比较两种方法在群体模型中估计隐藏状态的性能,发现针对个体预测用似然法更好。
Comparing Data Assimilation and Likelihood-Based Inference on Latent State Estimation in Agent-Based Models
- 对比数据同化与似然推断在群体模型中的状态估计效果
- 似然推断在个体层面更准确,即使模型有误设也表现稳定
- 数据同化更适合宏观预测,在不同聚合层级仍具竞争力
本文首次系统比较了数据同化(DA)与似然推断(LBI)在基于主体模型(ABM)中的隐状态估计表现。这类模型通过动态演化、部分可观测的微观状态生成可观测的时间序列,需估计隐状态以使模拟结果与真实数据对齐。传统上依赖数据同化,尤其适用于连续方程模型如天气预报,但其在离散、非线性的群体模型中面临挑战。数据同化以模型无关方式近似似然,适用性广但精度有限;而似然推断利用模型本身的似然函数,能更精准估计状态,但需手工构建特定模型的似然,可能复杂甚至不可行。我们在经典的‘界限信任模型’(Bounded-Confidence Model)上进行比较,该模型中个体仅受观点相近者影响。结果显示,即便在模型误设情况下,似然推断仍能更准确恢复个体层面的观点状态,提升个体预测性能;而在聚合层面,两种方法表现相当,且数据同化在某些参数设置下仍具竞争力。结论表明,数据同化适合宏观预测,似然推断则更适合个体级推断。
原文摘要 · Abstract (English)
In this paper, we present the first systematic comparison of Data Assimilation (DA) and Likelihood-Based Inference (LBI) in the context of an Agent-Based Model (ABM). These models generate observable time series driven by evolving, partially-latent microstates. Latent states must be estimated to align simulations with real-world data, a task traditionally addressed by DA, particularly in continuous and equation-based models used in weather forecasting. However, the nature of ABMs poses challenges for standard DA methods. Solving such issues requires adapting previous DA techniques or using ad hoc alternatives such as LBI. DA approximates the likelihood in a model-agnostic way, making it broadly applicable but potentially less precise. In contrast, LBI provides more accurate state estimation by directly leveraging the model's likelihood, but at the cost of requiring a hand-crafted, model-specific likelihood function, which may be complex or infeasible to derive. We compare the two methods on the Bounded-Confidence Model, a well-known opinion dynamics ABM, where agents are affected only by others holding sufficiently similar opinions. We find that LBI better recovers latent agent-level opinions, even under model mis-specification, leading to improved individual-level forecasts. At the aggregate level, however, both methods perform comparably, and DA remains competitive across levels of aggregation under certain parameter settings. Our findings suggest that DA is well-suited for aggregate predictions, while LBI is preferable for agent-level inference.
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