Mr Scott is known to be an active man who likes to be out and about, but suffers health problems and has mild dementia.
There have been no reported sightings of him since Tuesday, when he was seen in a Greggs bakery in Leith at around 4pm.
His grand-daughter, Charlotte, told STV he is a caring and thoughtful man who regularly calls on neighbours to see if they need milk or bread - and offers to clean their windows.
He also has five loving grandchildren who are looking forward to giving him Christmas cards - and are obviously worried at his disappearance.
Ms Gibson, anxious that he is outdoors in bad weather, wants him to be found, urgently, “so that he can be safe”.
Mr Scott is white, 5ft 1in, balding with white hair and has a small wound on his head.
He regularly wears glasses and when last seen was wearing a navy jacket, grey trousers and a dark-coloured flat cap.
Anyone with news of Mr Scott’s whereabouts should contact police via 101.