Overview
Joseph B. Kadane is a statistician at Carnegie Mellon University (Department of Statistics and Data Science) known for foundational contributions to Bayesian statistics, subjective probability elicitation, and sequential decision analysis. In Bayesian computation, he co-developed (with Luke Tierney) the Tierney-Kadane (1986) Laplace approximation for posterior moments and marginal densities, subsequently extended to nonlinear functions (TKK 1989a) and to fully exponential approximations of posterior expectations and variances (TKK 1989b).
Key Contributions
- Tierney-Kadane (1986) (JASA 81: 82–86): Coordinate-margin Laplace approximation for marginal posterior densities and posterior moments with O(n⁻¹) relative error; first systematic Bayesian application of Laplace's asymptotic method.
- TKK (1989a) (Biometrika 76: 425–433): Extension to marginal densities of arbitrary smooth nonlinear functions g(θ); derived via constrained optimisation without explicit global reparameterisation.
- TKK (1989b) (JASA 84: 710–716): Fully exponential Laplace approximation to posterior expectations E[g(θ)|y] and variances; incorporates log b(θ) into the exponent to achieve O(n⁻²) relative error.
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