Expected information of noisy attribute forecasts for probabilistic forecasts

This paper extends the maximum entropy (ME) model to include uncertainty about noisy moment forecasts. In this framework the noise propagates to the ME model through the constrained optimization's Lagrange multipliers. The mutual information and expected Fisher information are included for assessing effects of the noisy moment forecasts on the ME model and its parameters. A new mean–variance decomposition of the mutual information is derived for the normal distribution when the mean and variance are both noisy. A simulation estimator is used to estimate the expected information for noisy ME models on finite support. A family of ensemble of individual level noisy ME forecast models is introduced which includes individual level versions of the conditional logit and multiplicative competitive interaction models as specific cases. To illustrate the implementation and merits of the proposed noisy ME framework, the classic loaded dice problem and discrete choice analysis are examined.