Abstract
AbstractIt is usual to grasp the activity of the public sector as a cycle of inputs, outputs and outcomes. The inputs are the resources or expenditures, the outputs are the products or services achieved, and the outcome is the criterion to measure the results. We will consider an optimal expenditure policy by formulating it as a sequential decision problem with Markovian transition with the outcome as a state. Especially, the outcome relates to the cumulative amount of resources, but the strict relationship is unknown. The problem is how much to expend to the public services to improve the outcomes. We also consider this problem in which the state changes according to a Markovian transition based on the total positivity of order two. The total positivity of order two is a fundamental property to investigate the sequential decision problem, and it also plays an important role in the Bayesian learning procedure for a partially observable Markov process.
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