Mikael Sunnåker, Alberto Giovanni Busetto, Elina Numminen et al. · PLoS Computational Biology · 2013
Approximate Bayesian computation (ABC) constitutes a class of computational methods rooted in Bayesian statistics. In all model-based statistical inference, the likelihood function is of central importance, since it expresses the probability of the observed data under a particular statistical model, and thus quantifies the support data lend to particular values of parameters and to choices among different models. For simple models, an analytical formula for the likelihood function can typically be derived. However, for more complex models, an analytical formula might be elusive or the likelihood function might be computationally very costly to evaluate. ABC methods bypass the evaluation of the likelihood function. In this way, ABC methods widen the realm of models for which statistical inference can be considered. ABC methods are mathematically well-founded, but they inevitably make assumptions and approximations whose impact needs to be carefully assessed. Furthermore, the wider application domain of ABC exacerbates the challenges of parameter estimation and model selection. ABC has rapidly gained popularity over the last years and in particular for the analysis of complex problems arising in biological sciences (e.g., in population genetics, ecology, epidemiology, and systems biology).
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R. F. Guerrero, M. K Irkpatrick, N. Perrin · 2016
homomorphic sex chromosomes; Hyla; recombination suppression. Sex chromosomes are expected to evolve suppressed recombination, which leads to degeneration of the Y and heteromorphism between the X and Y. Some sex chromosomes remain homomorphic, however, and the factors that prevent degeneration of the Y in these cases are not well understood. The homomorphic sex chromosomes of the European tree frogs (Hyla spp.) present an interesting paradox. Recombination in males has never been observed in crossing experiments, but molecular data are suggestive of occa-sional recombination between the X and Y. The hypothesis that these sex chromosomes recombine has not been tested statistically, however, nor has the X-Y recombination rate been estimated. Here, we use approximate Bayesian computation coupled with coalescent simulations of sex chromo-somes to quantify X-Y recombination rate from existent data. We find that microsatellite data from H. arborea, H. intermedia and H. molleri support a recombination rate between X and Y that is significantly different from zero. We estimate that rate to be approximately 105 times smaller than that between X chromosomes. Our findings support the notion that very low recombination rate may be sufficient to maintain homomorphism in sex chromosomes.
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Ritabrata Dutta (11268329), Karim Zouaoui Boudjeltia (194378), Christos Kotsalos (12225898) et al. · Figshare · 2022
<p>Having observed data <i><b>x</b></i><sup><b>0</b></sup> from an individual patient (the gray dot), we sample parameter values <i>θ</i> from the prior and generate observations through the model simulator, , that are then accepted (green) or rejected (red) according to their distance from the observation measured by <i>d</i>(<i><b>x</b></i><sub>1</sub>, <i><b>x</b></i><sub>2</sub>) = ||<i>s</i>(<i><b>x</b></i><sub>1</sub>) − <i>s</i>(<i><b>x</b></i><sub>2</sub>))||<sub>2</sub> on the summary statistics space.</p>
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Cisewski-Kehe, Jessi · TIB KMO / FLOWWORKS GmbH · 2018
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Sen Li · 2016
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Brandon M. Turner, Trisha Van Zandt · Psychometrika · 2013
Approximate Bayesian computation (ABC) is a powerful technique for estimating the posterior distribution of a model's parameters. It is especially important when the model to be fit has no explicit likelihood function, which happens for computational (or simulation-based) models such as those that are popular in cognitive neuroscience and other areas in psychology. However, ABC is usually applied only to models with few parameters. Extending ABC to hierarchical models has been difficult because high-dimensional hierarchical models add computational complexity that conventional ABC cannot accommodate. In this paper, we summarize some current approaches for performing hierarchical ABC and introduce a new algorithm called Gibbs ABC. This new algorithm incorporates well-known Bayesian techniques to improve the accuracy and efficiency of the ABC approach for estimation of hierarchical models. We then use the Gibbs ABC algorithm to estimate the parameters of two models of signal detection, one with and one without a tractable likelihood function.
