The Expected Value Of Sampling Information For Nonlinear Decision Problem On Two Actions

Expected value of sampling information is an important problem in Bayesian statistics, the decision maker decide whether it is worth sampling by counting the expected value of sampling information of decision problem. So far, there have been many scholars research the linear decision problem in different models. But, there is no literature on the expected value of sampling information for nonlinear decision problem. In fact, the vast majority decision problems are nonlinear decision problem. There are infinitely models of nonlinear decision problem, so this article is about four kinds of nonlinear decision problems under strictly monotone increasing when apply conjugate prior distribution, they are under the convex model, convex model, convex model after the first convex and after the first convex convex model, in the back of these models have their expected value of sampling information. These results both in theory and in practice have important significance and in favor of researching the nonlinear decision problem in the future. This article is proposed and studied in this case.This article is divided into five parts.The first part, this article introduces the research background, the significance and the preliminary knowledge of expected value of sampling information.The second part, the four kinds of nonlinear decision problem on two actions under strictly monotone increasing are studied, they are under the convex model, convex model, convex model after the first convex and after the first convex convex model. Because the problem is more complex, this article solves it through the discussion of the intersection number.The third part and the fourth part, this article studies the expected value of sampling information for nonlinear decision problem on two actions under the model of Pareto distribution is conjugate to uniform distribution and Gamma distribution is conjugate to the Gamma distribution, its detailed processes of calculation are given and the results are been used in the real life.The fifth part is the conclusion. There is a relationship between the range of unknown parameter which calls ? in some distribution and the loss function, the conjugate prior distribution of ? in the specific distribution is given which is good for researching the nonlinear decision problems under the different models.This article analyzes nonlinear decision problem on two actions, gets the formulas of the expected value of sampling information for nonlinear decision problem on two actions under the two different models and their detailed processes of proof. These results have a certain degree of usability and universality.