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is on observation theory uh the

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background here is a

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photograph of uh of a

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plaster

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wall

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we might take a look at it and

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all agree and describe it as a brown

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wall

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but looking more closely we see that

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it

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has lots of different tones of wall and

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a lot of texture and

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describing that becomes more

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complicated say and indeed it's uh in

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the deviations from the brown where the

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beauty uh lies and

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we may say that the

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beauty is

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in the eye of the beholder

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ah

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deviate a little bit here i'm the editor

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of uh this publication earth zine it's

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an ieee publication uh and a

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contribution to the intergovernmental

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group on uh earth observation and it

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supports uh the establishment of a

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global earth observing system of systems

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and it's doing so and being designed

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around earth observation for the benefit

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of society and we may

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say well what does this have to do with

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observation theory it's

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in

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uh through observation that we become

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aware

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and this is true for the astronomer

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looking out into

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the universe and discovering new uh

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planetary systems or galaxies and uh for

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the

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monk who

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looks inward and

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discovers

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the divine or

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a mother who uh looks

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washes diligently uh

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after the

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her children um

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now

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this uh presentation deviates uh quite a

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bit from um

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uh presentations but uh the audience is

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significantly different and i imagine

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y'all uh recognize that uh the

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precognites in the audience and so uh

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i'm going to uh

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kind of

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uh into the

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gist of the theory and uh

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uh what leading to the concept of

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ensemble detection and analysis

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and um

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like to get into more uh what the

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interpretation of the underlying

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mathematics is

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pretty interesting

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now how i got into this was uh i

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designed radiometer systems and

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i found that there's not a general

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a single method and what i

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did as part of my dissertation studies

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is develop the methodology using

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measurement uncertainty as a figure of

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merit for

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comparative analysis of radiometer

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designs radiometers are

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the whole reason we

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have to have this fancy calibration

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architecture at the front of the end of

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the system is

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because

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the uh

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system response varies

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varies with time

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and um

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it's this uh temporal variability that

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leads to the non-stationary conundrum

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which is

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described

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take a look at a process at one space

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and time and you get

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one answer and look at it at a different

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place you get a get a different set of

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statistics and

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currently we really don't have a

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very good way of describing that well

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and i thought ran into this problem in

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developing a generalized methodology

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here

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uh you see a radiometer system with gain

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fluctuations and the gain fluctuations

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uh in observing each one of the uh

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temperature references appear

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as uh in each of the time series of the

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different references now what we do in

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radiometry is we apply

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a calibration algorithm f which combines

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the calibration references in making an

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estimate of what

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the brightness temperature is

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and we can

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take a look at what the uncertainty in

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the estimate is by uh and here i i show

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some analysis with the data and i uh the

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brackets here are the uh statistical

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operation

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statistical calculation from the data

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and we see that using a

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two pair algorithm using two pairs of

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calibration measurements to estimate

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what the

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brightness temperature at at some

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different time is and we can slide and

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slide this time across and what we see

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is we get minimum uncertainty at the

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time when

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the

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calibration a local maximum when it's

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right in between a local minimum and we

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can uh

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i've done i showed this for for

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different t1's now what

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enables this uh type of analysis is is

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that

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we have a collection of ensemble data

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which uh uh describes the the which has

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the fluctuations of the receiver

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the challenge challenges is in in

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modeling this okay taking um you know

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calculating what the uh uncertainty is

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from from uh

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a model and uh as

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leave it here now

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calibration has a few different things

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does a few different things for us one

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is it provides scale which we can assign

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value another is is that

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from that we are able to

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distinguish uh say a signal from

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background noise another thing that

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calibration does is it provides the

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means of comparing measurements made at

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one place in time say here in boulder

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yesterday to a measurement made tomorrow

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in france and it's these properties of

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calibration that make it very useful to

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studying and characterizing

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non-stationary prop

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non-stationary processes

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and there's lots of different uh

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approaches and uh to modeling and

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characterizing non-stationary processes

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that have been say fashionable over the

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years and

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more recently uh there's uh work by

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norton long and all uh empirical mode

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decomposition and

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uh all these have uh something in common

