Bayesian optimization (BO) is a powerful framework for estimating parameters of expensive simulation models, particularly in settings where the likelihood is intractable and evaluations are costly. In stochastic models every simulation is run with a specific parameter set and an implicit or explicit random seed, where each parameter set and random seed combination generates an individual realization, or trajectory, sampled from an underlying random process. Existing BO approaches typically rely on summary statistics over the realizations, such as means, medians, or quantiles, potentially limiting their effectiveness when trajectory-level information is desired. We propose a trajectory-oriented BO method that incorporates a Gaussian process surrogate using both input parameters and random seeds as inputs, enabling direct inference at the trajectory level. Using a common random number approach, we define a surrogate-based likelihood over trajectories and introduce an adaptive Thompson Sampling algorithm that refines a fixed-size input grid through likelihood-based filtering and Metropolis-Hastings-based densification. This approach concentrates computation on statistically promising regions of the input space while balancing exploration and exploitation. We apply the method to stochastic epidemic models, a simple compartmental and a more computationally demanding agent-based model, demonstrating improved sampling efficiency and faster identification of data-consistent trajectories relative to parameter-only inference.

翻译：贝叶斯优化（BO）是一种用于估计昂贵仿真模型参数的有效框架，特别适用于似然函数难以处理且计算成本高昂的场景。在随机模型中，每次仿真均使用特定参数集及显式或隐式随机种子运行，其中每个参数集与随机种子的组合均能生成从底层随机过程中采样的单次实现（即轨迹）。现有BO方法通常依赖基于各次实现的汇总统计量（如均值、中位数或分位数），在需要轨迹级信息时可能限制其有效性。我们提出一种面向轨迹的BO方法，该方法构建以输入参数和随机种子作为输入的高斯过程代理模型，从而在轨迹层面实现直接推断。通过采用公共随机数方法，我们定义了基于代理模型的轨迹似然函数，并提出一种自适应汤普森采样算法：该算法通过基于似然性的过滤和基于Metropolis-Hastings的稠密化策略，在固定大小输入网格上进行迭代优化。该方法将计算资源集中于输入空间中统计上具有潜力的区域，同时平衡探索与开发。我们将该方法应用于随机疫情模型（包括简单舱室模型与计算要求更高的基于智能体模型），实验表明：相较于仅依赖参数的推断方法，该方法显著提高了采样效率，并加速了与数据一致的轨迹的识别过程。