biostudies-literatureCarvalho LENHGRI NIH HHS3209-14https://www.ebi.ac.uk/biostudies/studies/S-EPMC2265131biostudies-literatureUnknown105(9)Maximum likelihood estimators and other direct optimization-based estimators dominated statistical estimation and prediction for decades. Yet, the principled foundations supporting their dominance do not apply to the discrete high-dimensional inference problems of the 21st century. As it is well known, statistical decision theory shows that maximum likelihood and related estimators use data only to identify the single most probable solution. Accordingly, unless this one solution so dominates the immense ensemble of all solutions that its probability is near one, there is no principled reason to expect such an estimator to be representative of the posterior-weighted ensemble of solutions, and thus represent inferences drawn from the data. We employ statistical decision theory to find more rProceedings of the National Academy of Sciences of the United States of AmericaCentroid estimation in discrete high-dimensional spaces with applications in biology.PMC2265131R01-HG01257R01 HG001257Carvalho LELawrence CEfalseCentroid estimation in discrete high-dimensional spaces with applications in biology.Maximum likelihood estimators and other direct optimization-based estimators dominated statistical estimation and prediction for decades. Yet, the principled foundations supporting their dominance do not apply to the discrete high-dimensional inference problems of the 21st century. As it is well known, statistical decision theory shows that maximum likelihood and related estimators use data only to identify the single most probable solution. Accordingly, unless this one solution so dominates the immense ensemble of all solutions that its probability is near one, there is no principled reason to expect such an estimator to be representative of the posterior-weighted ensemble of solutions, and thus represent inferences drawn from the data. We employ statistical decision theory to find more r2008-01-01T00:00:00Z2008 Mar2025-04-19T16:48:39.508Z2019-03-27T02:44:18ZS-EPMC22651311830516010.1073/pnas.0712329105