The Expected Value Of Sampling Information For Linear Or Quadratic Decision Problem On Two Actions Under The Be-B Model

In the first part,we introduce the background of the Expected Value of Sampling Information, which is defined as the increased value of the expected benefit gained from the best action before and after the sampling.In the second part, we discuss the linear decision problem on two actions under the (Be-B) model and the counting formula of the EVSI.Suppose X₁,X₂,……X_n is a sample of population X, whose density is given by θ^x(1-θ)^1-x withx=0,1,0<θ<1. We denote T=∑X_i, then T obeys binomial distribution which can be denoted by B(n,θ) with θ is given. Next suppose the priori distribution of θ is Beta distribution with parameter α andβ, denoted by Be(n,θ), where α and β are supposed to be known. We denote the model above by (Be-B). Suppose the benefit function is given byFirst,we give the best posterior action, choosing criteria, that is WhenT=t0,a₂ is the best action, and whenT=t=t₀, a₁ and a₂ are both the best action, when and T=t>t₀ , a₁is the best action.Second, we give the counting formula of EVSI for linear decision problem on two actions under the (Be-B) model. That is, when a₁ is the prior best action,and when a₂ is the prior best action,,whereIn the third part, we discuss the quadratic decision problem on two actions under the Be-B model, and give the counting formula of EVSI. Second, we give the counting formula of EVSI for quadratic decision problem on two actions under the (Be-B) model for (3). That is, when a₁ is the prior best action,and when a₂ is the prior best action,where A,B are borrowed from (2.9),and(2.10) andIn the last part, we make better the counting formula of EVSI for linear decision problem on two actions under the (г-P) model given by [6], and we give the counting formula of EVSI for quadratic decision problem on two actions under the same model. We can see the result of this part are similar with the result of the second and the third parts.