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Michael G. B. Blum, Viet Chi Tran · 2009
epidemiological models: Application to the Cuban HIV-AIDS epidemic with contact-tracing and unobserved infectious population
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Jessi Cisewski-Kehe · Open Collections · 2018
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2009
We present a sequential Monte Carlo sampler variant of the partial rejection control algorithm, and show that this variant can be considered as a sequential Monte Carlo sampler with a modified mutation kernel. We prove that the new sampler can reduce the variance of the incremental importance weights when compared with standard sequential Monte Carlo samplers. We provide a study of theoretical properties of the new algorithm, and make connections with some existing algorithms. Finally, the sampler is adapted for application under the challenging “likelihood free, ” approximate Bayesian computation modelling framework, where we demonstrate superior performance over existing likelihood-free samplers.
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Gilles Celeux · Statistics and Computing · 2012
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Robert, Christian P., Marin, Jean-Michel, Cornuet, Jean-Marie et al. · Base Institutionnelle de Recherche de l'université Paris-Dauphine (BIRD) (University Paris-Dauphine) · 2010
Le lien ci-dessous donne accès à la version working paper, intitulée "Adaptivity for ABC algorithms: the ABC-PMC scheme"
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Mark Beaumont, J. M. Cornuet, Jean‐Michel Marin et al. · Biometrika · 2009
Sequential techniques can enhance the efficiency of the approximate Bayesian computation algorithm, as in Sisson et al.’s (2007) partial rejection control version. While this method is based upon the theoretical works of Del Moral et al. (2006), the application to approximate Bayesian computation results in a bias in the approximation to the posterior. An alternative version based on genuine importance sampling arguments bypasses this difficulty, in connection with the population Monte Carlo method of Cappé et al. (2004), and it includes an automatic scaling of the forward kernel. When applied to a population genetics example, it compares favourably with two other versions of the approximate algorithm.
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Hyeontae Jo (20469463), Sung Woong Cho (20469466), Hyung Ju Hwang (20469469) · Figshare · 2024
<div><p>Differential equations are pivotal in modeling and understanding the dynamics of various systems, as they offer insights into their future states through parameter estimation fitted to time series data. In fields such as economy, politics, and biology, the observation data points in the time series are often independently obtained (i.e., Repeated Cross-Sectional (RCS) data). RCS data showed that traditional methods for parameter estimation in differential equations, such as using mean values of RCS data over time, Gaussian Process-based trajectory generation, and Bayesian-based methods, have limitations in estimating the shape of parameter distributions, leading to a significant loss of data information. To address this issue, this study proposes a novel method called Estimation of Parameter Distribution (EPD) that provides accurate distribution of parameters without loss of data information. EPD operates in three main steps: generating synthetic time trajectories by randomly selecting observed values at each time point, estimating parameters of a differential equation that minimizes the discrepancy between these trajectories and the true solution of the equation, and selecting the parameters depending on the scale of discrepancy. We then evaluated the performance of EPD across several models, including exponential growth, logistic population models, and target cell-limited models with delayed virus production, thereby demonstrating the ability of the proposed method in capturing the shape of parameter distributions. Furthermore, we applied EPD to real-world datasets, capturing various shapes of parameter distributions over a normal distribution. These results address the heterogeneity within systems, marking a substantial progression in accurately modeling systems using RCS data. Therefore, EPD marks a significant advancement in accurately modeling systems with RCS data, realizing a deeper understanding of system dynamics and parameter variability.</p></div>
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Maxime Lenormand · SPIRE - Sciences Po Institutional REpository · 2013
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Cisewski, Jessi · cIRcle (University of British Columbia) · 2018
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Andreas Meraner, Luca Cornetti, Andrea G et al. · 2016
Defining conservation units in a stocking-induced genetic melting pot: unraveling native and multiple exotic genetic imprints of recent and historical secondary contact in
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Beaumont, Mark A., Cornuet, Jean-Marie, Marin, Jean-Michel et al. · arXiv (Cornell University) · 2008
Sequential techniques can enhance the efficiency of the approximate Bayesian computation algorithm, as in Sisson et al.'s (2007) partial rejection control version. While this method is based upon the theoretical works of Del Moral et al. (2006), the application to approximate Bayesian computation results in a bias in the approximation to the posterior. An alternative version based on genuine importance sampling arguments bypasses this difficulty, in connection with the population Monte Carlo method of Cappe et al. (2004), and it includes an automatic scaling of the forward kernel. When applied to a population genetics example, it compares favourably with two other versions of the approximate algorithm.
