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In exploring how foragers perceive rewards, we often find that well-motivated individuals are not too choosy and unmotivated individuals are unreliable and inconsistent. Nevertheless, when given a choice we see that individuals can clearly distinguish between rewards. Here we develop the logic of using responses to two-choice problems as a derivative function of perceived reward, and utilize this model to examine honey bee perception of nectar quality. Measuring the derivative allows us to deduce the perceived reward function. The derivative function of the perceived reward equation gives the rate of change of the reward perceived for each reward value. This approach depends on presenting free-flying foragers with a series of two different rewards presented simultaneously (i.e., two-choice, binomial tests). We also examine how honey bees integrate information from a range of reward qualities to formulate a functional response. Results suggest that honey bees overestimate higher quality rewards and that direct comparison is an important step in the integration of information from a range of rewards.

We employ a regression model with errors that follow a continuous autoregressive process to analyse longitudinal studies. In this way, unequally spaced observations do not present a problem in the analysis. We employ a Bayesian approach, where our inferences are based on a direct resampling process that generates values from the posterior distribution of the parameters of the model. We illustrate these Bayesian inferences with an analysis of a longitudinal study that involves the regression of foetal head circumference on menstrual age. Using these same data, we contrast the Bayesian approach with a maximum likelihood technique.

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