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.

Is it equivalent to simply setting a threshold for P(door
open) > 0.5?

Yes.

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.

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

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.

On Apr 23, 9:43 pm, Affan <int...@gmail.com> 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

I am using a single frequency acoustic tone detection circuit (whose
threshold is set in hardware and is beyond my algorithm's control). I
can also send that acoustic tone for a fixed duration (say 5ms) and
then have to listen to the channel for echoes. The issue is that not
only can noise in the medium (underwater for my case) cause incorrect
detections, but also there might exists other nodes that
asynchronously send out similar tones for their own calibration. So my
sensor in some since is this binary tone detection circuit which might
be triggered by my own echoes, noise and other nodes calibration
tones...

One last question, given my above description... the independence of
my sensor readings is correct?

Affan wrote:

I am using a single frequency acoustic tone detection circuit (whose
threshold is set in hardware and is beyond my algorithm's control). I
can also send that acoustic tone for a fixed duration (say 5ms) and
then have to listen to the channel for echoes. The issue is that not
only can noise in the medium (underwater for my case) cause incorrect
detections, but also there might exists other nodes that
asynchronously send out similar tones for their own calibration. So my
sensor in some since is this binary tone detection circuit which might
be triggered by my own echoes, noise and other nodes calibration
tones...

One last question, given my above description... the independence of
my sensor readings is correct?

Could a passing marine animal emit sounds that would confuse the sensor?
If so, it seems you could lose sequential independence; the animal
might interfere with two or three consecutive pings but not with those
before or after. Similarly, if water conditions (something like a
thermocline) could interfere, and the interference were transient
(either because conditions changed or because the sensor was moving),
that could again induce sequential dependence.

/Paul

One last question, given my above description... the independence of
my sensor readings is correct?

Could a passing marine animal emit sounds that would confuse the sensor?
If so, it seems you could lose sequential independence; the animal
might interfere with two or three consecutive pings but not with those
before or after. Similarly, if water conditions (something like a
thermocline) could interfere, and the interference were transient
(either because conditions changed or because the sensor was moving),
that could again induce sequential dependence.


I agree, but if we decide based on a large window of inputs, or the
inputs are continuously repeated returning wouldn't these transients
get filtered out?

if not, what is the way of handling it.. remember
that I am not trying provide a closed form solution; this is meant to
be a working implementation and if such sequential dependence can be
dismissed based on some heuristic e.g. taking a window of samples to
make decision, or something else that can be suggested, i would still
be content.

So my sensor in some since is this binary tone detection circuit which
might be triggered by my own echoes, noise and other nodes calibration
tones.

One last question, given my above description... the independence of
my sensor readings is correct?