Complex sentence: Miller was often in the public eye, particularly during the late 1940s, 1950s and early 1960s, a period during which he testified before the House Un-American Activities Committee, received the Pulitzer Prize for Drama, and was married to Marilyn Monroe.
Split into simpler sentences: Miller was often in the public eye, particularly during the late 1940s, 1950s and early 1960s. During this time, he was awarded the Pulitzer Prize for Drama; testified before the House Un-American Activities Committee; and was married to Marilyn Monroe.