A Two Tiered Finite Mixture Modelling Framework to Cluster Customers on EFTPOS Network

Jin, Yuan; Rumantir, Grace Widjaja

doi:10.1007/978-3-319-26350-2_24

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2018

2024

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Cited by 2 publications

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“…Thus, risk-averse estimation provides a new theoretical foundation, unrelated to MML, that explains the empirical success of the MML recipe, for which recent examples include [17,16,15,8,9].…”

Section: Introductionmentioning

confidence: 99%

Risk-averse estimation, an axiomatic approach to inference, and Wallace-Freeman without MML

Brand

2018

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We define a new class of Bayesian point estimators, which we refer to as risk averse. Using this definition, we formulate axioms that provide natural requirements for inference, e.g. in a scientific setting, and show that for well-behaved estimation problems the axioms uniquely characterise an estimator. Namely, for estimation problems in which some parameter values have a positive posterior probability (such as, e.g., problems with a discrete hypothesis space), the axioms characterise Maximum A Posteriori (MAP) estimation, whereas elsewhere (such as in continuous estimation) they characterise the Wallace-Freeman estimator.Our results provide a novel justification for the Wallace-Freeman estimator, which previously was derived only as an approximation to the information-theoretic Strict Minimum Message Length estimator. By contrast, our derivation requires neither approximations nor coding.

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