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bayes_algorithm [2016/10/27 18:07] nikolaj |
bayes_algorithm [2016/10/30 17:43] nikolaj |
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| | @#FF9944: definition | @#FF9944: $\Gamma: (X\to {\mathbb R})\to X\to {\mathbb R}$ | | | @#FF9944: definition | @#FF9944: $\Gamma: (X\to {\mathbb R})\to X\to {\mathbb R}$ | | ||
| | @#FF9944: definition | @#FF9944: $bel_{\mathrm out}[bel_{\mathrm in}](x) := N^*W_z(x)\int_A K_u(x,x')\,bel_{\mathrm in}(x'){\mathrm d}x'$ | | | @#FF9944: definition | @#FF9944: $bel_{\mathrm out}[bel_{\mathrm in}](x) := N^*W_z(x)\int_A K_u(x,x')\,bel_{\mathrm in}(x'){\mathrm d}x'$ | | ||
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| + | >this is the algorithm for the case where all the ingredient have these types. In practice, Coming up with an initial $bel$ is a also part of the task. | ||
| + | >$N^*$ is supposed to be the normalization of the whole term on the right of it - a normalization to the sum/integral of $bel_{\mathrm in}$. In practice, the latter should normalize to $1$. | ||
| ----- | ----- | ||
| === Discussion === | === Discussion === | ||
| - | $N^*$ is supposed to be the normalization of the whole term on the right of it - a normalization to the sum/integral of $bel_{\mathrm in}$. In practice, the latter should normalize to $1$. | ||
| - | |||
| $K_u(x,x')$ ought to capture the propagation, possibly determined by actions $u$. | $K_u(x,x')$ ought to capture the propagation, possibly determined by actions $u$. | ||
| $W_z$ ought to capture a redistribution of believe, due to some observation $z$. | $W_z$ ought to capture a redistribution of believe, due to some observation $z$. | ||
| + | |||
| + | The relation with Bayes rule is discussed in [[Conditional probability ]]. | ||
| == Note == | == Note == | ||
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| [[Function]] | [[Function]] | ||
| === Related === | === Related === | ||
| - | [[Factorial function]] | + | [[Factorial function]], |
| + | [[Conditional probability ]] | ||
