Iterative approximation of Markov process parameters in a model of large scale business purchases

Abstract

Large scale business to business purchases often involve a series of vetting stages which must be satisfied prior to their resolution. This paper models the progression of sales projects through a company's sales pipeline via a stochastic process. The pipeline is viewed as a sequential Markov chain wherein each time step permits: failure, no movement, or advancement in a linear ordering of potential states terminating in a successful purchase. The transition probabilities which parameterize this model are determined via time series data of each salesman's progression in selling their products. In theory, the parameters guiding such a Markov process can be estimated analytically via the Maximum Likelihood procedure. However because the state transitions of sales projects can not be provided in real time, the Expectation Maximization algorithm is applied to estimate these parameters. Our results suggest that more data is needed to generate a reasonable approximation of transition probabilities.