 Missing-pulse bias in average-power inference

Missing-pulse bias in average-power inference arises when a nominal trigger rate is used as though every trigger emitted a pulse. With background removed and complete pulses counted, let $M$ be the number of triggers and $N$ the number of emissions during $T$. ThenThe quotient is mean energy per trigger, including failed triggers as zero-energy outcomes. It equals the conditional pulse-energy mean given emission only when every trigger emits, or after correction for the measured emission fraction. Historical calorimetric inference uses energy, injection time and pulse rate; those quantities must describe the same collection.^[ref]

For an original five-trigger record, suppose energies are $0,1,0,3,0\mu \mathrm{J}$. Mean energy per trigger is $0.8\mu \mathrm{J}$, while the two emitted pulses average $2\mu \mathrm{J}$. At a nominal $1\mathrm{kHz}$ trigger rate, their average power is $0.8\mathrm{mW}$. The actual emission rate is $400\mathrm{Hz}$, consistent with the same power and emitted-pulse mean.

A pulse monitor with a threshold above the weaker pulse could detect only the $3\mu \mathrm{J}$ event. Its detected-event average would then be $3\mu \mathrm{J}$, also different from the true emitted-pulse mean. Failure to detect is not automatically failure to emit. A calibrated pulse-resolving receiver and a trigger counter distinguish emitted, detected and commanded events. The average power of a laser pulse train article additionally treats continuous backgrounds and observation-window accounting.