Memoir on the Probability of the Causes of Events

By P. Laplace. 1986

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Citations in the corpus

Recasting Gradient-Based Meta-Learning as Hierarchical Bayes (2018, methodology): “The Laplace approximation (Laplace, 1986; MacKay, 1992a;b) is applicable in this case as it replaces a point estimate of an integral with the volume of a Gaussian centered at a mode of the integrand, thereby forming a local quadratic approximation.”
Moments in Time Dataset: One Million Videos for Event Understanding (2018, methodology): “101 [34], ActivityNet [6], Kinetics [19] and the Moments in Time Dataset) using Bayes Rule [23].”
Bayesian Estimation and Inference (2015, methodology): “Assuming a prior has been specified, Bayesian methods for computing posterior distributions has generated much discussion (see initial work by Bayes, 1763; Laplace, 1774, 1986; see modern work by Gelman et al., 2004; Gill, 2008).”
AUTO-ENCODING VARIATIONAL BAYES (2020, unknown): “Though the analysis is a special case, we believe that it gives intuition for performance of our decision-making procedures more generally because, for many models used in practice, a Gaussian distribution approximates the posterior well, as demonstrated by the success of the Laplace approximation [”
Integration of Spectral Feature Extraction and Modeling for HMM-Based Speech Synthesis (2014, methodology): “Therefore, Q (c) is assumed as a Gaussian probability distribution by using the Laplace approximation [14].”
A Tricentenary history of the Law of Large Numbers (2013, background): “In a paper of 1774 (Laplace (1986)) which Stigler (1986) regards as foundational for the problem of predictive probability, Pierre Simon de Laplace (1749–1827) sees that Bayes’s Theorem provides a means to solution of Jacob Bernoulli’s inversion problem.”
Hybrid Autoregressive Transducer (HAT) (2020, unknown): “However, the exact sum is not easy to derive, thus some approximation like Laplace’s methods for integrals [38] is needed.”
Explaining by Removing: A Unified Framework for Model Explanation (2020, background): “This definition of consistency describes a class of subset functions that obey fundamental probability axioms (Kolmogorov, 1950; Laplace, 1986).”
The Effective Sample Size (2014, background): “…correspondence to James Berger, Department of Statistical Science, Duke University, 221 Old Chemistry Building, Durham, NC 27708-0251, USA; E-mail: berger@stat.duke.edu 1992), Hsu (1995), Laplace (1986), Mackay (1998), Stone (1979), Tierney and Kadane (1986), and Tierney et al. (1989).”