### Abstract

In classification theory, it is generally assumed that the data are independent and identically distributed. However, in many practical applications, we face a set of observations that are collected sequentially with a dependence structure among samples. The primary focus of this investigation is to construct the optimal Bayesian classifier (OBC) when the training observations are serially dependent. To model the effect of dependency, we assume the training observations are generated from tVAR(p), which is a multidimensional vector autoregressive process of order p. At the same time, we assume there exists uncertainty about parameters governing the VAR(p) model. To model this uncertainty, we assume that model parameters (coefficient matrices) are random variables with a prior distribution, and find the resulting OBC under the assumption of known covariance matrices of white-noise processes. We employ simulations using both synthetic and real data to demonstrate the efficacy of the constructed OBC.

Original language | English |
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Article number | 8693865 |

Pages (from-to) | 3073-3086 |

Number of pages | 14 |

Journal | IEEE Transactions on Signal Processing |

Volume | 67 |

Issue number | 12 |

DOIs | |

Publication status | Published - Jun 15 2019 |

### Keywords

- Optimal Bayesian classification
- serially dependent training data
- vector autoregressive processes

### ASJC Scopus subject areas

- Signal Processing
- Electrical and Electronic Engineering

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## Cite this

*IEEE Transactions on Signal Processing*,

*67*(12), 3073-3086. [8693865]. https://doi.org/10.1109/TSP.2019.2912131