We have developed a fully Bayesian survival-analysis framework that reformulates inference about system lifetimes in terms of hazard and survival functions, and extends this representation to interacting actors. Starting from J.~Richard Gott's Copernican principle, we express the scale-free prior as a baseline hazard $λ(t)=1/t$, thereby linking a static prior over lifetimes to the dynamic language of survival analysis. In this formulation, Bayesian updating corresponds to conditioning on survival, while the resulting posterior distribution admits a natural representation in terms of hazard and survival functions. The approach is intended for settings where data are sparse or unreliable, and where a scale-free, assumption-light baseline is preferable to heavily parameterized models. Building on this foundation, we derive general expressions for two-actor systems that characterize joint survival, conditional lifetimes, and comparative outcomes without requiring a specific parametric form of interaction. This yields a flexible and modular framework in which baseline dynamics are separated from interaction effects, allowing different mechanisms to be incorporated transparently. Thus, the primary contribution is a general hazard-based formulation of Bayesian updating and its extension to interacting systems To illustrate the framework, we consider a multiplicative resource-depletion specification in which interaction modifies the baseline hazard through cumulative engagement intensity. This example demonstrates how interaction terms can be embedded while preserving analytical tractability, including closed-form expressions under simplifying assumptions. We further provide a stylized application to an asymmetric two-actor conflict, the 2026 US/Israel--Iran hostilities, to highlight the qualitative implications of the approach.

翻译：我们构建了一个完全贝叶斯生存分析框架，将系统寿命推断重新表达为风险函数和生存函数，并将此表示扩展至交互主体。从J.~Richard Gott的哥白尼原理出发，我们将无标度先验表达为基准风险率$λ(t)=1/t$，从而将寿命的静态先验与生存分析的动态语言联系起来。在该表述中，贝叶斯更新对应于对生存条件的制约，而所得后验分布自然地呈现出风险函数与生存函数的表示形式。该方法适用于数据稀疏或不可靠的场景，且相较于高度参数化的模型，以无标度、弱假设的基准更为可取。在此基础上，我们推导了两主体系统的一般表达式，在无需指定特定参数化交互形式的前提下，刻画了联合生存、条件寿命及比较结果。这产生了一个灵活且模块化的框架，其中基准动态与交互效应相互分离，使得不同机制得以透明地整合。因此，主要贡献在于提出了基于风险函数的贝叶斯更新一般形式，并将其扩展至交互系统。为阐明该框架，我们考虑了一种乘性资源消耗设定，其中交互通过累积参与强度修正基准风险率。该示例展示了如何在保持分析可处理性的前提下嵌入交互项，包括在简化假设下得到闭式表达式。我们进一步提供了一个不对称两主体冲突的程式化应用——2026年美以与伊朗敌对案例，以突出该方法的定性启示。