FIGURE C.11 Bayes risk for various linear functions using empirical prior fitted from Multnomah County ACS data.

NOTE: See Figure C.10 for derivation of the empirical prior using the “line” model as the true model.

case, evaluating it using simple decision-theoretic tools for various population characteristics, under various models, across a rangeof unknown model parameters.

The proposed MA strategy does poorly in this evaluation. It is not minimax (although this extremely conservative criterion is not very useful in practice). More importantly, it is generally not Bayes under any reasonable prior on the SNR. For example, under the I(1) model (and ruling out the temporal average for which all strategies are equally effective), MAs are Bayes only if the true SNR is zero, or equivalently if the true values are constant over time.

The question for this research was to determine if there are viable alternatives to the proposed MA strategy. The I(1) strategy meets the criteria set out at the beginning of this paper. It is simple and consistent. Its weights are unequal but fixed, so that large-scale implementation is no harder than MA, and comparability across domains is ensured. Its linear form means that tables add up. Guidance for users would seem to be no worse for a weighted MA than for an unweighted MA.

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