#How to get to g(x) = ln ( P(x|ω˅1) / P(x|ω˅2) ) + ln ( P(ω˅1) / P(ω˅2) ) ?

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signal escarp
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I can't get through the last formula of https://inf1421.teluq.ca/files/2021/10/INF1421-Module2-Bayes-Nov2022.pdf , which title is translated to Bayes decision theory, the larger of the attached with no hand drawing with a translation underneath. The best I come up with is from page 10, with hand drawing, but then I can't get anywhere near what's on the last line from that.

Would you kindly explain how to get to g(x) = ln ( P(x|ω˅1) / P(x|ω˅2) ) + ln ( P(ω˅1) / P(ω˅2) ) ?

coarse notchBOT
midnight vale
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