A uniformisation-driven algorithm for inference-related estimation of a phase-type ageing model

Boquan Cheng and Rogemar Mamon ()
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Boquan Cheng: The University of Western Ontario
Rogemar Mamon: The University of Western Ontario

Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, 2023, vol. 29, issue 1, No 6, 142-187

Abstract: Abstract We develop an efficient algorithm to compute the likelihood of the phase-type ageing model. The proposed algorithm uses the uniformisation method to stabilise the numerical calculation. It also utilises a vectorised formula to only calculate the necessary elements of the probability distribution. Our algorithm, with an error’s upper bound, could be adjusted easily to tackle the likelihood calculation of the Coxian models. Furthermore, we compare the speed and the accuracy of the proposed algorithm with those of the traditional method using the matrix exponential. Our algorithm is faster and more accurate than the traditional method in calculating the likelihood. Based on our experiments, we recommend using 20 sets of randomly-generated initial values for the optimisation to get a reliable estimate for which the evaluated likelihood is close to the maximum likelihood.

Keywords: Coxian model; Matrix exponential; Uniformisation method; Maximum likelihood; Rate of algorithm’s success (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10985-022-09577-1

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