Modelling Customer Relationships as Hidden Markov Chains

Models in behavioural relationship marketing suggest that relations between the customer and the company change over time as a result of the continuous encounter. Some theoretical models have been put forward concerning relationship marketing, both from the standpoints of consumer behaviour and empirical modelling. In addition to these, this study proposes the hidden Markov model (HMM) as a potential tool for assessing customer relationships. Specifically, the HMM is submitted via the framework of a Markov chain model to classify customers relationship dynamics of a telecommunication service company by using an experimental data set. We develop and estimate an HMM to relate the unobservable relationship states to the observed buying behaviour of the customers giving an appropriate classification of the customers into the relationship states. By merely accounting for the functional and unobserved heterogeneity with a two-state hidden Markov model and taking estimation into account via an optimal estimation method, the empirical results not only demonstrate the value of the proposed model in assessing the dynamics of a customer relationship over time but also gives the optimal marketing-mixed strategies in different customer state

A Comparison Between Long Short-Term Memory and Hidden Markov Model to Predict Productivity of Maize in Nigeria

Due to population increase and import constraints, maize, a key cereal crop in Africa, is experiencing a boom in demand. Given this, the study's focus is on determining how maize output in Nigeria interacts with various climatic factors, particularly rainfall and temperature. The Hidden Markov Model (HMM) and the Long Short-Term Memory neural network (LSTM) are compared in this context to assess their performance. A variety of performance indicators, such as correlation, mean absolute percentage error (MAPE), standard error of the mean (SEM), and mean square error (MSE), are used to evaluate the models. The outcomes show that the HMM performs better than the LSTM, with an RMSE of 1.21 and a MAPE of 12.98 demonstrating greater performance. Based on this result, the HMM is then used to forecast maize yield while taking the effects of temperature and rainfall into account. The estimates highlight the possibility for increasing local output by demonstrating a favorable environment for maize planting in Nigeria. In order to help the Nigerian government in its efforts to increase maize production domestically, these studies offer useful insights

Application of Weibull Distribution to Hidden Markov Model for Non-Negative Factorization Matrix

Probabilistic Nonnegative Matrix Factorizations (NMFs) are very useful in statistics when dealing with stochastic signals such as wave fronts, share prices, and volatility as a Nonnegative Matrix Factorization (NMF) approach. Little attention has been made in the literature to developing NMF algorithms that use moving average to exploit data's temporal dependencies. A hidden Markov model (HMM) using a Weibull distribution as the output density function was created in this study. The Weibull HMM was then reformulated as a probabilistic NMF. This demonstrates the connection between the proposed HMM and NMF, and will lead to a novel probabilistic NMF approach in which the model captures temporal dependencies inherently utilizing moving average. Furthermore, the model parameters were estimated using maximum likelihood estimation (MLE). The model's adaptability was compared to the existing probabilistic NMFs models of gamma and lognormal. Our trials with US COVID-19 data revealed that the proposed technique achieves a superior balance of sparsity, the goodness of fit, and temporal modeling than gamma and lognormal models.&nbsp