Basu's via media is what he referred to as the middle road between the Bayesian and frequentist poles. He seemed skeptical that a suitable via media could be found, but I disagree. My basic claim is that the likelihood alone can't reliably support probabilistic inference, and I justify this by considering a technical trap that Basu stepped in concerning interpretation of the likelihood. While reliable probabilistic inference is out of reach, it turns out that reliable possibilistic inference is not. I lay out my proposed possibility-theoretic solution to Basu's via media and I investigate how the flexibility afforded by my imprecise-probabilistic solution can be leveraged to achieve the likelihood principle (or something close to it).
翻译:巴苏所指的中间道路是介于贝叶斯派与频率学派之间的折中路径。他似乎对能否找到合适的中间道路持怀疑态度,但我并不认同。我的基本主张是,仅凭似然函数无法可靠地支持概率推断,而这一结论源于对巴苏在似然解释中陷入的技术陷阱的分析。尽管可靠的概率推断难以实现,但事实证明,可靠的可能性推断是可行的。我阐述了自己提出的基于可能性理论解决巴苏中间道路的方案,并探讨如何利用我所提出的非精确概率解法的灵活性来实现似然原理(或接近该原理的目标)。