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I've been writing both the likelihood function and log likelihood function for practice. At least write now, it's just tedious and doesn't bother me much.

shouldn't it be inverse at 48:54 ? If it's a very small interval, the probability of more events must be smaller ?

Agree, bugs are wild, both jumping in the race and those in the end of the video

Thank you ! We prooved this props of infinitely small functions during first semester in math analysis, but it's good to brush up🙂

In your last video what is a practical example that integral(X dp) is calculated using supremum?

Thank you, Professor, for another excellent video. I am eagerly looking forward to your lessons on Product Spaces and Fubini’s Theorem. However, I’m concerned that those videos may be released after the semester ends. Is there any possibility of accessing all the videos up to the topic of Martingales? I wouldn’t mind if they are unedited. I would be extremely grateful for the opportunity.

Thanks for the lecture series! It was really enjoyable and very well explained!

Thank you for uploading this on youtube

Who is this diva and I need her as my professor

Is anyone actively working on the R Project? I'm surprised that someone hasn't just stolen the script commands and made a new program out of them. Like..."Turtle-R" 😂

The RAND corporation was political on both sides; and, after the emergence of the Pentagon Papers, left little else. Pre-2001, Daniel Ellsberg was again politically active, and was a very outspoken opponent of nuclear war. Those same errors were probably apparent, then.

Oops, THIS algorithm. 😂 The MT Dr. Corcoran cited from (1996?) was implemented in the STL library (C++). I'd expect that that version is much faster than any virtual machine implementation; but that would be assumed. So, if it mattered, you could try writing a very fast version using Dr. Corcoran's suggestions about shift registers, probably in assembler (or you'd check the complied code for optimization). I'd recommend trying the C++ version. It's very easy to use; and comes with a complete library of PDF's that run on top of it. I would worry about people's concerns with precision because it's very difficult to keep track of machine error in an algorithm. Also, would there be any dependence of the MT, or even the LCRNG on function composition? Chaotic behavior would be implicit in the "fractal-ness" of either one of these, depending on its fixed point behavior...(correct?) Anyway, the history of this algorithm is very important, and was related to corporate politics of the Cold War Era.

Cool algorithm!

Thanks! And don't be worrying about the video quality! I didn't notice anything so it's probably just perfectionism fucking with you

Truly incredible! Thank you so much for continuing to put in such hard work and sharing it with us for free.

Is this a complete 1 semester course in masure theoretic probability?

Does this course qualify me for the markov processes ?

Great explanation.

Organized, easy to follow, and to the point. I'm appreciating this series so far; thank you for your efforts!

Hmmm. It would appear that variable names like s and f are chosen in textbooks without much consideration for speaking or listening. Would m work instead for simple measurable function?

I really enjoy these videos. Thank you for doing this series. The proof at about ~25:00, I was thinking you could define g(w) = f(w) for w in A and g(w)=0 for w in B\A. Then g<=f and the integral over B of g <= the integral over B of f. But also the integral over A of f = the integral over B of g. I guess that last part needs more rigorous explanation, but i think it works.

A full mersenne twister video would be great to have. How does the algorithm actually work. Apart from theorems about cycle length, are there any provable results about the quality of the Mersenne twister algorithm, or is this only studied empirically. If looking at n-tuples exposes the LCRG to let most points fall on a number of planes in $n$ dimensional space, then is there some other transformation (like the ones we use to transform uniform random variables to other distributions) that might expose the Mersenne twister? Great content.

The rand() function in the C standard library is a famous LCRNG. Toy card games written with it were infamous for shuffling their decks the same way with every start. The notation for remainder (circa four minutes) clashes with the typical congruence notation, where the parentheses applies across the equivalence relation and b is the remainder when a is divided by m: a === b (mod m), also called the modulus of the operation. And the remainder when b is divided by m follows as b mod m, without the parentheses, also called the modulo operation. Another video on the Mersenne Twister would be interesting and I would watch it, but I'm not a student, so maybe come back to it later as you see fit.

This is probably a silly question but as far as I understand, the notation X ~ geom is usually used with the left hand side of the tilde being a random variable. However, we used in this lecture this notation N | X_0 = i ~ geom indicating that the conditional of N on X_0 = i is geometrically distributed. But, the notation troubles be a bit, since N | X_0 = i is not a random variable (it is a symbol that we know its interpretation, yes, but it feels a bit of overloading the tilde, right?). So I was wondering if this is standard (I did see it in other resources) or is there alternative to that that adheres with the usual syntax and symantics of the tilde symbol?

hi thanks so much for your work. i was wondering if you have any more video series planned for the future? Will the measure theory one be continuing?

Are the homework assignments publicly available?

Thanks for the historical information about von Neumann's assistant. I believe Pennsylvania became very politically active after the war; but I don't really know why. It might've been a bigger Jewish academic population. I would worry, also, that Ulaf's "illness" was political.

I wonder what the actual model of nuclear decay is? Nuclear Decay: Given a mass m, of some atomic number Z, and half-life T. What are the sorts of distributions that would be possible to produce the exponential half life curve? Why would there be more than one possibility?

Wow! Fantastic! I've been waiting for this course for so long. Thank you, Prof. Corcoran! Looking forward to your Monte Carlo textbook this year!

any plans to write more books? I'm really enjoying your mathstats book!

Instant like!

It's here! I've been going through MCMC from scratch by Hanada and Matsuura.

JVN <3 one of my favs

Hi professor! One small thing that would be helpful as a self-learner browsing for lectures of this topic would be if you titled the lectures in your playlist so that people unfamiliar with your course have an idea at a glance if these contain the topics they are seeking to learn. (green screen was a fun touch btw)

The audio... Is AI Noise remover the culprit ?

Great Lecture! measure space is very similar to topological space by category theory. Can we convert a measure space to a topological space ? is the sigma field some how related to a topology, please?

Starting 2025 strong with Lesson 25!!

Just out of curiosity, how long do you envision this series lasting for?

What a great course, thank you!

32:34 there is no u2 because we can't go directly from state 3 to state 2 ?

Hi Doctor, Do you have any PDF notes you’re willing to share?

Thanks!

why do we miss w_152 in Q4 ? Ah ok you did it at the end.

i’m so grateful for your videos-they’re seriously the best thing ever! you explain concepts so clearly, and it’s been a huge help for me. thank you for all the effort you put into them. any chance you’ll doing anything on conditional expectation and martingales? would totally be here for it. thanks again, and sending lots of good vibes your way!

Thank you

I'm enjoying this so far. I just started my master's. Fall was my first 3 credit course (Applied Linear Models). My wife passed away in fall of 2023 so I decided to do something to keep busy and keep my mind active. I have no real reason to do this other than that, since I'm in the twilight of my career. However, I could retire and do some consulting with a Master's .

i.m looking forward to seeing a fish of length zero.

I love this series more than I can possibly express. I've painfully completed a time-series modeling and a Bayesian inference class without having this foundational material, and am now rushing to complete it before my Statistical Learning and Deep Learning classes start next year. I bought your book so I could follow along and do the exercises. Would love to know which exercises you assign for each lecture.

Hope your eye is fine now.