Coupling from the past
Coupling from the Past is like picking a random card from a deck of cards, but instead of using a regular shuffle, we use a special kind of shuffle. This special shuffle makes it so that all of the cards can be equally likely to be picked, no matter how the deck was shuffled in the past.
Imagine you have a deck of cards with 52 cards in it. You shuffle the deck, but instead of shuffling it the normal way, you shuffle it in a special way. Specifically, for each card in the deck, you look at all of the cards that come after it, and you swap the current card with one of the cards that comes after it at random.
So, for example, if you had a deck that looked like this:
Ace of Hearts, 2 of Spades, 3 of Diamonds, 4 of Clubs, 5 of Hearts, 6 of Spades, 7 of Diamonds, 8 of Clubs, 9 of Hearts, 10 of Spades, Jack of Diamonds, Queen of Clubs, King of Hearts
Then after doing the special shuffle, the deck might look like this:
King of Hearts, 2 of Spades, 3 of Diamonds, 4 of Clubs, 5 of Hearts, 6 of Spades, Ace of Hearts, 8 of Clubs, 9 of Hearts, 10 of Spades, Jack of Diamonds, Queen of Clubs, 7 of Diamonds
The special thing about this shuffle is that it doesn't matter how the deck was shuffled in the past. Every time you do the special shuffle, you are guaranteed to get a deck where every card is equally likely to be picked, no matter how the deck was shuffled in the past. This makes it a powerful tool for generating random samples in statistics and other fields.
Imagine you have a deck of cards with 52 cards in it. You shuffle the deck, but instead of shuffling it the normal way, you shuffle it in a special way. Specifically, for each card in the deck, you look at all of the cards that come after it, and you swap the current card with one of the cards that comes after it at random.
So, for example, if you had a deck that looked like this:
Ace of Hearts, 2 of Spades, 3 of Diamonds, 4 of Clubs, 5 of Hearts, 6 of Spades, 7 of Diamonds, 8 of Clubs, 9 of Hearts, 10 of Spades, Jack of Diamonds, Queen of Clubs, King of Hearts
Then after doing the special shuffle, the deck might look like this:
King of Hearts, 2 of Spades, 3 of Diamonds, 4 of Clubs, 5 of Hearts, 6 of Spades, Ace of Hearts, 8 of Clubs, 9 of Hearts, 10 of Spades, Jack of Diamonds, Queen of Clubs, 7 of Diamonds
The special thing about this shuffle is that it doesn't matter how the deck was shuffled in the past. Every time you do the special shuffle, you are guaranteed to get a deck where every card is equally likely to be picked, no matter how the deck was shuffled in the past. This makes it a powerful tool for generating random samples in statistics and other fields.