It was a horrifying case that defied belief.

Andrea Yates was a 36-year-old mother of five young children: Noah, 7; John, 5; Paul, 3; Luke, 2; and Mary, 6 months. When her husband went to work on June 20, 2001, Yates methodically drowned all five children in the bathtub of their Houston-area home. Then she called 911.

“I just killed my kids,” she told police when they arrived at her house.

During her high-profile trial, her attorneys argued that Yates suffered from psychotic delusions that were amplified by repeated episodes of postpartum depression. She was sentenced to prison in 2002, but the conviction was overturned on appeal. In her 2006 retrial,...