I am asking a question that might be very very stupid but after nearly
2 weeks of searching for an answer I am still not clear what to do.
here is the deal: I am a CS grad, with very topological understanding
of the bayesian framework. In one of my robotics classes I was
introduced to the recursive bayesian update about a paritcular
hypothesis i.e. p(door open|z) where z is a sensor reading whose p(z|
open) and p(z| not open) are known as probabilities (not as
distributions, If you can explain that case, I would love to talk
about it but lets keep it simple first). Multiple readings of this
sensor will allow us to increase the probability of p(door open) if it
really is open using the posterior of one update as the prior for the
next.

My issue is how to make a decision? In case my only hypothesis is that H_0: door is open, how can I make a decision.

Reading several books/articles/ papers on bayesian stats, one thing that I am sorts of inclined to do is the following: define a negative hypothesis say H_1:door is not open, and update both P(door open) and P(door not open) for every measurement z received from the sensor. Then after say 10 readings when I have to make a decision whether the door is open (and I can go through it) or that the door is not open, I compare P(H_1) and P(H_0). Whomever has higher probability is the hypothesis i accept. Is that a correct or accepted way of doing this decision? Is it equivalent to simply setting a threshold for P(door open) > 0.5? If not what would be the correct way in this case.

Thank you.

My issue is how to make a decision? In case my only hypothesis is that H_0: door is open, how can I make a decision.

Reading several books/articles/ papers on bayesian stats, one thing that I am sorts of inclined to do is the following: define a negative hypothesis say H_1:door is not open, and update both P(door open) and P(door not open) for every measurement z received from the sensor. Then after say 10 readings when I have to make a decision whether the door is open (and I can go through it) or that the door is not open, I compare P(H_1) and P(H_0). Whomever has higher probability is the hypothesis i accept. Is that a correct or accepted way of doing this decision? Is it equivalent to simply setting a threshold for P(door open) > 0.5? If not what would be the correct way in this case.

Thank you.