Markov model
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A Markov model is a mathematical model used to describe the behavior of a system that changes over time. It is particularly useful in analyzing systems that have a finite number of states and where the future state of the system depends only on its current state, not on any past states. Markov model is widely used in studies of consumer behavior.
It is a stochastic model, describing the problem of decision-making under risk. Main assessment criterion are: income, gain or loss, time.
According to Markov model the behavior of consumers in the market is a continuous decision-making process, in which specific states are following one after the other in a given period of time. They are dependent on the specific state of consumer or environment preceding this process. So this model adopts a conditional probability of reaching the individual states or results.
Elements of Markov model
The basic building block of a Markov model is a state transition matrix, which describes the probability of transitioning from one state to another. The matrix is defined by the transition probabilities between all states. The states are defined in such a way that the probability of transition between any two states is the same as the probability of transition between any other two states.
- option or variant of choice (state),
- cycle (time) - the shorter the cycle, the more the model reflects the real situation,
- probability of transition from one state to the next state in a given unit of time.
Application of Markov model
Markov model - is widely used in studies of consumer behavior. Is also used in the research of intentions to purchase goods, consumer preferences, order of purchase, goods substitution, needs etc.
Markov models can be used to model a wide variety of systems, including systems in finance, epidemiology, and manufacturing. Some examples include:
- Financial modeling: Markov models can be used to model the behavior of financial markets, such as the movement of interest rates or stock prices.
- Epidemiology: Markov models can be used to model the spread of infectious diseases and the effectiveness of different interventions.
- Manufacturing: Markov models can be used to model the reliability of manufacturing systems and the effectiveness of maintenance strategies.
Markov models are widely used in practice and have a wide range of applications, they have some limitations, such as assuming that the future states are independent of past states, which may not always be the case in real-world systems, and they also assume that the transition probabilities are constant over time, which may not always be true.
References
- Rabiner, L. R., & Juang, B. H. (1986). An introduction to hidden Markov models. ASSP Magazine, IEEE, 3(1), 4-16.
