncertainty estimates for a widely used measure of past climate change. This project also aims to develop statistical methods to characterize the shapes of the posterior distributions of stratigraphic alignments and orbital tuning. This alignment problem is in a large class of discrete high dimensional problems that often have complex multimodal solution spaces which are difficult to characterize. To date the characterization of these spaces has been limited to a point estimate(s) and Bayesian confidence limits around these high-D estimates. In this project novel methods will be developed for the identification of clusters from multiple modes in these high-D spaces and characterize them as specific probabilistic models using both direct samples from the posterior distribution and the probabilities of each sampled value. Given the limited utility of point estimates and confidence limits in such high-D spaces, these probabilistic characterizations of posterior spaces will greatly improve the ability to describe such posterior spaces. Broader Impacts: The current version of the alignment software developed by PI Lisiecki has been downloaded by users in many different countries and applied to a wide variety of data in many publications. The new software and δ18O stack with uncertainty analysis will be posted on the NOAA NCDC website, on Lisiecki's personal website, the Brown CCMB web server. The new software will improve stratigraphic alignments and estimation of their uncertainty, which ultimately will lead to a better understanding of the climate system and better climate change predictions. The alignment problem is one of many problems in discrete high-D inference, including: the prediction of RNA secondary structures; the characterization of segmental duplications in primate genomes; and stochastic context free grammars in linguistics. This work on the characterization of discrete high-D posterior spaces will have a direct impact in all of these other areas and beyond. This proposal will train undergraduate and graduate students and a post-doc in both stratigraphy and mathematical statistics. This proposal will also broaden participation of under-represented groups by supporting a female PI at the start of her career.