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probabilistic_robotics_._book [2016/10/26 22:45] nikolaj |
probabilistic_robotics_._book [2016/10/31 20:03] nikolaj |
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| Sections: | Sections: | ||
| - Introduction: "Probabilistic state estimation algorithms compute //believe distributions// over possible world states" | - Introduction: "Probabilistic state estimation algorithms compute //believe distributions// over possible world states" | ||
| - | - Probability theory basics | + | - Probability theory basics (see also [[Introduction To Modern Bayesian Econometrics]]) |
| - Mathematical world representation | - Mathematical world representation | ||
| - Bayes filters | - Bayes filters | ||
| Line 138: | Line 138: | ||
| This all has more connections to path integrals and stochastic integrals than I previously thought, so, to me, that's great and fun. | This all has more connections to path integrals and stochastic integrals than I previously thought, so, to me, that's great and fun. | ||
| + | |||
| + | == Exercises == | ||
| + | |||
| + | $bel_0(\neg faulty)=\frac{9}{10}$ | ||
| + | |||
| + | $bel_0(faulty)=\frac{1}{10}$ | ||
| + | |||
| + | $ p(z\in [0,1]\,|\, faulty) = 1 $ | ||
| + | |||
| + | $ p(z\notin [0,1]\,|\, faulty) = 0 $ | ||
| + | |||
| + | $ p(z\in [0,1]\,|\, \neg faulty) = \frac{1}{3} $ | ||
| + | |||
| + | $ p(z\notin [0,1]\,|\, \neg faulty) = \frac{2}{3} $ | ||
| + | |||
| + | $ p(faulty \,|\, z\in [0,1]) \proto p(z\in [0,1]\,|\, faulty)\cdot bel_0(faulty)$ | ||
| + | |||
| + | $ N = \sum_{x = faulty, \neg faulty} p(z\in [0,1]\,|\, x)\cdot bel_0(x)$ | ||
| + | |||
| ----- | ----- | ||
