Monte Carlo Methods of Inference for Implicit Statistical Models

By Peter J. Diggle, Richard J. Gratton. 1984

Subfields: Probabilistic & Bayesian Methods

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Citations in the corpus

The frontier of simulation-based inference (2019, methodology): “Such models are often referred to as implicit models and contrasted against prescribed models where the likelihood for an observation can be explicitly calculated (1).”
Learning in Implicit Generative Models (2016, background): “It is useful to make a distinction between two types of probabilistic models: prescribed and implicit models (Diggle and Gratton, 1984).”
VEEGAN: Reducing Mode Collapse in GANs using Implicit Variational Learning (2017, background): “Deep generative models are usually implicit statistical models [3], also called implicit probability distributions, meaning that they do not induce a density function that can be tractably computed, but rather provide a simulation procedure to generate new data points.”
Deep and Hierarchical Implicit Models (2017, methodology): “Furthermore the model is implicit , also known as a simulator: we can sample data from its generative process, but we may not have access to calculate its density (Diggle & Gratton, 1984; Hartig et al., 2011).”
Flow-GAN: Combining Maximum Likelihood and Adversarial Learning in Generative Models (2017, background): “Adversarially learned models such as generative adversarial networks (GAN; (Goodfellow et al. 2014)) can sidestep specifying an explicit density for any data point and belong to the class of implicit generative models (Diggle and Gratton 1984).”
Approximate Bayesian computation via regression density estimation (2012, background): “For this reason, Giordani et al. (2012) suggest recomputing the distribution of U j using another normal mixture, which would lead to replacing φ(U j , 0, 1) with this distribution in (7).”
Hierarchical Implicit Models and Likelihood-Free Variational Inference (2017, background): “Furthermore the model is implicit, also known as a simulator: we can sample data from its generative process, but we may not have access to calculate its density [11, 20].”
Asymptotically exact inference in differentiable generative models (2016, background): “itly [10, 40, 27] - that is where we can generate random values for the latent and observed variables in the model, but we cannot tractably evaluate a density function for the probability distribution on those variables.”
The stationarity paradigm revisited: Hypothesis testing using diagnostics, summary metrics, and DREAM(ABC) (2015, methodology): “ABC was introduced by Diggle and Gratton [1984] to permit inference of complex models for which the likelihood is intractable, computationally too expensive to evaluate, or not explicitly available.”
Strong plant-soil associations in a heterogeneous subtropical broad-leaved forest (2011, methodology): “Firstly, we estimated the optimally fitted dispersal parameters (k , δ, u) using the K-function with the Method of Minimum Contrast (Diggle and Gratton 1984; Moller and Waagepetersen 2003) for 102 species.”
Bayesian Optimization for Likelihood-Free Inference of Simulator-Based Statistical Models (2015, background): “Simulator-based models are also called implicit models because the pdf of yθ is not specified explicitly (Diggle and Gratton, 1984), or generative models because they specify how data are generated.”
Likelihood and Non‐parametric Bayesian MCMC Inference for Spatial Point Processes Based on Perfect Simulation and Path Sampling (2003, methodology): “Diggle & Gratton (1984) obtained the estimate ðrDG; qDG; bDGÞ ¼ ð19; 76; 1:67Þ by an ad hoc method.”
Non-linear regression models for Approximate Bayesian Computation (2008, methodology): “Although inference from synthetic data that mimic observations has a long lasting record in frequentist statistics (Diggle and Gratton 1984; Gourieroux et al. 1993), ABC is still in its infancy.”
Bridging the gap between GLUE and formal statistical approaches: approximate Bayesian computation (2013, background): “Likelihood-free inference was introduced in the statistical literature about three decades ago ( Diggle and Gratton, 1984) for cases where the likelihood is intractable, too expensive to be evaluated, or an explicit formulation is not available.”
Toward diagnostic model calibration and evaluation: Approximate Bayesian computation (2013, methodology): “This approach was introduced in the statistical literature about three decades ago [Diggle and Gratton, 1984], and is especially useful in situations where evaluation of the likelihood is computationally prohibitive, or for cases when an explicit likelihood (objective) function cannot be justified.”
Residual analysis for spatial point processes (with discussion) (2005, methodology): “Finally, goodness-of-fit testing or confirmation of the fitted model is performed by simulating realisations from the fitted model and comparing observed and simulated values of a summary statistic [35, 41, 51, 50, 79, 90].”
Dynamic Likelihood-free Inference via Ratio Estimation (DIRE) (2018, methodology): “The second is to run LFIRE with the model hβ(x) for the log-ratio in (3) and summary statistics defined by the learned predictors θ̂(x) as in (4).”