In this context, it is assumed that the model will be able to account for demand for an item over a series of transactions, rather than only for a single transaction. The model is developed on the basis of a hypothetical scenario where the consumption of a particular product is observed to be correlated inversely with the number of times the product is sold by the brand. An approach to estimating the infrequency of a hypothetical purchase is based on the Bayes' rule, the Bayesian Inference Procedure. In this approach, the probability of a certain type of product being sold is compared as follows: If a product is sold n times, the probability of a product being sold n+1 times is a function of the number of times the product is sold on average and the number of times the product is purchased. If n is the number of times the product is sold then the probability of a product being sold n+1 times is the product's frequency n/2 – 1. If n is the number of times the product is purchased, the function is the product's frequency — 1/2 -1/2. In this way, the probability that the product is sold/purchased is calculated for every sale/purchase transaction of the product. A simple version of this method was proposed by P. N. Borne in 1971. After extensive experience with a wide variety of consumer products which have been sampled continuously for more than 2 decades, the authors have developed a new Bayesian analysis technique which reduces the number of estimates necessary to make a reliable estimate of the probability of an ordered product being sold to n+1 or n+2. This technique also facilitates the development of a procedure for generating estimates of the probability of buying a particular product in a certain number of sales (or purchases) as a function of a specific customer characteristics. The analysis is particularly well suited to use for studies which measure the probability of a particular product being sold or purchased; the probability of one particular customer purchasing a product n times is expressed as if the product had been sold/bought n times and the customer had never purchased any other product in the experiment. The analysis is also an effective way of studying the frequency of sales/purchases through a variety of samples. In this section, the analysis and its application to studies of product demand for food is described and tested.
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MP A R Munich Personal Repel Archive Bayesian estimation of the infrequency of purchase model with an application to food demand in the UK R Ti n and M Arno ult University of Reading 26. August 2008
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