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A model and application of binary random sequence with probabilities depending on history

Petr Volf;  Tomáš Kouřim — 2024

Kybernetika

This paper presents a model of binary random sequence with probabilities depending on previous sequence values as well as on a set of covariates. Both these dependencies are expressed via the logistic regression model, such a choice enables an easy and reliable model parameters estimation. Further, a model with time-depending parameters is considered and method of solution proposed. The main objective is then the application dealing with both artificial and real data cases, illustrating the method...

Discrete random processes with memory: Models and applications

Tomáš Kouřim;  Petr Volf — 2020

Applications of Mathematics

The contribution focuses on Bernoulli-like random walks, where the past events significantly affect the walk's future development. The main concern of the paper is therefore the formulation of models describing the dependence of transition probabilities on the process history. Such an impact can be incorporated explicitly and transition probabilities modulated using a few parameters reflecting the current state of the walk as well as the information about the past path. The behavior of proposed...

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