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The probability of a 185 foot yacht named Bayseian sinking at anchor in some freak combination of circumstances ? I think some quantum entanglement double slit craziness had to happen .

10:43 this is essentially the total probability theorem in a continuous probability density function, for discrete probability functions, it should use summation.

I think in some ways the Bayesian method for testing vaccines make sense, it is a typical way to say the probability of getting covid given they have taken the vaccine is often used as a metric of how effective the vaccine instead of the probability of getting covid.

I have learned both ways in uni, it is interesting

It's χ not kai you god damned Statians.

far too many (hyper-)parameters to work IRL. overfitting nightmare.

What about chi Square goodness of fit

At 4:08, you say A is the prior probability of watching this video. Shouldn't that be the prior of subscribing instead?

How do you choose between using 2 sampled t-test and chi squared test? Are there any examples where one would be suitable and one wouldn't?

I liked this video. I just would have felt very confused by what "expected" means in this context had I not already known it. I think that a good place to quickly explain it would have been when you were explaining why a 2x2 table has one degree of freedom. On the other hand it might get someone still confused to research it more themselves. On the other other hand, I am not sure where they should go to find something like that out, as most resources are not easy for a beginner to approach for math.

Awesome content! You should definitely do a video about survival analysis

It would ‘ve been great if you had shown how the expected frequencies under the independence assumption are calculated.

One of my favorite channels thanks a lot.

I came here for the math. Disappoint.

This is a great video, but I'd like to make two comments for everybody: - "Chi Squared test" is an awful name, because there are many, many different statistical tests that have Chi-squared(n) as its null-distribution. As a group, let's all try to phase out the use of this terminology. - The test presented in this video is increasingly replaced by the G-test. The test statistic in this video is an asymptotic approximation of the G-test statistic. The asymptotic distribution of the G-test is Chi-squared (which comes back to the first point).

you have no idea how long I've waited for this

The degree of freedom for the same test statistics for bigger contingency tables with I rows and J columns should be (I-1)×(J-1), for those wondering

Just one question At the end when the p value is less than 5% we fail to reject the null hypothesis. Means our drug is not effective. Right?

😩😩😩 10/10 training without even having to apply to the job

Thanks!

best youtuber

Interesting. As it turns out, my undergrad was heavier into Bayesian probability.

Shit just got real.

Wake up babe. Very Normal uploaded a new video!

whats a stationary distribution

I heard Portland is pretty nice this time of year. I even think they did a show about Portland called Portlandia. Also based on what I've heard the "drinking craft brew" percentage should be increased by roughly 50 points.

How are the population units initialised? You couldn't have every single person you ask have an identical preference, so how does the algorithm decide some people prefer coffee to hiking, wheras aothers prefer hiking to coffee?

I just took a stats course in my Data Science Masters, and this video was a perfect summation of it. We also used R to visualize the distributions, albeit we didn't use ggplot (which looks nicer and is better IMO). Great job!

i dont understand how you can ask your model to have as many pis as yis....hmm...

majority of doctors fail simple questions on bayes theorem. hence the widespread misinterpretation of pcr testing that led to massively overstated case numbers

Don't ask the bartender!

Do you need a background in biology to get a degree in biostats?

I took a class on stochastic models which relied heavily on Bayesian methods. This video is helping me better understand my old notes. Thank you!!

What if i don't know how much the null and alternative distribution differ. Is 0.5 important? Sorry for not understanding

I am still training to prepare to apply in Very Normal Company, this video really helps

This video is fairly difficult because of the maintenance of jargon. I got the sense that the Conjugate or the property of Conjugacy is when the prior distribution has the same shape as the posterior distribution i.e. the new observation doesn't change the prior distribution which means the chosen prior is stable despite the new evidence i.e. you've chosen a particular belief/set of parameters and they fit the data processed so far. I may be wrong on this but that's the gist. Arbitrarily choosing a prior distribution is still a fanciful and mysterious thing given the information of this video.

Thank you 1:31

I hope you got a chance to go to Powell's!

