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arXiv 2009.06229math.PRstat.AP
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随机序列收敛性的贝叶斯估计及其在气候变化中的应用

Bayesian Appraisal of Random Series Convergence with Application to Climate Change

Sucharita Roy, Sourabh Bhattacharya

摘要:

Roy和Bhattacharya(2020)提供了无穷级数的贝叶斯特征,他们最重要的应用,即表征著名的黎曼假设的狄利克雷级数,揭示了150多年来最著名的猜想不支持的见解。与Roy和Bhattacharya(2020)考虑的确定性级数相比,在本文中,我们采用随机无穷级数进行研究。值得注意的是,我们的方法不需要任何简化的假设。虽然随机序列的贝叶斯特征理论与确定性设置的贝叶斯特征理论没有什么不同,但在随机设置中,部分和的有效上界的构建是一项具有挑战性的任务。本文构造了随机无穷级数部分和的参数和非参数上界形式,并证明了后者相对于前者的普遍性。仿真研究显示出高精度和效率的非参数约束在所有的设置,我们认为。最后,利用性质,在级数收敛的情况下,和项趋于零,我们考虑应用我们的非参数边界驱动贝叶斯方法对全球气候变化的分析。具体来说,通过分析1850- 2016年的全球平均温度记录和距今12,000年前的全新世全球平均温度重建数据,我们得出结论,尽管目前全球变暖的情况,全球气候动力学只受到暂时的变化,目前的全球变暖是一个例子,以及长期的全球变暖或变冷,无论是在过去还是在未来,都是极不可能的。

英文摘要:

Roy and Bhattacharya (2020) provided Bayesian characterization of infinite series, and their most important application, namely, to the Dirichlet series characterizing the (in)famous Riemann Hypothesis, revealed insights that are not in support of the most celebrated conjecture for over 150 years. In contrast with deterministic series considered by Roy and Bhattacharya (2020), in this article we take up random infinite series for our investigation. Remarkably, our method does not require any simplifying assumption. Albeit the Bayesian characterization theory for random series is no different from that for the deterministic setup, construction of effective upper bounds for partial sums, required for implementation, turns out to be a challenging undertaking in the random setup. In this article, we construct parametric and nonparametric upper bound forms for the partial sums of random infinite series and demonstrate the generality of the latter in comparison to the former. Simulation studies exhibit high accuracy and efficiency of the nonparametric bound in all the setups that we consider. Finally, exploiting the property that the summands tend to zero in the case of series convergence, we consider application of our nonparametric bound driven Bayesian method to global climate change analysis. Specifically, analyzing the global average temperature record over the years 1850--2016 and Holocene global average temperature reconstruction data 12,000 years before present, we conclude, in spite of the current global warming situation, that global climate dynamics is subject to temporary variability only, the current global warming being an instance, and long term global warming or cooling either in the past or in the future, are highly unlikely.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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