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is that they uh they're based upon a

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single realization of the data

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and

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analysis as a new method that

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complements these

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previous things

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looking more closely at at this

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stochastic process theory is kind of an

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outgrowth of probability theory where uh

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a

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ensemble set of

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time series well all these kind of

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exist

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say simultaneously and what we get

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from a single realization is a selection

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of one of these and this uh treatment of

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mathematics

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is has

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led to the auto correlation function and

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lots of uh

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from which we can

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calculate what the what the variance of

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the process is

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but

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there's really really a problem and this

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has been been a stigma in applying

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uh

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theory more broadly in in

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uh science and engineering practices and

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and that is that the uh ensemble

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statistics that that we get don't really

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match uh the

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measurements we get whenever we change

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the observation interval and

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that can be

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part of the problem i see is that the

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ensemble changes

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you know processes uh

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processes die and are born

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and

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alternatively

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and this kind of com has come out of uh

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the

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treatment of uh

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the uncertainty where uh

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i

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process um

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in estimating the mean value at one

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point in time from a measurement made at

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a different point in time

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and uh this

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uh and so during an uh kind of uh treat

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instead of the the process is

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non-stationary treated as a as an array

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of uh random events with each event

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having a conditional probability

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density function

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and

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the

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each random variable has

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the

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applied

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depends upon how how it's used and

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this

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kind of formulations kind of led me to

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realize that hey this has a

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connection with say conscious

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phenomena or or the experience that how

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an event in time

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be interpreted in two completely

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different ways

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from different points of time and it's

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about this uh when i was looking at this

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that a a friend of mine pointed me to

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the work of

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robert

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john and brenda dunn and i

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realized that you know what they were

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doing with

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the field regs and the random event

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generators it was was based upon noise

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measurements

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using a circuit much like

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we use in radiometry kind of like a

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dickey radiometer circuit

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so and that's how i came about

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being here and i certainly appreciate uh

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been pointing me in this direction

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here's a few uncertainty models uh kind

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of different for a stationary process uh

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the uncertainty is independent really of

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of the temporal separation between pc

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and ta here for a

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non-station uncertainty

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the uncertainty is minimum at the same

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time and increases uh

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way and we can have local stationary

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local non-stationary and

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here's an asymmetric uncertain certainty

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and these are uh kind of models that

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i've i've used in in my data this is a

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parametric fit to uh some radiometer

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data that i showed previously saying

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data and i'm using a four parameter

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model here

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to to

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characterize the

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the uh to a linear fit for the

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uncertainty and a linear fit to the

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correlation

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and

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what's interesting is that you know uh

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there's

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features in the this data uh

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but uh you see uh there's a core

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correlation at

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aspect when uh the the two pairs of

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calibration measurements are close in in

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uh time uh they produce a higher

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uncertainty whenever the uh

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calibration algorithm is

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extrapolated then uh as you separate so

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that kind of indicates another

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interesting feature as you take a look

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that uh if

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on on this side the

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uh uncertainty is is higher than what

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the model is and on this side it's

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lower you can see that in this red curve

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here well

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that indicates that the

300
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for this data set the

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calibration has greater uncertainty in

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uh estimating a future value than in in

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the past

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the

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in in this data set

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and

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using uh a one parameter asymmetry term

308
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and in my model i can uh uh correct for

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that and and get a really pretty nice

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fit and you can see that indeed there's

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there's an asymmetry in the model

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well

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two minutes okay

314
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uh

315
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has been applied to radiometry but it is

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any generalized uh too

317
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the math is very

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generalized and so

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the thought is to uh use calibrated

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noise uh in characterizing

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non-stationary forcing functions in

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uh what i call

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ensemble detection and analysis

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here

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applications one of the really neat

326
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things about this is that there are a

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wide number of

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applications that

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from instrument system analysis and

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sampling strategy optimization and

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in information processing which

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is uh quite useful i mean

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this is uh

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shows how a model can be uh

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used in uh say

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optimizing sampling strategy uh nasa be

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interested in this and

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determining well with uh one satellite

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we can sample uh

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with such a frequency and get get this

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type of uncertainty this level of

