[1] Neilson was born in New York into a naval family, the grandson of Rear Admiral Christopher Raymond Perry Rodgers.
[2]: 414 After re-joining the Navy in World War I and serving in London, Neilson began study at Boston's School of the Museum of Fine Arts in 1916.
He then studied under William Merritt Chase at the Art Students League of New York.
[2]: 415 Neilson taught at the Art Students League from 1926 to 1927, before becoming an instructor at the National Academy of Design from 1927 to 1934.
She filed for divorce in April 1924, arguing that he had failed to provide for her while he studied in Paris.