Re: Bayesian inference

On Apr 23, 9:43 pm, Affan <int...@xxxxxxxxx> wrote:

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.

Hmm, temporal dependence is always a lot of fun ....

one thing that I am sorts of inclined to do is the following:
define a negative hypothesis say H_1:door is not open,

(1) Your vocabulary here suggests that you have not yet
successfully forgotten the useless significance testing
stuff you were taught in undergrad stats classes.
You'll need to try harder.

(2) A complication you might not want to handle yet:
If the sensor reading is an analog signal (e.g. sonar)
you might want to model the door state as a continuous
variable (i.e. degree of opening) instead of open/closed.

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.

The right way to make the decision is to assess the
payoffs for different outcomes (rewards for correct
statements, penalties for incorrect statements) and
then choose the action which minimizes expected penalty,
taking the expectation with respect to the computed
posterior distributions.

A useful reference for you is "Making Hard Decisions"
by Robert Clemen.

You can also take a look at Chapter 6 of my dissertation
which is linked from: http://riso.sourceforge.net

HTH

Robert Dodier
.