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uncertainty but if we use three

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satellites we can increase the sampling

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frequency and and uh improve the

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uncertainty and the measurement

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and has uh application to to climate

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modeling as i show uh here it's uh

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interesting there's a uh other

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uh works are being published that i've

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seen in in the

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past few few years

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of

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finish up here with the

354
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interpretation of the mathematics what

355
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the mathematics

356
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means

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is

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that

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the time space comprise an array of

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events across which a stochastic wave

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propagates

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and

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the the present is characterized by

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minimum uncertainty uh

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and uh that

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time points in the direction of greater

367
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uncertainty if uh the past is equally

368
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uncertain

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as the future the the process would be

370
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uh stationary

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um and uh observation uh the outcome

372
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depends upon this perspective and uh as

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as well as uh the

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uh

375
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the the the values that we assign to our

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references and the way we use those

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references and

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and assigning value to uh our outcomes

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that we observe uh the

380
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character

381
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of this stochastic wave uh and uh the uh

382
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value of uncertainty depends upon uh the

383
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waiting of uh the future and and and

384
00:16:15,670 --> 00:16:12,880
past and uh and finally ensemble

385
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detection provides a means of uh

386
00:16:21,189 --> 00:16:18,720
detecting this uh stochastic wave

387
00:16:22,949 --> 00:16:21,199
you know i may uh stop there got a

388
00:16:32,230 --> 00:16:22,959
couple more but i'd certainly like to

389
00:16:34,550 --> 00:16:33,189
are there

390
00:16:36,550 --> 00:16:34,560
any questions

391
00:16:38,470 --> 00:16:36,560
yes i have a question uh thank you very

392
00:16:40,710 --> 00:16:38,480
much you've given me a lot to think

393
00:16:43,269 --> 00:16:40,720
about years ago i did a lot of signal

394
00:16:45,030 --> 00:16:43,279
analysis work and i'm wondering if

395
00:16:47,749 --> 00:16:45,040
you probably said it i didn't quite

396
00:16:49,910 --> 00:16:47,759
grasp it the connection between pattern

397
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adaptive pattern recognition as used in

