Optimal Budget-Constrained Sample Allocation for Selection Decisions with Multiple Uncertain Attributes

A decision-maker, when faced with a limited and fixed budget to collect data in support of a multiple attribute selection decision, must decide how many samples to observe from each alternative and attribute. This allocation decision is of particular importance when the information gained leads to uncertain estimates of the attribute values as with sample data collected from observations such as measurements, experimental evaluations, or simulation runs. For example, when the U.S. Department of Homeland Security must decide upon a radiation detection system to acquire, a number of performance attributes are of interest and must be measured in order to characterize each of the considered systems. We identified and evaluated several approaches to incorporate the uncertainty in the attribute value estimates into a normative model for a multiple attribute selection decision. Assuming an additive multiple attribute value model, we demonstrated the idea of propagating the attribute value uncertainty and describing the decision values for each alternative as probability distributions. These distributions were used to select an alternative. With the goal of maximizing the probability of correct selection we developed and evaluated, under several different sets of assumptions, procedures to allocate the fixed experimental budget across the multiple attributes and alternatives. Through a series of simulation studies, we compared the performance of these allocation procedures to the simple, but common, allocation procedure that distributed the sample budget equally across the alternatives and attributes. We found the allocation procedures that were developed based on the inclusion of decision-maker knowledge, such as knowledge of the decision model, outperformed those that neglected such information. Beginning with general knowledge of the attribute values provided by Bayesian prior distributions, and updating this knowledge with each observed sample, the sequential allocation procedure performed particularly well. These observations demonstrate that managing projects focused on a selection decision so that the decision modeling and the experimental planning are done jointly, rather than in isolation, can improve the overall selection results.

THE EFFECT OF A PROGRAM OF PORTABLE ELECTRONIC PIANO KEYBOARD EXPERIENCE ON THE ACQUISITION OF SIGHT-SINGING SKILL IN THE NOVICE HIGH SCHOOL CHORUS

The problem was to determine whether a method of aural and visual vocal training that included a program of portable electronic piano keyboard experience would be more effective in teaching sight-singing skills to novice high school chorus students than a method that included only aural and visual vocal training. A sub-problem was to determine whether novice chorus students enjoyed playing electronic keyboards in chorus as a reinforcement experience in sight-singing training. Students were randomly assigned to two treatment groups, tested with the Musical Aptitude Profile, Tonal Imagery, part A, and then trained separately. The experimental group sang repetitions of melodic patterns and utilized techniques associated with the Kodály Method while simultaneously playing keyboard. The comparison group received a similar treatment without using keyboards. The students were pre- and post-tested in sight-singing using the Vocal Sight-Reading Inventory. Results of the Analysis of Covariance using MAP scores as the covariate revealed no significant difference (p<.05) between post-test scores of the two groups. Improvement was noted in 96% of students from pre-test to post-test regardless of grouping. The repeated measures ANOVA revealed a significant relationship (p<.006) between aptitude group and post-test score. High aptitude students in both groups were found to benefit more from the training than low aptitude students. High aptitude keyboard group students achieved an average gain score that was 8.67 points higher than the comparison group. Of the total experimental group, 92% enjoyed playing keyboards in chorus. It is recommended that future research be undertaken to study the use of keyboards with advanced high school choruses and with uncertain singers in the high school chorus. Research is also needed to develop graded, valid, and reliable sight-singing tests for use in high school chorus. Techniques of the Kodály Method should be further investigated for use in high school sight-singing training.

An investigation of the stability and diffusivity of flexible lipid vesicles for transdermal insulin delivery

Gemstone Team No More Needles