Mathematical Sciences: Statistical Inference in Paleoclimatology

小行星9311071 该项目涉及根据环境变化的地质记录进行数据处理、分析和推断所产生的统计问题。 目前的建议是两名调查人员讨论统计问题和分析模型和方法问题的结果，特别是时间序列分析，以切合实际地评估与气候变化有关的沉积记录的时间变化模式。 该项目将启动一项合作研究和互惠培训计划，以解决这些问题。 重点将放在不确定性传播的过程和正式的统计推断气候变化的基础上从深湖沉积物的原始记录。 在评估深海沉积物、冰芯和树木年轮的数据时也存在类似的问题，值得注意。 从技术上讲，该项目涉及原始数据记录的统计校准和时间序列分析，以评估地质记录随时间的变化模式。 初步目标是对统计问题有一个认识，因为这些问题渗透到从深湖沉积物岩心分析同位素和其他代用气候变量的实验过程的各个阶段。 对每个研究者的跨学科培训将是合作的中心和持续的特点。 这将是针对弥合之间的鸿沟，一方面，现行标准的做法，在统计分析的古气候数据（例如Pisias和摩尔1981年; Hagelberg，Pisias和埃尔加1991年），另一方面，可访问和适当的现代统计 方法和模型。 互惠的培训和发展计划将为两名研究人员中的每一个提供机会，使他们能够充分精通对方专业领域的基本知识，从而启动并启动一项研究计划，重点是对深湖沉积物岩心产生的古气候数据进行严格的统计分析。 统计学家Mike West将熟悉用于选择沉积物岩心位置进行古气候分析的方法，沉积物岩心的各种地球化学分析方法（特别是由于各种自然过程，如侵蚀和再沉积、生物扰动、成岩作用和实验室污染，对沉积物的年龄确定存在局限性），碳定年评估的校准，以及古气候学中时间序列分析的常用方法。 地质学家汤姆约翰逊将熟悉统计方法的能力和缺陷，特别是目前在这一领域使用的时间序列分析方法，并获得在地质年代学的不确定性评估的后果升值。 研究人员预计，在实验过程的各个阶段，贝叶斯方法在统计校准中的最终发展，以及由此产生的时间序列分析在评估校准记录的周期性变异性。 两位研究人员还将熟悉14 C日期的统计问题和校准方法（以及相关的不确定性评估），以及最近在 领域 该项目最终将导致集中研究工作，开发贝叶斯统计模型和方法，适用于沉积物为基础的古气候学实验过程的所有阶段，并最终应用于其他地质和考古领域。 最乐观的是，希望这种合作将种子的发展，国际公认的中心，为统计分析的古气候代用记录在杜克大学。 ***

9311071 West This project concerns statistical issues arising in data processing, analysis and inference based on geological records of environmental change. The current proposal results from discussion between the two investigators about the statistical issues and problems for models and methods of analysis, especially time series analysis, geared to the realistic assessment of patterns of time variation in sedimentary records relevant to climate change. This project will initiate a collaborative research and reciprocal training program to address these issues. The focus will be on the processes of uncertainty propagation and formal statistical inference about climatic changes based on raw records from deep lake sediments. Similar issues exist and deserve attention in the assessment of data from deep sea sediments, ice cores, and tree rings. Technically, the project concerns statistical calibration of raw data records, and time series analysis to assess patterns of variation in the geological records over time. The initial objective will be to develop an appreciation of the statistical issues as they permeate the various stages of the experimental processes in analyzing isotope and other proxy climatic variables from deep-lake sediment cores. Cross- disciplinary training for each investigator will e a central and continuing feature of the collaboration. This will be directed at bridging the gulf between, on one hand, current standards of practice in statistical analysis of paleoclimate data (e.g. Pisias and Moore 1981; Hagelberg, Pisias and Elgar 1991) and, on the other hand accessible and appropriate modern statistical methods and models. A reciprocal training and development schedule will provide the opportunity for each of the two investigators to become sufficiently proficient in the fundamentals of the other's field of expertise so as to initiate and enable a research program focussed on rigorous statistical analysis of paleoclima te data generated from deep lake sediment cores. Statistician Mike West will become familiar with the methods used to select sediments core sites for paleoclimatic analysis, the various methods of geochemical analysis of sediment cores (and notably the limitations of age assignment to sediments as a result of various natural processes such as erosion and redeposition, bioturbation, diagenesis and laboratory contamination), calibration of carbon dating assessments, and current methods of time series analysis used in paleoclimatology. Geologist Tom Johnson will become familiar with the capabilities and pitfalls of statistical methods, especially methods of time series analysis that are currently used in this area, and gain appreciation of the consequences for uncertainty assessment in geochronology. The investigators anticipate eventual development of Bayesian methods in statistical calibration at the various stages of the experimental process, and resulting time series analysis in assessing cyclical variability in calibrated records. Both investigators will also become familiar with the statistical issues and methods of calibration of 14C dates (together with associated uncertainty assessments) to calendar dates, and with the recent development of advanced statistical methods in the field. This project will eventually lead to focussed research efforts in developing Bayesian statistical models and methods appropriate for all stages of the experimental process in sediment based paleoclimatology, and that will ultimately apply in other geological and archaeological arenas. Most optimistically, it is hoped that this collaboration will seed the development of an internationally recognised centre for the statistical analysis of paleoclimate proxy records at Duke University. ***