Kalman Filter and Family

Thought: My girl friend hasn't texted since an hour, she must have died!

Hypothesis: She is dead.

Evidence: She hasn't texted since in an hour.

$P(E) = $ Probability of her not texting given that she has died = 100%

$P(H) = $ Probability of suddenly dying = 0.01%

$P(E/-H) = $ Probability of her not texting (regardless of her well being) = 50%

Here in order to find the posterior $P(H/E)$ (Probability of her dying given that she did not text) Bayes theorem is used which can be written as,

$P(H/E) = \frac{P(E)P(H)}{(P(E)+P(H)) + (P(-H)P(E/-H))}$

References

[1] https://www.intechopen.com/books/kalman-filters-theory-for-advanced-applications/kalman-filter-for-moving-object-tracking-performance-analysis-and-filter-design

[2] https://towardsdatascience.com/kalman-filter-interview-bdc39f3e6cf3

[3] https://www.youtube.com/playlist?list=PLX2gX-ftPVXU3oUFNATxGXY90AULiqnWT

[4] http://ais.informatik.uni-freiburg.de/teaching/ws13/mapping/

[5] https://www.youtube.com/playlist?list=PLzCl0zqNaIBuo957MnuuDyNF2YqOYfaDP