Lower bound on the fraction of total information neglected by MID for a Bernoulli neuron, as a function of the marginal spike probability <i>p</i>(<i>spike</i>) = <i>p</i>(<i>r</i> = 1), for the special case of a binary stimulus.

<p>Information loss is quantified as the ratio <i>I</i>₀/(<i>I</i>₀+<i>I</i>_<i>ss</i>), the information due to no-spike events, <i>I</i>₀, divided by the total information due to spikes and silences, <i>I</i>₀+<i>I</i>_<i>ss</i>. The dashed gray line shows the lower bound derived in the limit <i>p</i>(<i>spike</i>) → 0. The solid black line shows the actual minimum achieved for binary stimuli <i>s</i> ∈ {0,1} with <i>p</i>(<i>s</i> = 1) = <i>q</i>, computed via a numerical search over the parameter <i>q</i> ∈ [0, 1] for each value of <i>p</i>(<i>spike</i>). The lower bound is substantially loose for <i>p</i>(<i>spike</i>) > 0, since as <i>p</i>(<i>spike</i>) → 1, the fraction of information due to silences goes to 1.