Extinction (psychology)
Extinction in psychology refers to the lowering of the probability of a response when a characteristic reinforcing stimulus is no longer presented. In Classical conditioning, this refers to the decline of a conditioned response when a conditioned stimulus repeatedly occurs without the presence of the unconditioned stimulus it had been paired with. In Operant conditioning, extinction is the decline of an operant response when it is no longer reinforced in the presence of its discriminative stimulus.

# Extinction in operant conditioning
In operant conditioning, extinction is the withholding of reinforcement for a previously reinforced behavior which decreases the future probability of that behavior. For example, a child who climbs under his desk, a response which has been reinforced by attention, is subsequently ignored until the attention-seeking behavior no longer occurs. In his autobiography, B. F. Skinner noted how he accidentally discovered the extinction of an operant response due to the malfunction of his laboratory equipment.
When the extinction of a response has occurred, the discriminative stimulus is then known as an extinction stimulus (S  or s delta). When an S delta is present, the reinforcing consequence which characteristically follows a behavior does not occur. This is the opposite of a discriminative stimulus which is a signal that reinforcement will occur. For instance, in an operant chamber, if food pellets are only delivered when a response is emitted in the presence of a green light, the the green light is a discriminative stimulus. If when a red light is present food will not be delivered, then the red light is an extinction stimulus. (food here is used as an example of a reinforcer).

# Successful extinction procedures
In order for extinction to work effectively, it must be done consistently. Extinction is considered successful when responding in the presence of an extinction stimulus (a red light or a teacher not giving a bad student attention, for instance) is zero. When a behavior reappears again after it has gone through extinction, it is called spontaneous recovery.

# Extinction burst
While extinction, when implemented consistently over time, results in the eventual decrease of the undesired behavior, in the near-term the subject might exhibit what is called an extinction burst. An extinction burst will often occur when the extinction procedure has just begun. This consists of a sudden and temporary increase in the response's frequency, followed by the eventual decline and extinction of the behavior targeted for elimination.
Take, as an example, a pigeon that has been reinforced to peck an electronic button. During its training history, every time the pigeon pecked the button, it will have received a small amount of bird seed as a reinforcer. So, whenever the bird is hungry, it will peck the button to receive food. However, if the button were to be turned off, the hungry pigeon will first try pecking the button just as it has in the past. When no food is forthcoming, the bird will likely try again... and again, and again. After a period of frantic activity, in which their pecking behavior yields no result, the pigeon's pecking will decrease in frequency.
The evolutionary advantage of this extinction burst is clear. In a natural environment, an animal that persists in a learned behavior, despite not resulting in immediate reinforcement, might still have a chance of producing reinforcing consequences if they try again. This animal would be at an advantage over another animal that gives up too easily.

# Extinction-induced variability
Extinction-induced variability serves an adaptive role similar to the extinction burst. When extinction begins, subjects can exhibit variations in response topography (the movements involved in the response).  Response topography is always somewhat variable due to differences in environment or idiosyncratic causes but normally a subject's history of reinforcement keeps slight variations stable by maintaining successful variations over less successful variations.  Extinction can increase these variations significantly as the subject attempts to acquire the reinforcement that previous behaviors produced.  If a person attempts to open a door by turning the knob, but is unsuccessful, they may next try jiggling the knob, pushing on the frame, knocking on the door or other behaviors to get the door to open.  Extinction-induced variability can be used in shaping to reduce problematic behaviors by reinforcing desirable behaviors produced by extinction-induced variability.