I'm not sure we can sure the screaming is fear-based without more analysis/details.
Google how to make an A-B-C chart (antecedent, behavior, consequence)--it's part of ABA (Applied Behavior Analysis) and it works for people and animals...
A=This is a way to keep track of what is happening right before a behavior (Antecedent)---this would include time, activity, people around the bird etc... whatever you are doing etc IMMEDIATELY before the behavior
B=The behavior itself (screaming)
C=The result (Consequence)- what you and everyone else does IMMEDIATELY after the scream--THIS DOES NOT HAVE TO BE A CONSEQUENCE like we traditionally tend to think of; it is ANY result that occurs immediately following the behavior)--Do you look at the bird, do you walk over to it, is the bird moved from on location to another, do you cover the cage, do you sing a song, do you walk away, make eye contact, do you say "no", do other people enter or leave the room, do you bring it a snack, does a dog bark, do babies cry.....?
Most behavior is linked to meeting one of 4 functions. All behavior has a function.
The 4 main functions of behavior are:
a. attention, b.escape from a situation, individual or demand, c. to get tangible items or treats, d. to meet a sensory need such as scratching an itch or eating when really hungry.
These don't always appear in such a linear fashion in real-life, and a behavior can serve a 2-part function, such as Escape to Attention, but for now, just focus on the basics.
Based on the results of your ABC chart, you will look at the consequence section and try to categorize responses according to the 4 functions above--following the scream, do you :
1.provide anything tangible (toys, favorite treat, etc)?
2.do you or any other people/animals provide any sort of attention (including eye-contact/proximity/verbal/physical)?
3.do demands on the bird get removed or do people go away (escape)?
4.does some sensory /physical need get met or attended to (feeding when ACTUALLY hungry, providing water, dimming the lights, hormone swings etc etc)?
After you determine what category most of the consequences fall in, then that is likely that that consequence's category (attention, escape, tangible or sensory) is linked to the function of your bird's behavior (because the screaming has increased over time). The more a behavior occurs following a response, the more you can assume that the response is linked to the function (reason) for the behavior.
Reinforcement occurs when any of the 4 functions are met by a response to that behavior (people and animals only do the bare minimum to get their needs met). If a behavior is happening all of the time, it is being reinforced.
When you figure out what is reinforcing your bird's screaming, then you can find a SOCIALLY ACCEPTABLE MEANS OF MEETING THOSE SAME NEEDS WITHOUT SCREAMING. You have to teach a replacement behavior that allows the bird to meet the same needs in a less obnoxious way.
Additionally, once you know the function of the screaming, you will want to remove any reinforcement following those screams....
SO for example: if a bird screams and a person is certain that it is attention-seeking, then anytime that bird screams, the person should leave the room and cut-off ALL attention. The bird wants attention, so it will have to be taught an alternative to screaming (talking, ringing a bell, doing a dance etc etc). When the preferred behavior occurs, then the person pours on the attention....They will IGNORE behaviors that are undesired IF linked to attention.