Actally the economics prize is not a Nobel. It's officially the Sveriges Riksbank Prize in Economic Sciences and was not part of the will of Alfred Nobel Just so the economist could sneak their beak in. Curiously enough The Nobel Foundation threatened legal action for a proposed "Michael Nobel Energy Award" " To the Nobel Foundation the 'Dr. Michael Nobel Award' represents a clear misuse of the reputation and goodwill of the Nobel Prize and the associations of integrity and eminence that has been created over time and through the efforts of the Nobel Committees"

Okay idk why but this is so cute hahahaha

its sort of like the way u can break down signals into sin and cos waves u can break samples into well behaved distributions

What does lowercase yi represent?

so good thank u for inspiring students to learn this

There's a cool application of this underlying principle with markov chains in that you can coordinate uncoordinated agents without having to track or communicate with them in real time. Taking your Portland Example, you would get your 100 people stationed at each activity in roughly the correct proportions by giving them a list of the other activities and the probability that they should stay put or go to each other place. They'll all shuffle around each hour, but they'll adhere closely to the target. This has applications for things like, say, a swarm of Drones spelling out a word in the sky. Sure, you could calculate a specific 3d coordinate for each specific drone and transmit that info to each of them 1 by 1 every time you want to change the word. Or you could just broadcast the 'pixel' locations you want the drones to occupy, and how densely filled each pixel is, and let them individually, randomly pick which space to occupy. Especially if you let them constantly cycle their positions, it'll do a good job with the task.

Thank you for a stimulating video on an important statistical method. The hand-written equation appearing on-screen from 0:10 to 0:22 and briefly captioned “Despite how it looks, this is just an average,” is a fundamental building block of thermodynamics. It was at the core of my doctoral dissertation project in polymer physical chemistry in the 1960s. A generation earlier the average geometric properties of a polymer such as its end-to-end distance or radius of gyration (average distance of component atoms from center of mass) were simulated with pencil and paper as a Brownian motion type random walk with a fixed step length representing the distance between atoms along the connected chain, often constrained to a 2- or 3-dimensional spatial lattice. Their mathematical properties were delineated by Einstein and others. However, a Brownian particle can visit the same lattice point indefinitely, while two real atoms cannot occupy the same point in space. This gave rise to the concept of the self-avoiding random walk, a much more difficult mathematical problem. The 1950s saw the proliferation of electronic computers like the Illiac, that made it possible to simulate more realistic average polymer properties with self-avoiding walks, but it was quickly found that the proportion of walks without self-intersections decreased rapidly as the chain length (no. of steps) increased. A few clever biasing techniques involving re-starting a self-intersecting walk improved things slightly but these were only minor tweaks. In the 1960s Moti Lal, a chemist at Unilever Labs in the UK, became aware of Metropolis’s paper and applied it to the polymer problem. However, his available computing power (IBM 360/50) confined his polymers to 30 monomer units on a 2-dimensional spatial lattice. As a graduate student at NYU in 1968 I had access to a Control Data Corp. CDC 6600 Cray Supercomputer at the Courant Institute of Mathematical Sciences (they let us chemists use their facilities). I used the Metropolis-Lal method to generate polymers with free rotation about their backbone bonds, i.e., not restricted to an artificial lattice. I used your hand-written equation with Boltzmann weighting exp(-E/kT) to generate average geometric and thermodynamic properties from thousands of Monte Carlo samples. The Metropolis importance sampling algorithm generated samples from more “important” regions of polymer conformation space so it took fewer samples and far less computer time to get stable averages. I could even generate numerical distributions of end-to-end distances of polymers with sufficient accuracy to discriminate among several distribution functions proposed by theoreticians.

The implementational concept sounds so simple at first, but the underlying math ... 😬💀😱

Thank you so much for making this video! I'm getting ready to apply to some masters programs in Canada but I have a mathematical physics undergrad degree, not a statistics degree. So hearing that you also had a non-statistics degree is encouraging. By the time I apply, I'll have about 5 statistics courses under my belt and I'm hoping that is sufficient.

Wonderful presentation, definitely better than I have been able to do so far. However, (maybe its somewhere down there in the comments). Bayes did it in 1763, not '1963.'

This is brilliant, as a physicist turned pseudo-statistician, the physics-motivated approach of MCMC makes more sense to me than the statistical approach. Fun story: despite bearing his name, Nicholas Metropolis didn't contribute at all to the algorithm. The concept was originally developed by physicist Marshall Rosenbluth at Los Alamos for studying thermonuclear explosions. His wife Arianna Rosenbluth (also a physicist) turned the concept into code. The Rosenbluths are the true pioneers. They struggled with a consistent way to pick an appropriate acceptance function. One day having dinner with Edward Teller and his wife Augusta Teller, they described the problem, the implementation, and the challenge. The Tellers being a couple of physicist+mathematician suggested the obvious choice for a physicist: simply use the Boltzmann distribution. And the first MCMC algorithm was born. What did Metropolis do? He had the keys of the computer lab, and the alphabetical order used for naming authors made his last name the name of the algorithm. I personally call it the Rosenbluth algorithm.

I hate/love you so much for the mid-term thing XD