trying to answer the question without looking at the answer: if we take temperature readings in the morning, like say sequence of values we are recording.. this is like we are recording one realization out of many possible realisations.. or we can say like we are sampling this random signal from the probability distribution over all possible realisations in morning time.. now we use this realisation to calculate statistical properties of the distribution we sampled from like trying to find say, mean, variance or other parameters.. now can we use these same stat properties in noon to say , ok morning we saw temperatures with variance of 0.2 degrees, so it will be the same in noon.. obviously no, because the probability distribution we modelled is not static, it changed with time and at noon we have a different distribution... so its not stationary (?!) let me continue the video and see if i am right.. now i see that some student said a similar answer..nice (patting myself :P)... i have a question now, what is so "process" about inferrring statistical properties from a stationary distribution? having stationary assumption means once we find some parameters of a distribution, it is kind of fixed and we can do experiments like predictions just like doing normal random variable prediction lol at 27:52
Dear Professor, I want to measure wind speed from 01:00PM-02:00PM. Suppose I have an analogue device which gives continuous measurement (a function). In this, if I treat measuring wind speed from 01:00AM to 02:00AM as my Random experiment, sample space consists of a set of functions(of time). Right? By that i mean out come of random experiment conducted once is a function of time, hence, ensemble is a set of functions. Now, by the definition of random variable, it is a map from sample space to R (real line). Does that mean, I have to define a map (may be some norm of function) to define a random variable?
A realisation in time-series analysis refers to one of the many possible signals (sequences) that a random process can generate. It is sometimes referred to as the sample path. The collection (ensemble) of all realisations is referred to as the random process. So a realisation refers to a sequence (finite- or infinite-length( and not to an observation (at an instant).
@@appliedtime-seriesanalysis7076 Dear Professor, Is it correct to say, in this random process, there are as many random variables as the number of samples in one realization (each described by its own probability distributions)?
@@appliedtime-seriesanalysis7076 Dr. T, What is the significance of making a dataset to 2^n in spectral analysis ? Is it related to distortion at the edges ? Can you give a better picture about this in your words please. Thank you.
best intro to random processes ! Thank you.
Best inroduction to random process on the internet!
Thank you Arnab for your kind comments.
I attended STC only taught by you. Sir. You are amazing teacher. Thank you for teaching
trying to answer the question without looking at the answer:
if we take temperature readings in the morning, like say sequence of values we are recording.. this is like we are recording one realization out of many possible realisations.. or we can say like we are sampling this random signal from the probability distribution over all possible realisations in morning time.. now we use this realisation to calculate statistical properties of the distribution we sampled from like trying to find say, mean, variance or other parameters.. now can we use these same stat properties in noon to say , ok morning we saw temperatures with variance of 0.2 degrees, so it will be the same in noon.. obviously no, because the probability distribution we modelled is not static, it changed with time and at noon we have a different distribution... so its not stationary (?!)
let me continue the video and see if i am right..
now i see that some student said a similar answer..nice (patting myself :P)... i have a question now, what is so "process" about inferrring statistical properties from a stationary distribution? having stationary assumption means once we find some parameters of a distribution, it is kind of fixed and we can do experiments like predictions just like doing normal random variable prediction
lol at 27:52
Dear Professor,
I want to measure wind speed from 01:00PM-02:00PM. Suppose I have an
analogue device which gives continuous measurement (a function). In
this, if I treat measuring wind speed from 01:00AM to 02:00AM as my
Random experiment, sample space consists of a set of functions(of time). Right? By that i mean
out come of random experiment conducted once is a function of time, hence, ensemble is a set of functions. Now, by the
definition of random variable, it is a map from sample space to R (real
line). Does that mean, I have to define a map (may be some norm of
function) to define a random variable?
Just excellent.
Regression&TimeSeries and Probs&Stats taught by my profs were just ridiculously awful.
Thank you for your kind words of appreciation for the lectures.
sir what does it mean by a realization? whether it represents a particular signal or the value of that signal at a particular time instant...
A realisation in time-series analysis refers to one of the many possible signals (sequences) that a random process can generate. It is sometimes referred to as the sample path. The collection (ensemble) of all realisations is referred to as the random process. So a realisation refers to a sequence (finite- or infinite-length( and not to an observation (at an instant).
@@appliedtime-seriesanalysis7076 Dear Professor,
Is it correct to say, in this random process, there are as many random variables as the number of samples in one realization (each described by its own probability distributions)?
great lecture. Professor Tangirala, would it be possible to share the lecture notes?
Thank you for the appreciation. The lecture notes can be downloaded by visiting the website nptel.ac.in and searching for this course.
@@appliedtime-seriesanalysis7076 Dear Sir, i have checked the notes/ slides are not available on above link.
is there any way to get slides ?
you mentioned Kolmogorov !! nice
Any course on stochastic process cannot proceed without referring to Kolmogorov!
@@appliedtime-seriesanalysis7076
Dr. T,
What is the significance of making a dataset to 2^n in spectral analysis ? Is it related to distortion at the edges ? Can you give a better picture about this in your words please. Thank you.