Reformulating Markovian processes for learning and memory from a hazard function framework

• Link hazard functions to the probabilities in a Markov model.
• Show that a Markov chain is linked to a Weibull model with a shape parameter c=1c=1.
• Show that a general Markovian model rather than a Markov chain is needed.
• Develop a Markovian model for the Chechile et al. (2012) IES model.

With the development of stimulus sampling theory (SST), William K. Estes demonstrated the importance of Markov chains for capturing many important features of learning. In this paper, learning and memory retention are reexamined from a hazard function framework and linked to the stochastic transition matrices of a Markov model. The probabilities in the transition matrix are shown to be discrete hazard values. In order for the stochastic matrix to be a homogeneous Markov chain, there is a requirement that the transition matrix values remain constant. Yet for some learning and memory retention applications, there is evidence that the transition matrix probabilities are dynamically changing. For list learning, the change in hazard is attributed in part to differences in the learning rate of individual items within the list. Even on an individual basis, any variability in item difficulty whatsoever is enough to induce a change in hazard with training. Another analysis was done to delineate the hazard function for memory loss. Evidence is again provided that the hazard associated with the loss of memory is systematically changing. A Markov chain is not a suitable model when there are dynamic changes in the hazard. However, for both the learning and memory applications, a general Markovian model can be used, where transition probabilities are a function of trial number or interpolated event number. Finally, a more complex, four-state application is considered. This application is based on the Chechile, Sloboda, and Chamberland (2012) multinomial processing tree model called the IES model. The IES model obtains probability estimates for the representation of target information in memory in terms of four possible states—explicit memory, implicit memory, fractional memory, and non-storage. Stochastic matrices for the IES model are provided and are shown to yield new insights about implicit memory.