Richard McElreath - Statistical Rethinking

Citation index

Akaike (1973), 451, 457

Akaike (1974), 451, 457

Akaike (1978), 450, 451, 457

Akaike (1981), 451, 457

Baker (1994), 453, 457

Berger and Berry (1988), 448, 457

Berger (1985), 451, 457

Betancourt and Girolami (2013), 454, 457

Bickel et al. (1975), 453, 457

Binmore (2009), 447, 457

Bolker (2008), 453, 457

Box and Tiao (1973), 448, 457

Box (1979), 445, 457

Box (1980), 448, 457

Breiman (1968), 448, 457

Brooks et al. (2011), 452, 457

Burnham and Anderson (2002), 450, 451, 457

Campbell (1985), 455, 457

Carroll et al. (2012), 454, 457

Casella and George (1992), 452, 457

Caticha and Griffin (2007), 452, 453, 457

Cho (2011), 446, 457

Claeskens and Hjort (2008), 451, 457

Clark (2012), 445, 458

Collins and Pinch (1998), 445, 446, 458

Cox (1946), 447, 458

Cushman et al. (2006), 453, 458

Daston and Galison (2007), 446, 458

Elias (1958), 450, 458

Fanelli (2012), 455, 458

Ferguson and Heene (2012), 455, 458

Feynman (1967), 448, 458

Fienberg (2006), 447, 451, 458

Fisher (1925), 447, 448, 458

Fisher (1955), 446, 458

Fisher (1956), 446, 448, 458

Fontani et al. (2014), 455, 458

Forer (1949), 455, 458

Franco et al. (2014), 455, 458

Frank (2007), 453, 458

Frank (2009), 448, 450, 458

Frank (2011), 450, 458

Fullerton (2009), 453, 458

Galton (1989), 449, 458

Gelfand et al. (1995), 454, 458

Gelman and Hill (2007), 450, 458

Gelman and Loken (2013), 455, 458

Gelman and Loken (2014), 455, 459

Gelman and Nolan (2002), 447, 459

Gelman and Robert (2013), 447, 459

Gelman and Rubin (1992), 452, 459

Gelman and Rubin (1995), 451, 459

Gelman and Stern (2006), 450, 459

Gelman et al. (2013a), 448, 451, 458

Gelman et al. (2013b), 451, 458

Gelman (2005), 454, 458

Gelman (2006), 452, 458

Geman and Geman (1984), 452, 459

Gigerenzer and Hoffrage (1995), 448, 459

Gigerenzer et al. (1990), 446, 452, 459

Gigerenzer et al. (2000), 447, 459

Gigerenzer et al. (2004), 447, 459

Gilad and Mizrahi-Man (2015), 455, 459

Gillespie (1977), 445, 459

Grafen and Hails (2002), 450, 452, 459

Griffin (2008), 452, 453, 459

Grosberg (1998), 452, 459

Grnwald (2007), 450, 451, 459

Hacking (1983), 445, 459

Hahn and Bentley (2003), 445, 459

Harte (2011), 450, 459

Hastie et al. (2009), 450, 459

Hastings (1970), 452, 459

Hauer (2004), 448, 459

Henrion and Fischoff (1986), 448, 459

Herndon et al. (2014), 455, 459

Hilbe (2011), 454, 459

Hinde and Milligan (2011), 450, 459

Hoffman and Gelman (2011), 452, 460

Horton (2015), 455, 460

Howell (2000), 449, 460

Howell (2010), 449, 460

Hubbell (2001), 445, 460

Hull (1988), 455, 460

Ioannidis (2005), 448, 451, 455, 460

Ioannidis (2012), 455, 460

Jaynes (1976), 450, 460

Jaynes (1984), 447, 460

Jaynes (1985), 447, 448, 460

Jaynes (1986), 449, 460

Jaynes (1988), 452, 453, 460

Jaynes (2003), 445, 447, 449453, 460

Jung et al. (2014), 454, 460

Kadane (2011), 448, 460

Kitcher (2000), 455, 460

Kitcher (2011), 446, 460

Kline and Boyd (2010), 453, 460

Kruscke (2011), 452, 460

Kullback and Leibler (1951), 450, 460

Kullback (1959), 450, 460

Kullback (1987), 450, 460

Lambert (1992), 453, 460

Lansing and Cox (2011), 445, 446, 460

Laudan (1981), 455, 460

Lee and DeVore (1976), 449, 460

Levins (1966), 445, 460

Lewandowski et al. (2009), 454, 460

Lightsey et al. (2006), 451, 460

Lin et al. (2014), 455, 461

Lindley (1971), 446, 461

Lunn et al. (2013), 451, 461

MacKay and Neal (1994), 454, 461

Mangel and Samaniego (1984), 451, 461

Marin and Robert (2007), 446, 461

McCullagh and Nelder (1989), 453, 461

