## Abstract

This article studies the maximum likelihood estimates of magnitude and scale parameters for a Gaussian process of Ornstein-Uhlenbeck type used to model a deterministic function that does not have to be a realisation of an Ornstein- Uhlenbeck process. Specifically, we derive explicit expressions for the limiting values of the maximum likelihood estimates as the number of observations increases. The results demonstrate that the function typically needs to be sufficiently similar to a sample path of an Ornstein-Uhlenbeck process or have discontinuities if the variance of the model is to remain non-zero. Numerical examples illustrate the behaviour of the estimates when the function is not a sample path of any Ornstein-Uhlenbeck process.

Original language | English |
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Title of host publication | Proceedings of the 29th IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2019 |

Number of pages | 6 |

ISBN (Electronic) | 9781728108247 |

DOIs | |

Publication status | Published - 1 Oct 2019 |

MoE publication type | A4 Article in a conference publication |

Event | IEEE International Workshop on Machine Learning for Signal Processing - Pittsburgh, United States Duration: 13 Oct 2019 → 16 Oct 2019 Conference number: 29 |

### Publication series

Name | IEEE International Workshop on Machine Learning for Signal Processing |
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Publisher | IEEE |

ISSN (Print) | 2161-0363 |

ISSN (Electronic) | 2161-0371 |

### Workshop

Workshop | IEEE International Workshop on Machine Learning for Signal Processing |
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Abbreviated title | MLSP |

Country/Territory | United States |

City | Pittsburgh |

Period | 13/10/2019 → 16/10/2019 |

## Keywords

- Gaussian process regression
- Maximum likelihood estimation
- Ornstein- Uhlenbeck process
- Probabilistic numerics