The problem of statistical inference for open chaotic systems measured with error is complicated by the interaction of the uncertainty introduced by chaos, and the various sources of random or external variation. Here a method of representing measured data from large open chaotic systems subject to error as collections of threads of plausible pseudo future histories to enable statistical analysis is described. This representation provides asymptotically consistent predictive distributions, for use in developing predictive likelihood methods which: 1. provide a framework for variable selection, 2. provide a framework for Bayesian updating, so for example 4 season ahead predictions learn naturally as the 3rd season ahead is measured. 3. allows examination of conditional scenarios along the future histories for planning purposes. 4. allows the ranking of variable, delay combinations with higher signal to noise ratio. The method is tested for learning and variable selection by examining its behavior in predicting 9 years across 4 seasons of climate variables, including local temperature and rainfall measurements at two locations, predicting up to 4 seasons ahead.

翻译：带误差测量开放混沌系统的统计推断问题因混沌引入的不确定性与各种随机或外部变异源的相互作用而变得复杂。本文描述了一种方法，将来自大规模开放混沌系统的带误差测量数据表示为合理伪未来历史轨迹的集合，以支持统计分析。这种表示能够生成渐近一致的预测分布，用于开发预测似然方法，该方法：1.提供变量选择框架，2.提供贝叶斯更新框架——例如，第4季度的预测会随着第3季度的测量结果自然习得，3.允许沿未来历史轨迹检验条件情景以支持规划，4.能够对信噪比更高的变量-延迟组合进行排序。通过预测9年间两个地点4个季节的本地温度与降雨量等气候变量（超前预测4个季节），测试了该方法在学习和变量选择方面的表现。