Concepedia

Concept

statistical inference

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Decision-Theoretic Inference

1936 - 1961

Inference during this period was increasingly framed as a decision problem under uncertainty, integrating formal decision theory with probability to justify and compare procedures. The era foregrounded adaptive and sequential approaches that update with accumulating data, including unbiased sequential estimation and sequential confidence intervals, and reinforced foundations of sufficiency, intrinsic accuracy, and minimax optimization in estimation and testing. These developments unified concerns about optimality, robustness, and interpretability within a decision-theoretic lens while expanding nonparametric and goodness-of-fit perspectives.

• Sequential and adaptive inference under uncertainty emphasizes procedures that update with accumulating data, featuring unbiased sequential estimation, and sequential confidence intervals. Evidence comes from results on unbiased sequential estimation, sequential confidence intervals, and sequential processes.

• Unbiasedness, local optimality, and minimax decision frameworks study when estimators are best under a point or class; includes conditions for best unbiased estimates and admissible procedures.

• Decision theory and inference as a formal decision problem critique of significance-testing practice; develops decision functions and probabilistic reasoning in inference.

• Foundations of sufficiency, intrinsic accuracy, and linear estimation center on sufficient statistics, intrinsic accuracy constraints, location-scale estimation, and variance components.

• Nonparametric inference and goodness-of-fit tools establish unbiasedness and consistency for nonparametric tests and provide practical goodness-of-fit estimators.

Bayesian and Likelihood Foundations

1962 - 1968

Bootstrap-EM Inference Era

1969 - 1989

Bayesian Model-Space Inference

1990 - 1997

Bayesian Model Averaging

1998 - 2004

High-Dimensional Regularized Inference

2005 - 2014

Validated Bayesian Practice

2015 - 2020

Estimand-Centered Robust Inference

2021 - 2024