Differences
This shows you the differences between two versions of the page.
Both sides previous revision Previous revision Next revision | Previous revision | ||
probabilistic_robotics_._book [2016/10/26 22:45] nikolaj |
probabilistic_robotics_._book [2016/10/31 20:03] nikolaj |
||
---|---|---|---|
Line 43: | Line 43: | ||
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]) \propto 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)$ | ||
+ | |||
----- | ----- |