Use of estimating functions to improve sequential adaptive decisions and dynamic regularization

我的愿景是将创新的统计理论和方法发展到涉及动态因素和不确定性的广泛应用中，受到这一愿景的启发，我的长期研究计划一直受到来自重要社会经济需求的实际问题和影响的激励，包括金融建模，保险风险管理和复杂的健康数据分析。具体来说，我的研究兴趣包括(I)统计建模各种应用的自适应决策过程，（II）降低数据维数和问题复杂性，统计估计状态并预测具有未知动态的自适应决策过程的未来运动，（III）有效地平衡利用（即，应用我们迄今为止所采取的决策中似乎最好的决策）和探索(即，承担风险并尝试新的决策)以获得顺序自适应决策过程的最佳全局性能。这种自适应决策过程通常具有显著的方法挑战和实际限制，包括建模动态数据流（例如，时间序列模型，状态空间模型和过滤），自适应但动态决策（例如，强盗模型和马尔可夫决策过程），复杂的数据结构（例如空间和时间，高光谱数据），以及底层环境的随机性（例如马尔可夫切换）。与我的长期研究目标一致，这个NSERC提案的重点是增强统计模型和方法的具体目标，如正则化和广义贝叶斯估计函数，以及各种应用，如风险管理、算法交易、保险控制和强化学习。我将在我目前关于估计函数的研究成果的基础上建立这个NSERC项目，并寻找贝叶斯和频率估计函数的相互作用，以更好地进行状态估计，并通过将相互作用纳入强盗模型，状态空间模型和滤波，以及稳定噪声驱动的复杂模型与马尔可夫切换，更好地解决开发和探索困境。本研究计划对培养HQP的跨学科研究能力具有重要意义。在未来五年，我计划培养5名本科生，5名硕士，1名博士（2024年9月开始）。我的研究小组目前有4名硕士生和1名研究助理。高素质的人员将参与拟议的研究计划和目标的各个阶段。我的小组成员和我期待高质量的出版物，会议报告和跨学科合作的研究成果。

Inspired by my vision of developing innovative statistical theories and methods to a broad range of applications involving dynamic factors and uncertainty, my long term research program has been motivated by practical issues and impact arising from important socioeconomic needs including financial modeling, insurance risk management and complex health data analysis. Specifically my research interests include (I) statistically modeling adaptive decision processes for a variety of applications, (II) reducing data dimensionality and problem complexity, and statistically estimating the state and predicting the future movement of adaptive decision processes having unknown dynamics, (III) effectively balancing between exploitation (i.e., applying what appears to be the best among the decisions we have taken so far) and exploration (i.e., taking risk and trying a new decision) for the best global performance of the sequential adaptive decision process. Such adaptive decision processes are typically characterized with significant methodological challenges and practical constraints, including modelling dynamic data streams (e.g., time series models, state space models and filtering), adaptive but dynamic decisions (e.g., bandit models and Markov decision processes), complex data structures (such as of spatial and temporal, hyperspectral data), and randomness of the underlying environment (such as Markov switching). Aligned to my long term research goals, this NSERC proposal is focused on specific goals of enhancing statistical models and approaches such as regularization and generalized Bayesian estimating functions, with various applications such as risk management, algorithmic trading, insurance control, and reinforcement learning. I will build this NSERC program on my current research achievements on estimating functions and search for the interplay of the Bayesian and frequentist estimating functions for better state estimation, and better address the exploitation and exploration dilemma by incorporating the interplay into the bandit models, state space models and filtering, and complex models driven by stable noise with Markov switching. The proposed research program is important for training HQP on interdisciplinary research. In the next five years, I propose to train five undergraduate students, five M.Sc. students, and one Ph.D. student (to start September 2024). My research group currently has four M.Sc. students and one research assistant. The highly qualified personnel will be involved in all stages of the proposed research program and objectives. My group members and I anticipate high quality publications, conference presentations and interdisciplinary collaborations from the achieved research.