McCullagh (1980), 453, 461

McElreath and Smaldino (2015), 455, 461

McGrayne (2011), 447, 461

McHenry and Coffing (2000), 450, 461

Meehl (1956), 455, 461

Meehl (1967), 445, 461

Meehl (1990), 449, 461

Metropolis and Ulam (1949), 452, 461

Metropolis et al. (1953), 452, 461

Molenberghs et al. (2014), 454, 461

Morison (1942), 447, 461

Mulkay and Gilbert (1981), 445, 446, 461

Neal (1996), 454, 461

Neal (1998), 454, 461

Nelder and Wedderburn (1972), 453, 461

Nettle (1998), 452, 461

Nieuwenhuis et al. (2011), 450, 461

Nunn and Puga (2011), 451, 461

Nuzzo (2014), 453, 461

ORourke and Detsky (1989), 455, 462

Ohta and Gillespie (1996), 445, 462

Papaspiliopoulos et al. (2007), 454, 462

Pearl (2014), 449, 453, 462

Polson and Scott (2012), 452, 462

Popper (1963), 455, 462

Popper (1996), 445, 455, 462

Proulx and Adler (2010), 445, 462

Rao (1997), 446, 452, 462

Reilly and Zeringue (2004), 449, 462

Reinhart and Rogoff (2010), 455, 462

Rice (2010), 448, 462

Riley et al. (1999), 451, 462

Robert and Casella (2011), 452, 462

Robert (2007), 447, 448, 451, 462

Roberts and Sahu (1997), 454, 462

Rommel et al. (2007), 451, 462

Rosenbaum (1984), 450, 462

Rosenthal (1979), 455, 462

Rubin and Little (2002), 454, 462

Rubin (1976), 454, 462

Rubin (2005), 449, 462

Sankararaman et al. (2012), 447, 462

Savage (1962), 447, 462

Schwarz (1978), 451, 462

Sedlemeier and Gigerenzer (1989), 455, 462

Senn (2003), 453, 462

Shannon (1948), 450, 462

Shannon (1956), 450, 463

Silk et al. (2005), 453, 463

Silver (2012), 447, 463

Simmons et al. (2011), 451, 453, 455, 463

Simmons et al. (2013), 455, 463

Simon (1969), 447, 463

Simpson et al. (2014), 452, 463

Simpson (1951), 449, 453, 463

Sober (2008), 446, 463

Speed (1986), 454, 455, 463

Stein (1955), 454, 463

Stigler (1981), 450, 463

Stone (1977), 451, 463

Theobald (2010), 447, 463

Van Horn (2003), 447, 463

Vehtari and Gelman (2014), 451, 463

Venn (1876), 446, 463

Vonesh and Bolker (2005), 454, 463

Wald (1939), 451, 463

Wald (1943), 451, 463

Wald (1950), 451, 463

Wang et al. (2015), 447, 463

Watanabe (2010), 451, 463

Wearing (2005), 454, 463

Welsh and Lind (1995), 453, 463

Williams (1975), 453, 463

Williams (1980), 452, 453, 464

Williams (1982), 453, 464

Wittgenstein (1953), 445, 464

Wolpert and Macready (1997), 447, 464

14: Missing Data and Other Opportunities

A big advantage of Bayesian inference is that it obviates the need to be clever. For example, theres a classic probability puzzle known as Bertrands box paradox . The version that I prefer involves pancakes. Suppose I cook three pancakes. The first pancake is burnt on both sides (BB). The second pancake is burnt on only one side (BU). The third pancake is not burnt at all (UU). Now I serve youat random-one of these pancakes, and the side facing up on your plate is burnt. What is the probability that the other side is also burnt?

This is a hard problem, if we rely upon intuition. Most people say one-half, but that is quite wrong. And with no false modesty, my intuition is no better. But I have learned to solve these problems by cold, hard, ruthless application of conditional probability. Theres no need to be clever when you can be ruthless.

So lets get ruthless. Applying conditional probability means using what we do know to refine our knowledge about what we wish to know. In other words:

Pr ( want to know | already know )

In this case, we know the up side is burnt. We want to know whether or not the down side is burnt. The definition of conditional probability tells us: