Approximate Bayesian computational methods

Marin, Jean‐Michel; Pudlo, Pierre; Robert, Christian P.; Ryder, Robin

doi:10.1007/s11222-011-9288-2

Cited by 670 publications

(639 citation statements)

References 49 publications

(95 reference statements)

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“…Whilet ij· is a biased approximation to t ij· , it appears that by having a similar bias in all treatment groups of a trial the bias often approximately cancels out when it comes to the estimation of the hazard ratio. Further alternatives include approximate Bayesian computations (Marin et al, 2012), which would avoid the need to derive and evaluate an AD likelihood.…”

Section: Discussionmentioning

confidence: 99%

Meta-analysis of aggregate data on medical events

Holzhauer

2016

Statist. Med.

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A meta-analysis combines analysis results from multiple independent sets of data. Metaanalyses to assess whether a treatment affects the occurrence of a medical event are frequently based on published aggregate data from controlled clinical trials. In that setting, the number of patients with an event in each trial is often treated as a binomial random variable. This assumes that censoring times have the same distribution in all treatment groups of a trial, and are independent of event times.To allow for different drop-out time distributions across treatment groups, we derive a likelihood for commonly available aggregate data that assumes specific event and drop-out time distributions for a number of situations. These include exponentially or Weibull distributed event and drop-out times, event-driven trials, the situation when a patient may experience multiple potentially fatal events, and when individual patient data are available for some trials.The assumption that parameters of survival distributions are exchangeable between trials is more plausible than for the expected proportion of patients with an event.For this reason the proposed likelihood is more suitable than a binomial likelihood for use in hierarchical meta-analysis models and for incorporating prior information from historical control group data. Hierarchical models and prior information are useful in sparse data settings and to avoid parameter identifiability problems. We use simulations to compare hierarchical Bayesian models with the proposed trial-level likelihood against other meta-analysis methods and to compare methods for using historical control group data. We also demonstrate how conjugate priors may be used to analyze exponentially distributed failure times without the need for Markov chain Monte Carlo methods.

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Section: Discussionmentioning

confidence: 99%

Meta-analysis of aggregate data on medical events

Holzhauer

2016

Statist. Med.

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“…ABC comprises several simulation-based methods to obtain samples from the posterior distribution when the likelihood function is not known (for review papers, see, e.g., Lintusaari et al 2017;Marin et al 2012). ABC algorithms are iterative: The basic steps at each iteration are as follows:…”

Section: Bayesian Inference Via Classificationmentioning

confidence: 99%

“…Both the distance function used and the summary statistics are critical for the success of the inference procedure (see, for example, the reviews by Lintusaari et al (2017) and Marin et al (2012). Traditionally, researchers choose the two quantities subjectively, relying on expert knowledge about the observed data.…”

Section: Introductionmentioning

confidence: 99%

Likelihood-free inference via classification

et al. 2017

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Increasingly complex generative models are being used across disciplines as they allow for realistic characterization of data, but a common difficulty with them is the prohibitively large computational cost to evaluate the likelihood function and thus to perform likelihood-based statistical inference. A likelihood-free inference framework has emerged where the parameters are identified by finding values that yield simulated data resembling the observed data. While widely applicable, a major difficulty in this framework is how to measure the discrepancy between the simulated and observed data. Transforming the original problem into a problem of classifying the data into simulated versus observed, we find that classification accuracy can be used to assess the discrepancy. The complete arsenal of classification methods becomes thereby available for inference of intractable generative models. We validate our approach using theory and simulations for both point estimation and Bayesian inference, and demonstrate its use on real data by inferring an individual-based epidemiological model for bacterial infections in child care centers.

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“…To remedy this situation, the ABC filters 20,21,25,30 provide the point-mass approximation (21) of the target density π(ξ 1:k |y 1:k ) using a different strategy. The Monte Carlo samples ξ (i) k , i = 1, … , I drawn from the state space are directly plugged into the observation model (19).…”

Section: Approximate Filteringmentioning

confidence: 99%

“…[16][17][18][19] The generic ABC filter 20 is not an exception in this respect. As a result, it has attractive asymptotic properties ensuring convergence to the true state value, however, at the cost of rather impractical assumptions 21 requiring carefully designed adaptation of the kernel scale, eg, using a linear schedule 22 or effective sample size-based scale contraction. 23,24 An alternative method partially solving these issues is inspired by the kernel density estimation (KDE) theory.…”

Section: Introductionmentioning

confidence: 99%

Marginalized approximate filtering of state‐space models

Dedecius

2017

Adaptive Control & Signal

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SummaryThe marginalized particle filtering (MPF) is a powerful technique reducing the number of particles necessary to effectively estimate hidden states of state-space models. This paper alleviates the assumption of a fully known and computationally tractable observation model. Exploiting the recent developments in the theory of approximate Bayesian computation (ABC) filtration, an ABC counterpart of MPF is proposed, applicable when the observation model is too complex to be evaluated analytically or even numerically, but it is still possible to sample from it by plugging in the state. The novelty is 2-fold. First, ABC methods have not been used in marginalized filtering yet. Second, a new multivariate robust method for evaluation of particle weights is proposed. The goal of this paper is to demonstrate the idea on the background of the MPF with a particular accent on exposition.

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Approximate Bayesian computational methods

Cited by 670 publications

References 49 publications

Meta-analysis of aggregate data on medical events

Meta-analysis of aggregate data on medical events

Likelihood-free inference via classification

Marginalized approximate filtering of state‐space models

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