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Lucas Castillo (17743423), Pablo León-Villagrá (13262417), Nick Chater (124386) et al. · Figshare · 2024
<div><p>In many tasks, human behavior is far noisier than is optimal. Yet when asked to behave randomly, people are typically too predictable. We argue that these apparently contrasting observations have the same origin: the operation of a general-purpose local sampling algorithm for probabilistic inference. This account makes distinctive predictions regarding random sequence generation, not predicted by previous accounts—which suggests that randomness is produced by inhibition of habitual behavior, striving for unpredictability. We verify these predictions in two experiments: people show the same deviations from randomness when randomly generating from non-uniform or recently-learned distributions. In addition, our data show a novel signature behavior, that people’s sequences have too few changes of trajectory, which argues against the specific local sampling algorithms that have been proposed in past work with other tasks. Using computational modeling, we show that local sampling where direction is maintained across trials best explains our data, which suggests it may be used in other tasks too. While local sampling has previously explained why people are unpredictable in standard cognitive tasks, here it also explains why human random sequences are not unpredictable enough.</p></div>
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Chaya Weerasinghe, David T. Frazier, Rubén Loaiza‐Maya et al. · ArXiv.org · 2025
Approximate Bayesian computation (ABC) is one of the most popular "likelihood-free" methods. These methods have been applied in a wide range of fields by providing solutions to intractable likelihood problems in which exact Bayesian approaches are either infeasible or computationally costly. However, the performance of ABC can be unreliable when dealing with model misspecification. To circumvent the poor behavior of ABC in these settings, we propose a novel ABC approach that is robust to model misspecification. This new method can deliver more accurate statistical inference under model misspecification than alternatives and also enables the detection of summary statistics that are incompatible with the assumed data-generating process. We demonstrate the effectiveness of our approach through several simulated examples, where it delivers more accurate point estimates and uncertainty quantification over standard ABC approaches when the model is misspecified. Additionally, we apply our approach to an empirical example, further showcasing its advantages over alternative methods.
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Paul Fearnhead, Dennis Prangle · Journal of the Royal Statistical Society Series B (Statistical Methodology) · 2012
Summary Many modern statistical applications involve inference for complex stochastic models, where it is easy to simulate from the models, but impossible to calculate likelihoods. Approximate Bayesian computation (ABC) is a method of inference for such models. It replaces calculation of the likelihood by a step which involves simulating artificial data for different parameter values, and comparing summary statistics of the simulated data with summary statistics of the observed data. Here we show how to construct appropriate summary statistics for ABC in a semi-automatic manner. We aim for summary statistics which will enable inference about certain parameters of interest to be as accurate as possible. Theoretical results show that optimal summary statistics are the posterior means of the parameters. Although these cannot be calculated analytically, we use an extra stage of simulation to estimate how the posterior means vary as a function of the data; and we then use these estimates of our summary statistics within ABC. Empirical results show that our approach is a robust method for choosing summary statistics that can result in substantially more accurate ABC analyses than the ad hoc choices of summary statistics that have been proposed in the literature. We also demonstrate advantages over two alternative methods of simulation-based inference.
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