Okay, so you may remember we were talking about probabilistic reasoning, no decisions

right now, and modeling time. Just like what we did last week or the early last

week and before, talking about models, modeling worlds that have a time component

under uncertainty. And the model I tried to sell to you was something like this.

But the idea is that we model the world in two kinds of random variables, the state

variables that express this state of the world, typically non observable, and the

evidence variables, variables we can actually observe. That's the same as without

the world, right? We had evidence and we wanted to look at the probability of

some state variable given the evidence, given what we see. The only difference is

now we do everything time-slice. We have assumed we have some kind of a time

structure or simplicity we're just basically assuming the natural numbers as

a time structure, which means the model have variables for every time point. And to

make things easy, we assume mark of properties. One means that we have only

finitely many other earlier variables that influence the state variables. That

the observable variables, the evidence variables are only also influenced by

finitely many earlier things. In this case, no earlier influences. We will

mainly be looking at mark of change, where we have a first order mark of

property, meaning it's just basically influenced by the state in front.

That makes life much easier, but we need more. We also, and that's why there are

not only two conditional probability tables here, we also assume we have a

stationary problem, namely that the conditional probability is able for the

transition model that tells us how the world evolves from time to time,

step-to-step is actually stationary, is always the same independent of time.

And we have the sensor, we have the stationarity of the sensor model is the

same thing for the sensor model, right? The arrows between the state variables and

the evidence variables are essentially the sensor model. If we think of the

umbrella as being the sensors for rain possibilities, that's the sensing.

And then we have the transition model, those are the horizontal lines. Both

we assume to be stationary, why? Because otherwise it gets so complicated that

we don't want to do it. And mostly it's easy to make it stationary by

introducing additional state variables, and possibly even additional

evidence variables, right? We did this, where did we go here, where we had the

battery and the battery sensor, which made things easier, made things much

worse, made it easier to assume stationary transitions by having more

influences, right? The non-stationary thing where the battery degrades, we've

kind of factored out into a new state variable. And given that we know what the

battery level is, the holding is stationary, right? We're not actually looking at

that the tires are getting bad and brittle and all of those kind of things. And if

we worry about this, we have a tire age variable which we may even be able to

observe or remember or whatever, okay? So that's kind of the, that's the idea

yeah, those are the processes we look at. And what we want to do is what we call

inference. And we briefly talked about this, there are four major mark of

inference procedures, one is called filtering, which is really asking about the

state of a current state variable, given evidence about the past, right? That's

that's the question of, well, is it actually raining today? Given that I saw

umbrella, no umbrella, umbrella umbrella, umbrella, umbrella, umbrella, umbrella,

umbrella, umbrella, okay? That's the question of filtering. The idea here for the

name is that we filter out the kind of improbable world states in our

belief model. Now, a more ambitious thing is something you also know, which is

prediction, which is exactly what a weather forecast does, right? We have the