One of the key memory tests in the clinical assessment and diagnosis of Alzheimers Disease (AD) is the recognition memory task. Models developed in cognitive psychology have previously been applied to help understand clinical data. In particular, Signal Detection Theory (SDT) models have been used, to separate peoples memory capabilities from their decision-making strategies. An important finding in this literature is that people with AD change their decision strategy in response to memory impairment, applying a more liberal criterion than people without AD. In this paper, we analyze clinical data that measures the progression of AD in a detailed way, using a theoretically motivated version of SDT, and applying hierarchical Bayesian methods to model individual differences. Our results corroborate many of the previous findings, but provide a more detailed focus on recognition performance with AD progression.