Generalised likelihood profiles for models with intractable likelihoods

Warne, David J.; Maclaren, Oliver J.; Carr, Elliot J.; Simpson, Matthew J.; Drovandi, Christopher

doi:10.1007/s11222-023-10361-w

Cited by 5 publications

(8 citation statements)

References 81 publications

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“…( 2019 ), who also discuss how naive application of the bootstrap typically fails in the poorly identified setting (which is consistent with our recent results in Warne et al. ( 2024 ) and those of Fröhlich et al. ( 2014 )).…”

Section: Introductionsupporting

confidence: 89%

Making Predictions Using Poorly Identified Mathematical Models

Simpson,

Maclaren

2024

Bull Math Biol

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Many commonly used mathematical models in the field of mathematical biology involve challenges of parameter non-identifiability. Practical non-identifiability, where the quality and quantity of data does not provide sufficiently precise parameter estimates is often encountered, even with relatively simple models. In particular, the situation where some parameters are identifiable and others are not is often encountered. In this work we apply a recent likelihood-based workflow, called Profile-Wise Analysis (PWA), to non-identifiable models for the first time. The PWA workflow addresses identifiability, parameter estimation, and prediction in a unified framework that is simple to implement and interpret. Previous implementations of the workflow have dealt with idealised identifiable problems only. In this study we illustrate how the PWA workflow can be applied to both structurally non-identifiable and practically non-identifiable models in the context of simple population growth models. Dealing with simple mathematical models allows us to present the PWA workflow in a didactic, self-contained document that can be studied together with relatively straightforward Julia code provided on GitHub. Working with simple mathematical models allows the PWA workflow prediction intervals to be compared with gold standard full likelihood prediction intervals. Together, our examples illustrate how the PWA workflow provides us with a systematic way of dealing with non-identifiability, especially compared to other approaches, such as seeking ad hoc parameter combinations, or simply setting parameter values to some arbitrary default value. Importantly, we show that the PWA workflow provides insight into the commonly-encountered situation where some parameters are identifiable and others are not, allowing us to explore how uncertainty in some parameters, and combinations of parameters, regardless of their identifiability status, influences model predictions in a way that is insightful and interpretable.

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Section: Introductionsupporting

confidence: 89%

Making Predictions Using Poorly Identified Mathematical Models

Simpson,

Maclaren

2024

Bull Math Biol

Self Cite

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“…Zivot et al's study is computational, while [24,74] supplement this with additional asymptotic arguments. A more recent review of these and similar results, again in econometrics, is given by Andrews et al [2], who also discuss how naive application of the bootstrap typically fails in the poorly identified setting (which is consistent with our recent results in [75] and those of [27]). In light of these results we expect that likelihood-based confidence intervals for parameters in poorly identified problems may still perform well.…”

Section: Introductionsupporting

confidence: 81%

“…This approach has the advantage of being computationally efficient and more broadly applicable than using simple grid searchers. As we show, the PWA leads to sensible results for these two simple case studies, and we anticipate that the PWA will also leads to useful insights for other non-identifiable models because related likelihood-based approaches are known to perform well in the face of non-identifiability [24, 27, 75, 81]. Open source software written in Julia is provided on GitHub to replicate all results in this study.…”

Section: Introductionmentioning

confidence: 69%

“…When it comes to considering different measurement models it is also relevant to consider how trajectories for data realisations are impacted, since our previous experience has shown that different measurement models can lead to similar mean trajectories but very different data realisations [64]. In addition, these approaches can also be applied to stochastic models if a surrogate likelihood is available, as discussed in [63] and implemented by Warne et al [75].…”

Section: Discussionmentioning

confidence: 99%

“…One limitation of our approach is that the theoretical underpinnings are asymptotic and that finite sample corrections may be needed when data is sparse and the parameter space is large. One approach to address this would be applying the calibration methods from [75], which can be used with minimal modifications to our overall workflow. We leave this for future work.…”

Section: Introductionmentioning

confidence: 99%

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Making predictions using poorly identified mathematical models

Simpson,

Maclaren

2023

Preprint

Self Cite

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Many commonly used mathematical models in the field of mathematical biology involve challenges of parameter non-identifiability. Practical non-identifiability, where the quality and quantity of data does not provide sufficiently precise parameter estimates is often encountered, even with relatively simple models. In particular, the situation where some parameters are identifiable and others are not is often encountered. In this work we apply a recent likelihood-based workflow, called Profile-Wise Analysis (PWA), to non-identifiable models for the first time. The PWA workflow addresses identifiability, parameter estimation, and prediction in a unified framework that is simple to implement and interpret. Previous implementations of the workflow have dealt with idealised identifiable problems only. In this study we illustrate how the PWA workflow can be applied to both structurally non-identifiable and practically non-identifiable models in the context of simple population growth models. Dealing with simple mathematical models allows us to present the PWA workflow in a didactic, self–contained document that can be studied to-gether with relatively straightforward Julia code provided onGitHub. Working with simple mathematical models allows the PWA workflow prediction intervals to be compared with gold standard full likelihood prediction intervals. Together, our examples illustrate how the PWA workflow provides us with a systematic way of dealing with non-identifiability, especially compared to other approaches, such as seeking ad hoc parameter combinations, or simply setting parameter values to some arbitrary default value. Importantly, we show that the PWA workflow provides insight into the commonly–encountered situation where some parameters are identifiable and others are not, allowing us to explore how uncertainty in some parameters, and combinations of some parameters, regardless of their identifiability status, influences model predictions in a way that is insightful and interpretable.

show abstract

Parameter identifiability and model selection for partial differential equation models of cell invasion

Liu,

Suh,

Maini

et al. 2024

J. R. Soc. Interface.

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When employing mechanistic models to study biological phenomena, practical parameter identifiability is important for making accurate predictions across wide ranges of unseen scenarios, as well as for understanding the underlying mechanisms. In this work, we use a profile-likelihood approach to investigate parameter identifiability for four extensions of the Fisher–Kolmogorov–Petrovsky–Piskunov (Fisher–KPP) model, given experimental data from a cell invasion assay. We show that more complicated models tend to be less identifiable, with parameter estimates being more sensitive to subtle differences in experimental procedures, and that they require more data to be practically identifiable. As a result, we suggest that parameter identifiability should be considered alongside goodness-of-fit and model complexity as criteria for model selection.

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Generalised likelihood profiles for models with intractable likelihoods

Cited by 5 publications

References 81 publications

Making Predictions Using Poorly Identified Mathematical Models

Making Predictions Using Poorly Identified Mathematical Models

Making predictions using poorly identified mathematical models

Parameter identifiability and model selection for partial differential equation models of cell invasion

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