The better way to do statistics 

I went out with a Bayesian probabilist. She had a great posterior, but too many priors.

I used to be a frequentist, but then I updated my beliefs.

Half my professors would fight you over this title, the other half would agree with you

Math finance PhD student here. Great video! Just so you know there's a book called "Deep Learning" by Ian Goodfellow et al. It covers Bayesian stats, including MCMCs and other things. It's a great resource and if you wanna know more about this stuff I found it a pretty reasonable read! :)

Wow, nobody has ever explained to me that Bayes' Theorem is derived from p(a|b)p(b) = p(b|a)p(a). That makes way more sense now.

As a PhD student who has used frequentist statistics for as long as I remember, I’d only ever heard gossip and rumours about Bayesian statistics, but your video hooked me from start to finish on such a fascinating subject! Great video!!!

I'm an astrophysicist, and in our field Bayesian statistics is the way. Great and all, except everyone seemingly expected me to know what an MCMC analysis was (it wasn't mentioned anywhere in the refresher lectures at the start of my PhD) despite never having heard of it before I started. This video was a massive help.

As an introduction to Bayes theorem, i think that 3b1b really helped me form an intuition about this statistics using his "bayes ratio" of multiplying your prior by a ratio formed by the likelihood and margin to form the posterior, a new prior

I always get excited when I see one of your uploads; I've been studying heavily about statistics coming from a pure mathematics background, and your videos are always very helpful to build the conceptual foundations that textbooks often obscure in favor of specialized, theoretical language. This has already cleared up several things I didn't quite understand about Bayesian statistics, so thank you (for this and your other videos)! :^)

For some reason I always love when someone says “hi mom” in a video. It’s just wholesome and nice to know they are getting their mom’s support.

Best video i’ve seen on this so far. I like the comparison between the two methods and that fact that you map back the data and parameter variables back to the typical A and B seen in the Baye’s thm definition. edit: I should have phrased this instead as how you connected Baye’s thm to distributions.

Ive studied math as a degree and specialized in statistics and finance. Had rhe same experience with numerous frequentist clases but few bayesian. Ive studied on my own and with a couple of clases that were available to me in grad. Struggled a lot to get the gist of bayesian statistics. This video is s perfect for people with knowledge of frequientist view who wish to then learn bayesian

RU-vid recommended this video to me on my recommended feed. Only about one in twenty videos is any good. The odds were low that someone would make a video worth while, subbed, liked.

I started off with "Yeh, yeh, yeh. Conditional Probability, meh" and ended with "This is how the world works. I must learn this!" Great introduction on why Bayesian Statistics is so important.

Could you please make a video on Generalized Linear Models too? These explanations are soooo helpful.

Its so cool to see MCMCs get some love. The only use I’ve ever seen of it in my field (Psychology) is in Item Response Theory. Awesome video!

I’m currently finishing up my first of many statistic courses and the first month of the course we spent on Bayesian statistics then started focusing more on the frequency side of things. I had no idea these are often were even considered different things. Very cool video!

I used Bayes Theorem for a simple learning model for establishing categories for various phrases that were similar but not exactly the same. Going through thousands of records manually was possible, but using this allowed me to do it in a day with the help of excel and python.

Great video once again! You mentioned MCMC algorithms, to add some details, they work by constructing a regular/ergodic markov chain that has a unique stationary distribution, and we want that stationary distribution to be the target distribution so you can, say, sample it for inference. So the real question is now, how do you design a transition kernel that (if converges) leads an initial vector to the proper stationary distribution you wish to sample after some burn in time. I know this from a probabilistic graphical models perspective where this is used extensively in the form of Gibbs sampling, a special case of Metropolis-Hastings algorithm, and Rao-Blackwellized particles, which sample certain (more complex/loopy) parts of a network then does exact (analytical) inferencing on the rest. Variational inference is a form of inferencing as an optimization problem, such as in mean field approximation where you choose a simpler distribution Q and compute new parameters that gets it close to your actual distribution P. The main way I have learned is to minimize the KL divergence (relative entropy) between Q and P (in that order since KL is not symmetric). If anyone would like to read more Bayesian Reasoning and Machine Learning by David Barber is really good (IIRC variational inference in particular is in chapter 28).

