Sufficiency and Approximate Sufficiency

Cam, Lucien Le

doi:10.1214/aoms/1177700372

Cited by 204 publications

(87 citation statements)

References 11 publications

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“…where the number of statistics is equal to the number of parameters to be estimated -they are restricted to problems that can be described in terms of models that belong to the exponential family (Lehmann & Casella, 1993;Didelot et al, 2010). As previous authors have pointed out it is necessary to develop methods that construct sets of statistics that are (at least approximately (Le Cam, 1964;Kusama, 1976)) sufficient (Joyce & Marjoram, 2008;Nunes & Balding, 2010;Fearnhead & Prangle, 2010a,b). It is either this, or reinterpreting ABC-based inferences not as approximations to the full Bayesian (and thus likelihood-based) apparatus but as inference procedures in their own right (Wilkinson, 2008;Drovandi et al, 2011), potentially systematically biased or for approximate models.…”

Section: Discussionmentioning

confidence: 99%

Considerate approaches to constructing summary statistics for ABC model selection

et al. 2012

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For nearly any challenging scientific problem evaluation of the likelihood is problematic if not impossible. Approximate Bayesian computation (ABC) allows us to employ the whole Bayesian formalism to problems where we can use simulations from a model, but cannot evaluate the likelihood directly. When summary statistics of real and simulated data are compared -rather than the data directly -information is lost, unless the summary statistics are sufficient. Here we employ an information-theoretical framework that can be used to construct (approximately) sufficient statistics by combining different statistics until the loss of information is minimized. Such sufficient sets of statistics are constructed for both parameter estimation and model selection problems. We apply our approach to a range of illustrative and real-world model selection problems.

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Section: Discussionmentioning

confidence: 99%

Considerate approaches to constructing summary statistics for ABC model selection

et al. 2012

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“…This prior density P (φ) is taken to be a uniform density over a compact rectangle to allow simple interpretations from Bayesian, frequentist and information-theoretic schools of inference. We are interested in approximately sufficient statistics (Cam 1964) for the purpose of computational efficiency. Recall that a statistic…”

Section: N-coalescent Experimentsmentioning

confidence: 99%

Experiments with the Site Frequency Spectrum

et al. 2010

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Evaluating the likelihood function of parameters in highly-structured population genetic models from extant deoxyribonucleic acid (DNA) sequences is computationally prohibitive. In such cases, one may approximately infer the parameters from summary statistics of the data such as the site-frequency-spectrum (SFS) or its linear combinations. Such methods are known as approximate likelihood or Bayesian computations. Using a controlled lumped Markov chain and computational commutative algebraic methods, we compute the exact likelihood of the SFS and many classical linear combinations of it at a non-recombining locus that is neutrally evolving under the infinitely-many-sites mutation model. Using a partially ordered graph of coalescent experiments around the SFS, we provide a decision-theoretic framework for approximate sufficiency. We also extend a family of classical hypothesis tests of standard neutrality at a non-recombining locus based on the SFS to a more powerful version that conditions on the topological information provided by the SFS.

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“…Le Cam (1964Cam ( , pp. 1419Cam ( -1455 presented a complicated formula for comparing two experiments based on the comparison of their risk functions.…”

Section: Deficiency and Insufficiencymentioning

confidence: 99%