Computational Sensitivity Analysis for Decision-Making under Data Uncertainty

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Quantitative models for making complex decisions require various parameters to be specified before a decision is derived. Those parameters are often uncertain estimates from data. Since a derived decision is dependent on the parameters, it is an essential part of decision-making to analyze how the decision changes when the estimated parameters are perturbed. The proposed research aims to develop novel methods to analyze the sensitivity of decisions obtained through complex models. Even with the modern advancement of computing power, it is still a challenging task to analyze the sensitivity of high-dimensional models that contain a large number of parameters that can be simultaneously perturbed. The proposed research will develop computationally practical algorithms to perform sensitivity analysis for high-dimensional models. This research will achieve the goal for two types of decision-making problems separately, the one where a complex decision is made once and the other where a series of decisions need to be made over multiple stages, that is, sequential decision-making.***This proposal also aims to study how the use of data from heterogeneous systems affects sequential decision-making. A series of decisions are made based on knowledge obtained from historical data about how the system evolves over time. Recently, sequential data from large populations have become more readily available and such data are likely to contain heterogeneous transition patterns. For example, in a large population with a certain disease, the disease status of some patients might progress faster than for other patients. If this is the case, then modeling each transition pattern separately and applying a treatment plan that is optimal for the specific transition pattern can result in better outcomes. This research will formally study the following general question: under what conditions is it beneficial to model heterogeneous patterns and to assign decisions tailored to each pattern?***To people who use analytical methods to make complex decisions, the proposed research will provide computationally tractable methods to understand the sensitivity of decisions. The two long-term objectives of this proposal, analyzing the sensitivity of optimal decisions under parameter uncertainty and studying the benefit of modeling distinct transition trends, align with personalized decision-making, which is gaining a lot of attention particularly in health care applications. The proposed research will provide methods to analyze the sensitivity of treatment plans under data uncertainty and to find optimal care plans for heterogeneous patient types. Furthermore, this proposal focuses on issues arising in decision-making based on large-scale data sets, so the need for the proposed methods will keep rising as we face more complex decisions to be made based on larger data sets.