I’m in final year of undergrad, my exams on all these topics in Bayesian inference and constructing credible intervals, Bayes decision rules, minimax and admissibility, and sampling methods such as MCMC/Metropolis Hastings are all on it next week 😭 Thank u for explaining this so simply in a way anyone could understand and enjoy, you really did earn a new subscriber

Great video as the rest of your content. You have a pleasantly simple, intuitive and concise way of presenting the D :) I would very much like for you to dive deeper into the Likelihood in particular, and why it isn't a real PDF even though it can look like one. Cheers!

The cool thing about variational inference is that it converts the problem of computing the intractable integral into a more manageable optimization problem of, with respect to the parameters, optimizing some quantity, the variational free energy! This not only makes the problem often easier (through the more flexible variational graphical model) and more tractable (than e.g. MCMC, etc..), but also enables borrowing insights from mathematical optimization theory, to solve the particular formulation of the problem. By the way, this connection to mathematical optimization is why it is called "variational" inference in the first place, directly connected to calculus of variations! Also, VI has amazing applications in deep learning, namely, variational autoencoders (VAEs), in which it's applied to the latent space for the induced probability distribution, for explaining the data distribution, to become much, much more complex, compared to the classical examples you've shown in this video. For example, diffusion models, that can create those amazing images, can indeed be seen as an instance of VAE! Thank you for this great video! I learned a lot! :)

Loved this! Definitely a subscriber now 🎉 I got confronted with Bayes in a Seminar where we used various Machine learning and deep learning models with the expectation of already knowing all this prior to starting. It led to me having no confidence in the model results even though they outperformed some other approaches.

Amazing video, provides great intuitive understanding!

Very comprehensible video about Bayesian Statistics. I have seen most of your videos and i will recommend it to my students. I am teaching undergraduate basic Statistics and i must stay, ur videos are very well-made. I will put it in my course sites so my students could learn from you as well. ❤

Really great explanation! Love the progression from elementary to more advanced topics. A video on empirical Bayes methods could also be cool :)

Very nice introduction to Bayesian Statistics. What I like about Bayesian Statistics is that one can in many contexts interpret Frequentist methods just as a special case of Bayesian methods with uninformative priors. Also from my experience many people are just Bayesian for pragmatic reasons because for many problems Bayesian methods just work better (frequentists also just discover the importance of shrinkage estimation and the most generalized way to apply shrinkage methods is through Bayesian priors). So I think the philosophical debate between Frequentist and Bayesian methods is somewhat overhyped. The biggest downside of Bayesian methods is their computational cost. Currently working with a model that doesn't even have a computable expression of the Likelihood. MCMC somehow still works (magic) but estimation even for a relatively small model takes several hours

Thanks to your channel i'm considering chosing a biostat MSc. Thanks for explaining and inspiring

Thank you for this!

Another good one. Thanks

Looking forward to more on variational inference, it's really doing my head in

This is a great video on the subject. I really hope you produce more content on Bayesian stats. (maybe dive into PyMC.?) Thank you!

What's funny about this presentation is that it makes it look like the MCMC approach is the one only the deep practitioners use. In reality, non-statisticians who need to use this stuff prefer the MCMC approach because it's *very flexible* and just requires we provide a model and priority and then then an optimizer and the data fight it out in the computation. So in a very real sense, the MCMC approach is easier for non-statisticians and preferred.

Great video, thanks!!

Very helpful! I did get a little lost when trying to think about applications from my experiences.

Cool. Nice overview. This is the most rigorous presentation I've seen. I get Bayesian statistics at an intuitive level, but was curious about how it works mathematically. And there it is.

