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Continous Observation with HMM & Gaussian

0

$begingroup$

I've read that for HMMs with a discrete output we assign an emission probability $b_j(o_t)$ of emitting symbol $o_t$ when in state $S_j$. What I don't understand is why, in the case of continous outputs, we can set $b_j(o_t)$ to be a mixture of probability density functions (i.e. Gaussians). To my knowledge a PDF does not directly represent probabilites.

probability density-function hidden-markov-models

share|cite|improve this question

edited Mar 30 at 21:57

krueger_fl

asked Mar 30 at 20:44

krueger_flkrueger_fl

12

$endgroup$

add a comment | 

0

$begingroup$

I've read that for HMMs with a discrete output we assign an emission probability $b_j(o_t)$ of emitting symbol $o_t$ when in state $S_j$. What I don't understand is why, in the case of continous outputs, we can set $b_j(o_t)$ to be a mixture of probability density functions (i.e. Gaussians). To my knowledge a PDF does not directly represent probabilites.

probability density-function hidden-markov-models

share|cite|improve this question

edited Mar 30 at 21:57

krueger_fl

asked Mar 30 at 20:44

krueger_flkrueger_fl

12

$endgroup$

add a comment | 

$begingroup$

I've read that for HMMs with a discrete output we assign an emission probability $b_j(o_t)$ of emitting symbol $o_t$ when in state $S_j$. What I don't understand is why, in the case of continous outputs, we can set $b_j(o_t)$ to be a mixture of probability density functions (i.e. Gaussians). To my knowledge a PDF does not directly represent probabilites.

probability density-function hidden-markov-models

share|cite|improve this question

edited Mar 30 at 21:57

krueger_fl

asked Mar 30 at 20:44

krueger_flkrueger_fl

12

$endgroup$

share|cite|improve this question

edited Mar 30 at 21:57

krueger_fl

asked Mar 30 at 20:44

krueger_flkrueger_fl

12

share|cite|improve this question

edited Mar 30 at 21:57

krueger_fl

asked Mar 30 at 20:44

krueger_flkrueger_fl

12

asked Mar 30 at 20:44

krueger_flkrueger_fl

12

asked Mar 30 at 20:44

krueger_flkrueger_fl

12