1. A system comprising: a computer-readable memory storing executable instructions; and one or more processors in communication with the computer-readable memory, wherein the one or more processors are programmed by the executable instructions to at least: obtain (1) a model for detecting a keyword in an audio sample and (2) a first detection threshold corresponding to the model, wherein a detection score greater than the first detection threshold indicates that the keyword is present in the audio sample, and wherein the detection score is computed using the audio sample and the model; determine a first cost of computing a first incorrect detection hypothesis, wherein the first incorrect detection hypothesis corresponds to a detection score greater than the first detection threshold for an audio sample in which the keyword is not present, and wherein the first cost represents a cost of computing the first incorrect detection hypothesis at least a predetermined time period after computation of all prior incorrect detection hypotheses occurring before the first incorrect detection hypothesis; determine a second cost of computing a second incorrect detection hypothesis, wherein the second cost represents a cost of computing the second incorrect detection hypothesis within the predetermined time period following the first incorrect detection hypothesis, and wherein the second cost is different than the first cost; determine a second detection threshold based at least partly on the first and second costs, wherein the second detection threshold is determined such that the first and second costs are minimized; transmit the second detection threshold to a client device; receive audio data from the client device, wherein the client device transmits the audio data based at least partly on a detection score, determined using the audio data, satisfying the second detection threshold; and performing automatic speech recognition using at least a portion of the audio data to determine that data representing the keyword is present in the audio data, wherein the keyword comprises a word likely indicating device-directed speech.