398
00:16:52,949 --> 00:16:51,519
signal processing and what you're

399
00:16:55,110 --> 00:16:52,959
talking about here

400
00:16:59,509 --> 00:16:55,120
how do those correlate

401
00:17:02,310 --> 00:17:00,310
this

402
00:17:05,669 --> 00:17:02,320
technique ensemble detection and

403
00:17:07,029 --> 00:17:05,679
analysis certainly has uh application to

404
00:17:15,669 --> 00:17:07,039
uh

405
00:17:27,350 --> 00:17:15,679
i

406
00:17:28,390 --> 00:17:27,360
between

407
00:17:31,830 --> 00:17:28,400
um

408
00:17:35,590 --> 00:17:31,840
sampled events uh and in terms of uh its

409
00:17:40,470 --> 00:17:35,600
utilization one is coming up with a uh

410
00:17:45,110 --> 00:17:42,950
evaluating calculating what a a

411
00:17:47,990 --> 00:17:45,120
stochastic parametric model which

412
00:17:50,630 --> 00:17:48,000
describes that data and then uh take new

413
00:17:53,430 --> 00:17:50,640
data coming in and and compare

414
00:17:57,590 --> 00:17:53,440
the the data and either we detect a

415
00:18:00,710 --> 00:17:57,600
change or uh uh adapt that the model

416
00:18:03,110 --> 00:18:00,720
kind of like that

417
00:18:04,390 --> 00:18:03,120
so perhaps following from that question

418
00:18:06,230 --> 00:18:04,400
uh

419
00:18:09,029 --> 00:18:06,240
it would be helpful to me

420
00:18:14,549 --> 00:18:09,039
can you give a specific example

421
00:18:17,830 --> 00:18:14,559
of say a random event generator output

422
00:18:20,549 --> 00:18:17,840
something like from the pair lab

423
00:18:22,789 --> 00:18:20,559
how you would analyze it what would you

424
00:18:26,070 --> 00:18:22,799
take what would you do with that data

425
00:18:27,350 --> 00:18:26,080
and how would that help in understanding

426
00:18:31,750 --> 00:18:27,360
uh

427
00:18:32,789 --> 00:18:31,760
effects

428
00:18:36,070 --> 00:18:32,799
yeah

429
00:18:38,710 --> 00:18:36,080
that's an interesting question and i uh

430
00:18:42,150 --> 00:18:38,720
have some thoughts about how to

431
00:18:46,390 --> 00:18:42,160
kind of uh adapt the the regs to uh

432
00:18:47,270 --> 00:18:46,400
using this technique really it's uh

433
00:18:52,870 --> 00:18:47,280
in

434
00:18:57,830 --> 00:18:52,880
series of random events from say a

435
00:19:00,070 --> 00:18:57,840
a single noise source use uh

436
00:19:01,909 --> 00:19:00,080
and having that be the the

437
00:19:04,549 --> 00:19:01,919
the control signal that we're looking at

438
00:19:07,669 --> 00:19:04,559
as you know how it goes up and goes down

439
00:19:10,630 --> 00:19:07,679
and uh the role uh

440
00:19:13,350 --> 00:19:10,640
have the say the control signal that is

441
00:19:16,150 --> 00:19:13,360
being analyzed be the

442
00:19:19,510 --> 00:19:17,430
gain of the

443
00:19:20,470 --> 00:19:19,520
of the receiver say

444
00:19:21,270 --> 00:19:20,480
and

445
00:19:23,270 --> 00:19:21,280
use

446
00:19:27,830 --> 00:19:23,280
calibrated noise

447
00:19:31,669 --> 00:19:28,789
to

448
00:19:34,549 --> 00:19:31,679
detect changes in that game

449
00:19:36,150 --> 00:19:34,559
that would allow

450
00:19:38,470 --> 00:19:36,160
more

451
00:19:41,830 --> 00:19:38,480
temporal processing of the data say

452
00:19:46,310 --> 00:19:41,840
being able to apply uh a calibration

453
00:19:51,190 --> 00:19:48,630
fluctuations that are being seen during

454
00:19:53,510 --> 00:19:51,200
say an event of interest

455
00:19:55,590 --> 00:19:53,520
as you may know the roger nelson's

456
00:19:57,750 --> 00:19:55,600
global consciousness project has all of

457
00:19:59,830 --> 00:19:57,760
its data available online

458
00:20:02,070 --> 00:19:59,840
and it may be really interesting for

459
00:20:02,870 --> 00:20:02,080
someone with your perspective to take a

460
00:20:05,750 --> 00:20:02,880
look

461
00:20:09,110 --> 00:20:05,760
at that data and just see if you can

462
00:20:11,270 --> 00:20:09,120
glean uh different information from it

463
00:20:15,510 --> 00:20:11,280
yeah

464
00:20:17,990 --> 00:20:15,520
certainly i i'm uh interested in in uh

465
00:20:21,350 --> 00:20:19,510
it's

466
00:20:24,310 --> 00:20:21,360
you know i um

467
00:20:27,669 --> 00:20:24,320
um see uh

468
00:20:30,710 --> 00:20:27,679
advantages in kind of uh adapting the

469
00:20:34,470 --> 00:20:30,720
design where instead of using like a

470
00:20:39,590 --> 00:20:34,480
a single uh random event generator

471
00:20:43,350 --> 00:20:39,600
uh albeit um the eggs are discrete but

472
00:20:45,750 --> 00:20:43,360
uh coupling them together and using uh

473
00:20:48,710 --> 00:20:45,760
a random event generator with uh

474
00:20:52,230 --> 00:20:48,720
calibrated noise with and and when i say

475
00:20:53,830 --> 00:20:52,240
calibrated noisy uh the the noise has

476
00:20:56,549 --> 00:20:53,840
and uh

477
00:21:00,470 --> 00:20:56,559
has different noise power levels to it

478
00:21:03,270 --> 00:21:00,480
which have an a priori uh

479
00:21:05,830 --> 00:21:03,280
statistical relationship from which you

480
00:21:06,870 --> 00:21:05,840
can detect deviations from