Application of hidden Markov model to products shelf lives
2008
Ledauphin, S. | Pommeret, D. | Qannari, E.M.
We consider an experiment where a panel of assessors are asked to assess the quality of a product at different intervals of time by means of sensory evaluation. The aim is to study the dynamic of degradation and assess the shelf lives of the products. The assessment of the panellists consists in the rating of the products on the basis of a categorical scaling. We propose to use hidden Markov chains (HMC) to model the decay of the products in the course of time. In comparison to a previous model based on Markov chains [Ledauphin, S., Pommeret, D., & Qannari, E. M. (2006). A Markovian model to study products shelf lives. Food Quality and Preference, 17(7-8), 598-603], this model makes it possible to take account of the assessors' variability. Hidden Markov models (HMM) are based on the estimation of a transition matrix which states the probability that the assessment of a product changes from one category to another. They also include conditional probabilities that reflect random errors in the assessment. The parameters of the HMM are estimated by means of EM algorithm (expectation and maximisation) and the outcomes are used in conjunction with correspondence analysis in order to compare the evolution of the decay of several products. The approach is mainly meant to be descriptive as it makes it possible to depict and compare the evolution of the decay of various products. However, it is possible to predict the future states of decay for a product by using the Markovian model. The efficiency of the general approach is demonstrated on the basis of a real data set.
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