Bayesian Theory

By J. Bernardo, Adrian F. M. Smith. 2001

615 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Computer Networks and Communications, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/eac02bb2fea61889b5577db5321e0c2fc90ac39b

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In Biomedical Engineering

In Computer Networks and Communications

In Statistics and Probability

Citations in the corpus

Estimating frequency of change (2003, positive): “To obtain a single number for . from the distribution, we can either use the maximum a posteriori estimator or the posterior expectation [Bernardo and Smith 1994; Lee 1997].”
A tutorial introduction to the minimum description length principle (2004, neutral): “Bayesian statistics [Lee 1997; Bernardo and Smith 1994] is one of the most well-known, frequently and successfully applied paradigms of statistical inference.”
Robust generalised Bayesian inference for intractable likelihoods (2021, positive): “Outside of the M-closed setting such concentration is problematic, often leading to over-confident predictions (Bernardo & Smith, 2009).”
Bayesian parameter estimation via variational methods (2000, methodology): “The formalism also allows ready incorporation of prior knowledge and the seamless combination of such knowledge with observed data (Bernardo and Smith 1994, Gelman 1995, Heckerman, Geiger and Chickering 1995).”
Comparing dynamic causal models (2004, background): “In Bayesian decision theory the choice of cut-off is guided by a ‘loss function’ or ‘utility’ which captures the costs of making false positive and false negative decisions [6].”
Bayesian and likelihood-based methods in multilevel modeling 1 A comparison of Bayesian and likelihood-based methods for fitting multilevel models (2006, neutral): “, Bernardo and Smith (1994), Kass and Wasserman (1996), Spiegelhalter et al. (1997), Gelman et al. (2003)), leading in some models to more than one intuitively reasonable approach.”
Forecast Combination and Model Averaging Using Predictive Measures (2007, neutral): “This corresponds to the M−closed view of Bernardo and Smith (1994), when the true model is assumed to be part of the model set.”
On Choosing and Bounding Probability Metrics (2002, background): “In Bayesian statistics, Bernardo and Smith (1994, p. 75) suggest that relative entropy is the nat-ural measure for the lack of ﬁt of an approximation of a distribution when preferences are described by a logarithmic score function.”
Stochastic Optimization: a Review (2002, neutral): “Other, continuous, approaches to the quantification of predictive utility are possible (e.g., a log scoring method as in Bernardo & Smith, 1994; Lindley, 1968 uses squared-error loss to measure predictive accuracy in a less problem-specific framework than the one presented here).”
Link analysis ranking: algorithms, theory, and experiments (2005, methodology): “Bharat and Henzinger [1998] and Chakrabarti et al. [1998] consider improvements on the HITS algorithm by using textual information to weight the importance of nodes and links.”
Expected Value of Sample Information Calculations in Medical Decision Modeling (2004, background): “This section rehearses the standard results of Bayesian theory, 37,38 as they would be applied to single parameters, or sets of single parameters, within our Monte Carlo implementation of EVSI calculations.”
A Bayesian model of shape and appearance for subcortical brain segmentation (2011, positive): “(5), (6) and using sufficient statistics, t( ), it can be shown (see Bernardo and Smith, 2000) that (A.1) We use the sufficient statistics for the multivariate Gaussian given by the number of samples, sample mean and sample covariance: t( ) = (n s , x̄ S ), , and .”
Bayesian approach for neural networks--review and case studies (2001, neutral): “Good references for Bayesian data analysis are (Berger, 1985; Bernardo and Smith, 1994; Gelman et al., 1995).”
Bayesian clustering and product partition models (2003, positive): “It follows (Bernardo and Smith, 1994) that the optimal partition ρ Å satisﬁes is the expected loss at the optimal action aÅ ρ . y / , which minimizes l.M ρ , a ρ , ω / p. ω | y , ρ / d ω : In this work we shall consider loss functions of the form where K represents the cost of adopting the model…”