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What you show is what you get: sampling biases in determining biological sensory function


Classical studies of biological sensory systems use the following main technique: sensory stimuli are drawn from a pre-determined distribution P(stim) and presented to the animal; the ensemble associated with sensory response is collected and used to characterize the conditional distribution P(stim|resp) (or parameters thereof) as a model of sensory system function. However, most of the standard statistical tool used in neuroscience to estimate P(stim|resp) are valid under a very fundamental condition – that the samples used to estimate P(stim|resp) are drawn from the same distribution. This is obviously not the case in most studies of sensory system, where the samples are drawn explicitly from a different distribution, P(stim) (the sampling distribution), selected by the scientist. We demonstrate here that in this case the observed conditional distribution is P*(stim|resp) = P(stim|resp)*P(stim) and expectations estimated with this dataset are parameters of P*, not P. To characterize the actual functional properties of the system, one needs to use estimators developed within unequal probability sampling theory [1]. We apply one of these estimators, the Horvitz-Thompson estimator of the mean mHT = Σi xi/P(xi), to observations {xi} from the cricket cercal sensory system and illustrate the ensuing changes in apparent functionality (Figure 1).

Figure 1
figure 1

The spike-triggered average (STA) of air current stimulis sampled from a band-limited GWN distribution (5–500 Hz) is shown in blue. The corresponding Horvitz-Thompson estimate of the STA is plotted in green.


  1. Thomson SK: Sampling. 2002, New York: Wiley Interscience, 2

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Correspondence to Alexander G Dimitrov.

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Open Access This article is published under license to BioMed Central Ltd. This is an Open Access article is distributed under the terms of the Creative Commons Attribution 2.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Dimitrov, A.G. What you show is what you get: sampling biases in determining biological sensory function. BMC Neurosci 9 (Suppl 1), P121 (2008).

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