Multivariate Poisson Markov-dependent finite mixture models for analysis of weed counts

Abstract

Multivariate count data occurs in different variety of fields. For modeling such data, one may consider the multivariate Poisson distribution. Overdispersion is a problem when modeling the data with the multivariate Poisson distribution. Therefore in this paper, we propose a new Multivariate Poisson Markov-Dependent Finite Mixture Models based on the extension of independent multivariate Poisson finite mixture models proposed by Brijs et al. [39] as a solution to this problem. This model, which can take into account spatial nature of weed counts, is applied to weed species counts in an agricultural field for the first time. The distribution of counts depends on the underlying sequence of states, which are unobserved or hidden. These hidden states represent the regions where weed counts are relatively homogeneous. Analysis of this data involves the estimation of the number of hidden states, Poisson means and covariances. The parameter estimation is done using a modified EM algorithm for maximum likelihood estimation. Results suggest that the multivariate Poisson Markov-dependent finite mixture with five components and the independent covariance structure gives a better fit to this dataset. Since this model deals with overdispersion and spatial information, it will help to get an insight of weed distribution for herbicide applications. The other advantage is that, this model may leads researchers to find other factors such as soil moisture, fertilizer level etc. to determine the states which govern the distribution of weed counts.