Overview of ABC

Sisson, Scott A.; Fan, Yanan; Beaumont, Mark A.

doi:10.1201/9781315117195-1

Cited by 82 publications

(120 citation statements)

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“…However, in practice, this transformation of the uncertainty is not performed owing to a gap in knowledge about an appropriate methodology. A new methodology that uses approximate Bayesian computation [28] and results in a distribution representing the measurement and its uncertainty in the component or feature vector space is described later.…”

Section: Proposed Methodologymentioning

confidence: 99%

Transformation of measurement uncertainties into low-dimensional feature vector space

2021

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Advances in technology allow the acquisition of data with high spatial and temporal resolution. These datasets are usually accompanied by estimates of the measurement uncertainty, which may be spatially or temporally varying and should be taken into consideration when making decisions based on the data. At the same time, various transformations are commonly implemented to reduce the dimensionality of the datasets for postprocessing or to extract significant features. However, the corresponding uncertainty is not usually represented in the low-dimensional or feature vector space. A method is proposed that maps the measurement uncertainty into the equivalent low-dimensional space with the aid of approximate Bayesian computation, resulting in a distribution that can be used to make statistical inferences. The method involves no assumptions about the probability distribution of the measurement error and is independent of the feature extraction process as demonstrated in three examples. In the first two examples, Chebyshev polynomials were used to analyse structural displacements and soil moisture measurements; while in the third, principal component analysis was used to decompose the global ocean temperature data. The uses of the method range from supporting decision-making in model validation or confirmation, model updating or calibration and tracking changes in condition, such as the characterization of the El Niño Southern Oscillation.

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Section: Proposed Methodologymentioning

confidence: 99%

Transformation of measurement uncertainties into low-dimensional feature vector space

2021

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“…Approximate Bayesian Computation (ABC) originated as a class of algorithms designed to sample from the approximate posterior density of a vector of parameters, θ, given an observed data set, D, without direct evaluation of the likelihood function, f (D|θ). This class of algorithms is especially useful in complex and high-dimensional settings where the likelihood function is not available in a usable form (see Sisson, Fan and Beaumont (2019) for a recent overview).…”

Section: Approximate Bayesian Computationmentioning

confidence: 99%

Quantification of the weight of fingerprint evidence using a ROC-based Approximate Bayesian Computation algorithm for model selection

Hendricks

Neumann

Saunders

2021

Electron. J. Statist.

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For more than a century, fingerprints have been used with considerable success to identify criminals or verify the identity of individuals. The categorical conclusion scheme used by fingerprint examiners, and more generally the inference process followed by forensic scientists, have been heavily criticised in the scientific and legal literature. Instead, scholars have proposed to characterise the weight of forensic evidence using the Bayes factor as the key element of the inference process. In forensic science, quantifying the magnitude of support is equally as important as determining which model is supported. Unfortunately, the complexity of fingerprint patterns render likelihood-based inference impossible. In this paper, we use an Approximate Bayesian Computation (ABC) model selection algorithm to quantify the weight of fingerprint evidence. We supplement the original ABC model selection algorithm using a Receiver Operating Characteristic curve to mitigate its known shortcomings with respect to the choice of a suitable threshold and the curse of dimensionality. In a sense, we offer an alternative to other methods that have tried to address the same issues. Our method is straightforward to implement, computationally efficient, and visually intuitive for lay individuals (i.e., jurors). We apply our method to quantify the weight of fingerprint evidence in forensic science, but we note that it can be applied to any other forensic pattern evidence.

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“…While efficient methods exist for parameter estimation using maximum likelihood or Bayesian inference for similar models, for these discrete stochastic models, the intractability of the likelihood function forces researchers to rely on the growing class of Likelihood-Free Inference (LFI) methods [ 5 – 7 ], which depend only on the availability of a model simulator. Recently, Approximate Bayesian Computation (ABC) [ 8 , 9 ] has become one of the most popular LFI methods for discrete stochastic models due to its simplicity and demonstrated effectiveness.…”

Section: Introductionmentioning

confidence: 99%

“…Given a prior over parameters and a stochastic simulator , Approximate Bayesian Computation (ABC) approximates the posterior distribution using only forward simulations and without computing the likelihood [ 8 ]. The basic Rejection ABC is presented in Algorithm 1.…”

Section: Introductionmentioning

confidence: 99%

“…The performance of ABC is highly dependent on having an effective set of summary statistics for the experimental data, which becomes increasingly difficult for domain experts to hand-select as the dimensionality of the problem grows [ 8 ]. For stochastic biochemical reaction systems, where data is often in the form of sample paths of molecular species over time, this is a common issue due to complexity of trajectories where simple means and correlations may not effectively capture the features.…”

Section: Introductionmentioning

confidence: 99%

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Accelerated regression-based summary statistics for discrete stochastic systems via approximate simulators

et al. 2021

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Background Approximate Bayesian Computation (ABC) has become a key tool for calibrating the parameters of discrete stochastic biochemical models. For higher dimensional models and data, its performance is strongly dependent on having a representative set of summary statistics. While regression-based methods have been demonstrated to allow for the automatic construction of effective summary statistics, their reliance on first simulating a large training set creates a significant overhead when applying these methods to discrete stochastic models for which simulation is relatively expensive. In this τ work, we present a method to reduce this computational burden by leveraging approximate simulators of these systems, such as ordinary differential equations and τ-Leaping approximations. Results We have developed an algorithm to accelerate the construction of regression-based summary statistics for Approximate Bayesian Computation by selectively using the faster approximate algorithms for simulations. By posing the problem as one of ratio estimation, we use state-of-the-art methods in machine learning to show that, in many cases, our algorithm can significantly reduce the number of simulations from the full resolution model at a minimal cost to accuracy and little additional tuning from the user. We demonstrate the usefulness and robustness of our method with four different experiments. Conclusions We provide a novel algorithm for accelerating the construction of summary statistics for stochastic biochemical systems. Compared to the standard practice of exclusively training from exact simulator samples, our method is able to dramatically reduce the number of required calls to the stochastic simulator at a minimal loss in accuracy. This can immediately be implemented to increase the overall speed of the ABC workflow for estimating parameters in complex systems.

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Overview of ABC

Cited by 82 publications

References 1 publication

Transformation of measurement uncertainties into low-dimensional feature vector space

Transformation of measurement uncertainties into low-dimensional feature vector space

Quantification of the weight of fingerprint evidence using a ROC-based Approximate Bayesian Computation algorithm for model selection

Accelerated regression-based summary statistics for discrete stochastic systems via approximate simulators

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