My university UG finance course has taught me rudimentary statistics but not to the level that I want. Your videos are genuinely amazing self-studying and really bring out the logic in statistic, which textbooks almost never do. Thank you! Please keep it up!

It’s funny because when I was a Physics major two professors in the department argued over whether frequentist or Bayesian Stats were better and would teach their labs differently based on their preference.

when i first saw the concept of bayesian statistics, i thought: "wow, thats dumb, having probabilities only rely on your own belief" but now i see that it is a way of deducing what is likely the real probability and im like"WOW, AMAZING"

thx a lot

I'm still learning frequentist statistics right now in university (first year psychology) so this video still goes way over my head, but it was a really nice overview to get a general idea of the concept of bayesian statistics. All we learned about it is "btw there's a thing called bayesian statistics. ok... let's move on." not kidding.

my good sir . u have my attention and subscription thank you

That was the best explanation for me at least thank a lot keep going

The best book on this is Jayne's "the logic of science"

thanks

Anyone wanting a deep dive into Bayesian stats as it applies to research should consider the book Statistical Rethinking by Richard McElreath. He has also prepared a semester’s worth of lectures available on RU-vid. This is not a quick fix, but essentially a graduate course. It is IMHO quite accessible and doesn’t assume too much in terms of math background.

Currently taking statistical physics, found out some similarities between the two, such as prior probability in Bayesian statistics and priori theorem for each microstates of a system in statistical physics. Interesting to learn about Bayesian statistics from a physics major’s perspective nonetheless

Really cool video and it's easy to follow. I just think it would be better with the frequentist bashing. I think the parts about what frequentists hope they could do or fool themselves into thinking are more a reflection of misinformed /poorly trained frequentists. Ultimately frequentism has itself two main approaches, the Neyman Pearson NHST approach and the Fisher compatibility approach. The search for p

This video was great. As someone who is studying data science on my own online, I'm 32 right now, I had a hard time understanding the Bayesian Theorem for a bit there. I wish I saw this video way earlier, it would have saved me weeks of wrapping my brain around it.

My university teaches both approaches to statistics, but professors and lecturers don't make the distinction known (at least for a bachelor's degree). Bayes' theorem is taught, including how probability densities may differ, how we arrive at the prior belief (or distribution), and the difference in philosophy that affects where Bayesian statistics are often used. Ultimately though, we employ frequentist approaches for theses since it's easier to teach and more common for bachelor's degrees since there's less credibility to design models (i.e., there's little mastery of the field to justify the prior beliefs that will affect the distribution). However, as a civil engineering student, I most often see studies that do not incorporate prior beliefs when modeling real world phenomena that would incredibly affect data interpretation. For instance, studies on flooding, landslides, groundwater flow, the structural health of bridges and concrete buildings, and project management are heavily time-dependent, which makes prior beliefs more significant, but I only encounter risk reports and models that only focus on the current data. I do think that for most studies, frequentist methods are more applicable and would quite suffice given the more theoretical nature of the data and of the methodologies, since most call for single-parameter hypothesis testing. But given the cost of testing materials and tools, I believe the Bayesian approach (incorporating expert knowledge and credible intervals instead of "typical confidence intervals") could be incredibly helpful for handling smaller sample sizes.

haha a brilliant example in the introduction. suscribed.

Fantastic as always, I am starting on the biostatistics track myself!

Love the videos, bit of friendly criticism: when working with a specific example (like 3:35 on), it would help to switch from generic variable names like A and B to something more specific to the example (e.g., S and W in this case). It could even be looser for pedagogical purposes, like replacing A with "Sub" and B with "Watch", though I know not everyone likes that.

What a coincidence I am starting bayesian analysis next week on my Stohastic Probability class😂

First time. Thank you for sharing!

Using p notation sometimes indicates discrete random variables and calculating the marginal would be summation, f would denote probability density functions of continous random variable which the marginal could be calculated by integrating with respect to theta

If my understanding is correct, Bayesians are basically frequentists plus moving average. Frequentists draw conclusions about probabilities based on historic observations and take for granted of its probability. Bayesians subset the historic observation by time-scale, then make predictions for the next time-scale. If the next time-scale probabilities don't match the historic probabilities, update probability.

