Approximate Bayesian Inference for Discretely Observed Continuous-Time Multi-State Models

Tancredi, Andrea

doi:10.1111/biom.13019

Cited by 9 publications

(20 citation statements)

References 42 publications

(45 reference statements)

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“…Since then, it has been successfully applied in a wide range of fields; see, e.g., Barnes et al (2012); Blum (2010a); Boys et al (2008); McKinley et al (2017); Moores et al (2015); Toni et al (2009). Moreover, ABC has also been proposed to infer parameters from time series models (see, e.g., Drovandi et al 2016;Jasra 2015), state space models (see, e.g., Martin et al 2019;Tancredi 2019) and SDE models (see, e.g., Kypraios et al 2017;Maybank et al 2017;Picchini 2014;Picchini and Forman 2016;Picchini and Samson 2018;Sun et al 2015;Zhu et al 2016). Several advanced ABC algorithms have been proposed in the literature, such as, ABC-SMC, ABC-MCMC, sequential-annealing ABC, noisy ABC; see, e.g., Fan and Sisson (2018) and the references therein for a recent review.…”

Section: Introductionmentioning

confidence: 99%

Spectral density-based and measure-preserving ABC for partially observed diffusion processes. An illustration on Hamiltonian SDEs

2019

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Approximate Bayesian Computation (ABC) has become one of the major tools of likelihoodfree statistical inference in complex mathematical models. Simultaneously, stochastic differential equations (SDEs) have developed to an established tool for modelling time dependent, real world phenomena with underlying random effects. When applying ABC to stochastic models, two major difficulties arise. First, the derivation of effective summary statistics and proper distances is particularly challenging, since simulations from the stochastic process under the same parameter configuration result in different trajectories. Second, exact simulation schemes to generate trajectories from the stochastic model are rarely available, requiring the derivation of suitable numerical methods for the synthetic data generation. To obtain summaries that are less sensitive to the intrinsic stochasticity of the model, we propose to build up the statistical method (e.g., the choice of the summary statistics) on the underlying structural properties of the model. Here, we focus on the existence of an invariant measure and we map the data to their estimated invariant density and invariant spectral density. Then, to ensure that these model properties are kept in the synthetic data generation, we adopt measure-preserving numerical splitting schemes. The derived property-based and measure-preserving ABC method is illustrated on the broad class of partially observed Hamiltonian type SDEs, both with simulated data and with real electroencephalography (EEG) data. The proposed ingredients can be incorporated into any type of ABC algorithm and directly applied to all SDEs that are characterised by an invariant distribution and for which a measure-preserving numerical method can be derived.

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Section: Introductionmentioning

confidence: 99%

Spectral density-based and measure-preserving ABC for partially observed diffusion processes. An illustration on Hamiltonian SDEs

2019

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“…These Bayesian approaches are also used for parameter estimation from observational data [37,40]. The rise of approximate Bayesian computation methods provides new toolsets for parameter inference [41]. This method consists in the definition of a metric to measure the adequacy of the model outcomes with observed data.…”

Section: Mat 1)mentioning

confidence: 99%

Modelling infectious viral diseases in swine populations: a state of the art

Andraud

Rose

2020

Porc Health Manag

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Mathematical modelling is nowadays a pivotal tool for infectious diseases studies, completing regular biological investigations. The rapid growth of computer technology allowed for development of computational tools to address biological issues that could not be unravelled in the past. The global understanding of viral disease dynamics requires to account for all interactions at all levels, from within-host to between-herd, to have all the keys for development of control measures. A literature review was performed to disentangle modelling frameworks according to their major objectives and methodologies. One hundred and seventeen articles published between 1994 and 2020 were found to meet our inclusion criteria, which were defined to target papers representative of studies dealing with models of viral infection dynamics in pigs. A first descriptive analysis, using bibliometric indexes, permitted to identify keywords strongly related to the study scopes. Modelling studies were focused on particular infectious agents, with a shared objective: to better understand the viral dynamics for appropriate control measure adaptation. In a second step, selected papers were analysed to disentangle the modelling structures according to the objectives of the studies. The system representation was highly dependent on the nature of the pathogens. Enzootic viruses, such as swine influenza or porcine reproductive and respiratory syndrome, were generally investigated at the herd scale to analyse the impact of husbandry practices and prophylactic measures on infection dynamics. Epizootic agents (classical swine fever, foot-and-mouth disease or African swine fever viruses) were mostly studied using spatio-temporal simulation tools, to investigate the efficiency of surveillance and control protocols, which are predetermined for regulated diseases. A huge effort was made on model parameterization through the development of specific studies and methodologies insuring the robustness of parameter values to feed simulation tools. Integrative modelling frameworks, from within-host to spatio-temporal models, is clearly on the way. This would allow to capture the complexity of individual biological variabilities and to assess their consequences on the whole system at the population level. This would offer the opportunity to test and evaluate in silico the efficiency of possible control measures targeting specific epidemiological units, from hosts to herds, either individually or through their contact networks. Such decision support tools represent a strength for stakeholders to help mitigating infectious diseases dynamics and limiting economic consequences.

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“…Note that a stochastic EM algorithm was recently proposed also for the semi-Markov case by Aralis and Brookmeyer [1], but the reconstruction of the sample paths was performed by a naive rejection sampling. Finally Tancredi [26] proposes approximate Bayesian computation (ABC) techniques for Markov and Semi-Markov cases by approximately matching the observed and simulated state transition matrices between different observation times.…”

Section: Introductionmentioning

confidence: 99%

Bayesian inference for discretely observed continuous time multi-state models

Barone¹,

Tancredi²

2022

Preprint

Self Cite

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Multi-state models are frequently applied for representing processes evolving through a discrete set of state. Important classes of multi-state models arise when transitions between states may depend on the time since entry into the current state or on the time elapsed from the starting of the process. The former models are called semi-Markov while the latter are known as inhomogeneous Markov models.Inference for both the models presents computational difficulties when the process is only observed at discrete time points with no additional information about the state transitions. In fact, in both the cases, the likelihood function is not available in closed form. In order to obtain Bayesian inference under these two classes of models we reconstruct the whole unobserved trajectories conditioned on the observed points via a Metropolis-Hastings algorithm. As proposal density we use that given by the nested Markov models whose conditioned trajectories can be easily drawn by the uniformization technique. The resulting inference is illustrated via simulation studies and the analysis of two benchmark data sets for multi state models.

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Approximate Bayesian Inference for Discretely Observed Continuous-Time Multi-State Models

Cited by 9 publications

References 42 publications

Spectral density-based and measure-preserving ABC for partially observed diffusion processes. An illustration on Hamiltonian SDEs

Spectral density-based and measure-preserving ABC for partially observed diffusion processes. An illustration on Hamiltonian SDEs

Modelling infectious viral diseases in swine populations: a state of the art

Bayesian inference for discretely observed continuous time multi-state models

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