Models and Estimation Methods in Visual Scanning Experiments

Abstract

This paper deals with a problem that often arises in visual scanning experiments in particle physics, viz. that of estimating the number of undetected particles from the scanning record. This problem is formulated here as one in estimating the size of a multinomial population from an incomplete observation of the cell totals under constraints on the cell probabilities. These constraints differ according to the assumptions made about the scanners and the particles, thus giving rise to different probability models. Several models are considered here-existing ones as well as a new generalized model (Sections 2, 4, 5) Estimation procedures corresponding to these models are discussed (Sections 6–10). A discussion of the applicability of the techniques presented here to other areas is also included (Section 1). A table of the notation used in this paper is provided in Section 3.

Key Words:

• Visual Scanning Models in Particle Physics
• Estimating the Number of Undetected Particles
• Population Size Estimation and Applications
• Incomplete Multinomial Data with Constraints on Cell Probabilities
• Capture-Recapture Method
• Principle of Local Independence
• Modified Binomial Model
• Item Analysis
• Logistic Model
• Conditional Maximum Likelihood Method
• Method of Moments
• Standard Error Formulas