Parameter estimation for multivariate population processes: a saddlepoint approach

Gunst, Mathisca de; Hautphenne, Sophie; Mandjes, Michel; Sollie, Birgit

doi:10.1080/15326349.2020.1832895

Cited by 2 publications

(2 citation statements)

References 23 publications

(33 reference statements)

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“…Another interesting extension concerns the multivariate model in which a population of individuals lives on a network and can move between its nodes. In this respect we refer to our recent paper (de Gunst et al 2021), approximating time-dependent probabilities in such a network, relying on saddlepoint approximations. The crucial simplification made in de Gunst et al ( 2021) is that a discrete-time model is considered, as opposed to the continuous-time model featuring in the present paper.…”

Section: Discussionmentioning

confidence: 99%

A Numerical Approach for Evaluating the Time-Dependent Distribution of a Quasi Birth-Death Process

Mandjes

Sollie

2021

Methodol Comput Appl Probab

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This paper considers a continuous-time quasi birth-death (qbd) process, which informally can be seen as a birth-death process of which the parameters are modulated by an external continuous-time Markov chain. The aim is to numerically approximate the time-dependent distribution of the resulting bivariate Markov process in an accurate and efficient way. An approach based on the Erlangization principle is proposed and formally justified. Its performance is investigated and compared with two existing approaches: one based on numerical evaluation of the matrix exponential underlying the qbd process, and one based on the uniformization technique. It is shown that in many settings the approach based on Erlangization is faster than the other approaches, while still being highly accurate. In the last part of the paper, we demonstrate the use of the developed technique in the context of the evaluation of the likelihood pertaining to a time series, which can then be optimized over its parameters to obtain the maximum likelihood estimator. More specifically, through a series of examples with simulated and real-life data, we show how it can be deployed in model selection problems that involve the choice between a qbd and its non-modulated counterpart.

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Section: Discussionmentioning

confidence: 99%

A Numerical Approach for Evaluating the Time-Dependent Distribution of a Quasi Birth-Death Process

Mandjes

Sollie

2021

Methodol Comput Appl Probab

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“…When this latent space is enormous, fitting stochastic epidemic models becomes a highly non‐trivial exercise due to the increased computational complexity 4,5 . This has spurred recent work on numerical approaches and approximation methods toward likelihood‐based inference 6–10 …”

Section: Introductionmentioning

confidence: 99%

Fitting a stochastic model of intensive care occupancy to noisy hospitalization time series during the COVID‐19 pandemic

Awasthi,

Minin,

Huang

et al. 2023

Statistics in Medicine

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Intensive care occupancy is an important indicator of health care stress that has been used to guide policy decisions during the COVID‐19 pandemic. Toward reliable decision‐making as a pandemic progresses, estimating the rates at which patients are admitted to and discharged from hospitals and intensive care units (ICUs) is crucial. Since individual‐level hospital data are rarely available to modelers in each geographic locality of interest, it is important to develop tools for inferring these rates from publicly available daily numbers of hospital and ICU beds occupied. We develop such an estimation approach based on an immigration‐death process that models fluctuations of ICU occupancy. Our flexible framework allows for immigration and death rates to depend on covariates, such as hospital bed occupancy and daily SARS‐CoV‐2 test positivity rate, which may drive changes in hospital ICU operations. We demonstrate via simulation studies that the proposed method performs well on noisy time series data and apply our statistical framework to hospitalization data from the University of California, Irvine (UCI) Health and Orange County, California. By introducing a likelihood‐based framework where immigration and death rates can vary with covariates, we find, through rigorous model selection, that hospitalization and positivity rates are crucial covariates for modeling ICU stay dynamics and validate our per‐patient ICU stay estimates using anonymized patient‐level UCI hospital data.

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Parameter estimation for multivariate population processes: a saddlepoint approach

Cited by 2 publications

References 23 publications

A Numerical Approach for Evaluating the Time-Dependent Distribution of a Quasi Birth-Death Process

A Numerical Approach for Evaluating the Time-Dependent Distribution of a Quasi Birth-Death Process

Fitting a stochastic model of intensive care occupancy to noisy hospitalization time series during the COVID‐19 pandemic

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