statisticalrethinkin..

W L W W W L W L W2.2. COLOMBO’S FIRST BAYESIAN MODEL 39W Ln W= 0W W L W L Wn = 1W L W W W L W L Wn = 2W L W W W L W L Wn = 3confidence plausibilityW L W W W L W L W0 0.5 1 0 0.5 1W 0 Ln probability W= 0W W of L 0.5 proportion water W LwaterW W Lprobability W 1 W W of L water W L Wn = 4n = 50 0.5 1W Lprobability W W W of L water W L Wn = 6plausibilityconfidence plausibilityW L W W W L W WL LWW W W L W WL LWW W W L W L W0W L W0.5W W L1W0L W0.5 1 0 0.5 1n =W 0 0Lprobability n W= 0W W of L water0.5 n = 0W L W W Lprobability W 1n = 0W W of L water W L W W Lprobability W W W of L water W L Wproportion watern = 7n = 8n = 9confidence plausibilityplausibilityplausibility0 0.5 1 0 0.5 1 0 0.5 10 0 0.5probability of water0.5 0 1proportion water probability 10.5 0 1 0.5 1proportion waterproportion waterproportion waterof water probability of waterFIGURE 2.5. How a Bayesian model learns. Each toss of the globe producesan observation of water (W) or land (L). e model’s estimate of the proportionof water on the globe is a plausibility for every possible value. elines and curves in this figure are these collections of plausibilities. In eachplot, a previous plausibilities (dashed curve) are updated in light of the latestobservation to produce a new set of plausibilities (solid curve).In the remaining plots in FIGURE 2.5, the additional samples from the globe are introducedto the model, one at a time. Each dashed curve is just the solid curve from the previousplot, moving le-to-right and top-to-bottom. Every time a “W” is seen, the peak of the plausibilitycurve moves to the right, towards larger values of p. Every time an “L” is seen, itmoves the other direction. e maximum height of the curve increases with each sample,