Probability Matching Priors: Higher Order Asymptotics

By Gauri Sankar Datta, R. Mukerjee. 2004

207 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computer Networks and Communications, Signal Processing

View Paper: https://www.semanticscholar.org/paper/b2663a77aafb0b8dcfcb189cc1c2fba0becb49ac

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Computer Networks and Communications

In Signal Processing

Citations in the corpus

Probability matching priors (2004, methodology): “We note, however, that in the PMP literature priors that we call here second-order matching are often referred to as first-order matching, and priors which are defined third-order matching here are referred to as second-order matching (see, for example, Mukerjee and Ghosh, 1997; Datta and Mukerjee, ”
Prior Distributions From Pseudo-Likelihoods in the Presence of Nuisance Parameters (2009, methodology): “We give a four-step proof of (10) that is based on a shrinkage argument popular in Bayesian asymptotics (see, among others, Ghosh and Mukerjee 1991; Datta and Ghosh 1995; Mukerjee and Reid 1999, 2001; Datta and Mukerjee 2004; Chang and Mukerjee 2006).”
Ltd Registered in England and Wales Registered Number : 1072954 Registered office : (2004, unknown): “The normal approximation to r∗ F was derived using the method outlined in Davison et al. (2006). It is difficult to do a full set of simulations over the parameter space for with small values of n, as many parameter pairs lead to large numbers of samples for which the maximum likelihood estimates ca”
Intrinsic credible regions: An objective Bayesian approach to interval estimation (2005, background): “Third order coverage does not necessarily apply for Jeffreys’ prior, though (see Datta and Mukerjee, 2004 or Rousseau, 1997).”
Default priors for Bayesian and frequentist inference (2010, methodology): “μ/dμ∝ dμwas pointed out in Stein (1959) and was discussed in detail in Cox and Hinkley (1974), pages 46 and 383.”
THE FORMAL DEFINITION OF REFERENCE PRIORS (2009, background): “There is a considerable body of conceptual and theoretical literature devoted to identifying appropriate procedures for the formulation of objective priors; for relevant pointers see Section 5.6 in Bernardo and Smith [13], Datta and Mukerjee [20], Bernardo [11], Berger [3], Ghosh, Delampady and Sama”
Recent advances on Bayesian inference for $P(X < Y)$ (2011, methodology): “The strong matching prior π∗(R) is thus also an HPD matching prior (see, e.g., Datta and Mukerjee, 2004) for R based on the modified profile likelihood.”
Objective Priors: An Introduction for Frequentists (2011, methodology): “…case a first-order quantile matching prior π(θ1, θ2, . . . , θp)∝ I1/211 (θ)h(θ2, . . . , θp) is also secondorder matching if and only if h satisfies (cf. Datta and Mukerjee, 2004, page 27) the differential equation p ∑ s=2 p ∑ u=2 ∂ ∂θu { I −1/2 11 I suE ( ∂3 log f ∂θ21 ∂θs ) h ∣ ∣ ∣ θ } +…”
Objective priors for the bivariate normal model (2008, background): “Datta and Mukerjee [9] and Datta and Ghosh [12] discuss how to determine first-order matching priors for functions of parameters; these are priors such that the frequentist coverage of a one-sided credible interval is equal to the Bayesian coverage up to a term of order n−1.”
Calibrating general posterior credible regions (2015, methodology): “Since this prior is probability-matching for the location-scale model (e.g., Datta and Mukerjee 2004), we may expect that the posterior credible intervals would be approximately calibrated for our linear regression.”
The case for objective Bayesian analysis (2006, background): “Invariance priors, as mentioned above, matching priors (see Datta and Mukerjee (2004)), and admissible priors (cf. Berger et al. (2005b)) are other approaches being extensively studied today.”