Doctor Anderson is a psychiatrist tasked by Secretary Bishop to convince Olivia that she is the "Olivia Dunham" from the other universe (or Fauxlivia). In a therapy session, Anderson explains to Olivia that her belief of another universe is not real and actually the result of head trauma she experienced recently in her last mission. Anderson further explains that she is there to help "Bolivia" get over the idea of another universe
Dr. Anderson shows Olivia various pictures of "Bolivia" and close friends and family. Anderson in an attempt to poke holes in Olivia's story asks about Peter, the name Olivia mumbled while under anesthesia. Olivia explains that he is a civilian consultant. Her team crossed over to bring him back home. When asked their whereabouts, Olivia assumes that they went home without her
Dr. Anderson did not end up being effective as Olivia states her mother died when she was 14; that Charlie Francis is dead and that she never won an Olympic medal for marksmanship and ultimately it was the drugs and adrenaline that gave Olivia "Fauxlivia's" memories.
"...what is happening to you, given the nature of your job, the upsetting events you come in contact with on a regular basis, coupled with the injury to your head... it's not surprising your mind has created this fantasy... a means of processing the trauma."