update12:09 PM PT -- CBS just spoke on Bob's passing, saying ... "We lost a beloved member of the CBS family today with the passing of Bob Barker. "His generous donation allowed PETA to open its West Coast headquarters, the Bob Barker Building, in 2012, and it stands as a testament to his legacy and profound commitment to making the world a kinder place. Bob Barker, the iconic American game show host and animal rights activist, has died ... TMZ has learned. Barker died peacefully at his home Saturday morning in L.A. His rep tells TMZ Bob died of natural causes. Barker has appeared in a number of other TV shows and films over the years, oftentimes starring as himself.