Expected Information as Expected Utility

By J. Bernardo. 1979

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Proper local scoring rules (2011, background): “[Dawid (2007)]. 2.3. Log score. For φ(s)≡−slnswe obtain the logarithmic scoring rule, or log score, deﬁned by S(x,Q)=−lnq(x). This is essentially the only scoring rule of the form S(x,Q) = ξ{x,q(x)} [Bernardo (1979), Dawid (2007)]. For this case we obtain H(P)=− Z dµ(x)p(x)lnp(x), the Shannon entrop”
Bayesian Active Learning for Classification and Preference Learning (2011, background): “Although the latter approach was proposed several decades ago [Lindley, 1956, Bernardo, 1979], it is not always straightforward to apply the criteria to complicated models such as nonparametric processes with inﬁnite parameter spaces.”
A guide to Bayesian model selection for ecologists (2015, methodology): “Out-of-sample validation relies on the ability to compute a similarity statistic or scoring rule to obtain a measure of closeness between our out-of-sample data yoos and the predictions ŷoos (e.g., Bernardo 1979, Czado et al. 2009, Gneiting and Raftery 2007, Gneiting 2011).”
Measurement Error Models (2000, background): “The reference priors proposed by Bernardo (1979b) are obtained by maximizing 6(0 A X ) with respect to f ( 0 ) (see Berger 2000).”
Forecasting with DSGE Models (2010, unknown): “Under the assumption that only local scoring rules are considered, Bernardo (1979) showed that every proper scoring rule is equivalent to a positive constant times the log predictive score plus a real valued function that only depends on the observed data. For a survey of scoring rules, see Gneiting”
Bayesian Networks for Data Mining (2004, unknown): “, Bernardo and Smith, 1994, pp. 199–202). Next, we determine the configuration of φs that maximizesp(φs | Dc, Sh). Finally, we transform this MAP configuration to the original coordinate system. Using the MAP configuration corresponding to the coordinate systemφs has several advantages, which are di”
Near-optimal sensor placements in Gaussian processes (2005, unknown): “Maximizing mutual information between sets of random variables has a long history of use in statistics (Lindley, 1956; Bernardo, 1979), machine learning (Luttrell, 1985; MacKay, 1992).”
Strictly Proper Scoring Rules, Prediction, and Estimation (2007, background): “That said, Bernardo (1979) studied local scoring rules S(p,ω) that depend on the predictive density p only through its value at the event ω that materializes.”
A general framework for updating belief distributions (2013, background): “…π ( θ ) , so that the cumulative loss becomes In order to calibrate the information in the data relative to the prior we now assume that both loss functions, l ( θ, x ) and log { π ( (cid:98) θ ) /π ( θ ) } are non-negative, and we standardise l ( θ, x ) such that min θ l ( θ, x ) = 0 for any x .”
Near-Optimal Sensor Placements in Gaussian Processes: Theory, Efficient Algorithms and Empirical Studies (2008, unknown): “Maximizing mutual information between sets of random variables has a long history of use in statistics (Lindley, 1956; Bernardo, 1979), machine learning (Luttrell, 1985; MacKay, 1992).”
Why hydrological predictions should be evaluated using information theory (2010, methodology): “A similar argument in the context of experimental design was made by Bernardo (1979).”
Assessing probabilistic forecasts of multivariate quantities, with an application to ensemble predictions of surface winds (2008, background): “Allowing for affine transformations, this is the only ‘local’ proper scoring rule, in the sense that it depends on the predictive distribution only through the value p(x) that the predictive density attains at the observation (Bernardo 1979). The logarithmic score has many appealing properties (Bröc”
Scoring Rules for Forecast Verification (2010, unknown): “A more formal and cumbersome demonstration of an equivalent result may be found, for example, in a paper by Bernardo (Bernardo 1979) on the procedure for experiments design by maximizing the expected information.”
A survey of Bayesian predictive methods for model assessment, selection and comparison (2012, methodology): “The reference predictive model selection presented by Bernardo and Smith (1994) follows the general decision theoretic outline illustrated in Fig.”
The geometry of proper scoring rules (2007, background): “It is well known (Bernardo 1979) that the logarithmic score is essentially the only proper scoring rule having the form S(x, Q) ≡ −ξ{q(x)}, i.”
On the measure of the information in a statistical experiment (2007, methodology): “Taking advantage of the analogy between (25) and (37), DeGroot (1962, 1979) and Bernardo (1979a) pose IπMI (E) as an example of EVSI.”
Finding the Number of Clusters in a Dataset (2003, background): “…ciency (Kullback and Leibler 1951), the construction of multivariate measures of dependence (Joe 1989), the selection of reference priors (Bernardo 1979; Berger and Bernardo 1989), the Akaike information criterion (Akaike 1973), and Bayesian interpretation of experiments (Lindley 1956).”
Understanding predictive information criteria for Bayesian models (2013, background): “The logarithmic score is the unique (up to an aﬃne transformation) local and proper scoring rule (Bernardo, 1979), and appears to be the most commonly used scoring rule in model selection.”