A Closed-Form EVSI Expression for a Multinomial Data-Generating Process

Abstract

This paper derives analytic expressions for the expected value of sample information (EVSI), the expected value of distribution information, and the optimal sample size when data consists of independent draws from a bounded sequence of integers. Because of the challenges of creating tractable EVSI expressions, most existing work valuing data does so in one of three ways: (1) analytically through closed-form expressions on the upper bound of the value of data, (2) calculating the expected value of data using numerical comparisons of decisions made using simulated data to optimal decisions for which the underlying data distribution is known, or (3) using variance reduction as proxy for the uncertainty reduction that accompanies more data. For the very flexible case of modeling integer-valued observations using a multinomial data-generating process with Dirichlet prior, this paper develops expressions that (1) generalize existing beta-binomial computations, (2) do not require prior knowledge of some underlying “true” distribution, and (3) can be computed prior to the collection of any sample data.