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The principle of maximum entropy provides a useful method for inferringstatistical mechanics models from observations in correlated systems, and iswidely used in a variety of fields where accurate data are available. While theassumptions underlying maximum entropy are intuitive and appealing, itsadequacy for describing complex empirical data has been little studied incomparison to alternative approaches. Here data from the collective spikingactivity of retinal neurons is reanalysed. The accuracy of the maximum entropydistribution constrained by mean firing rates and pairwise correlations iscompared to a random ensemble of distributions constrained by the sameobservables. In general, maximum entropy approximates the true distributionbetter than the typical or mean distribution from that ensemble. This advantageimproves with population size, with groups as small as 8 being almost alwaysbetter described by maximum entropy. Failure of maximum entropy to outperformrandom models is found to be associated with strong correlations in thepopulation.

Random versus maximum entropy models of neural population activity