I began studying Bayesian Statistics last year for developing the tools toward an applied study with Climate Change model data, and the main tool that facilitates the posterior calculation is somewhat recent, called INLA. The theory that gives it structure is pretty dense and difficult, but by far is the easiest to implement and has the least computational costs for the cases that it is applied to. A year deep into this I've found it fascinating how these perspectives open up so much compared to the restrictive nature of frequentist analysis. I recommend the Rethinking Statistics course for all audiences and the Gelman book (Bayesian Data Analysis) for a more mature audience with background in math and Statistics.

Bayesian statistics is common in computer science, I’ve studied it at least twice during my degree.

I don't know much about Bayesian methods beyond the most basic premises of it. However, even at that basic level, I can see the power of it. As an engineer, I was really only taught the fundamentals of frequentist statistics. While it has proven useful to understand that (despite my grumbling at the time I took the class), I could see the problem of assumptions being required in the analysis. Bayesian methods seem to account for that.

Likelihoodists: are we a joke to you?

Did my Masters Degree using the concepts from Bayesian Reliability Analysis applied to radiation carcinogenesis.

The Bayesian method sounds similar to how neural networks update their nodes to new data. There are Bayesian neural networks that implement Bayes theorem which allows them have a confidence percentage instead of just an answer to some presented data.

I had to take bayesian statistics for my machine learning classes. I didn't know know that they aren't as taught in other places, since in Germany they're fairly popular. They are even taught in highschool

Where was this video two weeks ago when i was writing my exam project on HMM's, this shit is too hard to comprehend for a second year bachelor student :( such a great video!!

Baysian statistics provides a way to get a complete picture about the uncertainty in our beliefs that the parameter estimation and hypothesis testing methods from frequentist statistics cannot match.

To understand variational distribution better, perhaps understanding variational autoencoder can be a good start

what I love about bayesian statistics is the way i can get almost whatever results i want by changing the prior

So, I never knew the thing I hated most about statistics was called the frequencist approach, and I always hated p values and null hypothesis, which is my opinion is worthless. I knew of Bayes, but when I went to school, it was never taught. Great video and now I'm subscribed.

It's important to note that priors are not subjective; subjectivity is purely a semantic problem solved by definitive terminology prior to priors priorization 🤓😋😉

Yep, undergrad psych we got told to avoid it or we'd be excommunicated lol in masters of org psych we ended up using BN models and it was amazing

A pdf is a density function not a distribution function. At least in the text books I’ve taught from. I understand this isn’t a big deal, but you made a whole thing.

In the realm of chance where priors dwell, Bayesian paths weave complex spells. With data new, we seek to blend Beliefs of old, to truths we bend. A prior’s whisper, soft and slight, Adjusts with evidence brought to light. Yet minds may twist and turn in vain, To grasp the likelihood's arcane chain. Conjugates and posteriors deep, In nested sums that never sleep. A dance of numbers, hard to track, Where certainty, forever, lacks. Through the haze of dense equations, We seek insight, past frustrations. A Bayesian view, so broad, so vast, Yet understanding, comes not fast.

We used Bayes theorem a lot in discrete math, stats, machine learning, and AI classes. I markov chains in a couple personal programming projects.

Very interesting video. Can u suggest some books, i really want to learn about bayesian statistics.

Hi everyone here! Which book(s) do you recommend as great for learning monte carlo methods with REAL applications? By "real" I mean real-world examples where MCMC is used to solve a problem. Thanks in advance

I am suprised the statisticians don't use Bayesian methods more often. They are the basis for a lot of estimation algorithms. I want to say that it requires to much modeling for the statisticians and to much statistics for the engineers :P.

What a time to be alive!

lmao im taking the required entry level stats/prob class for my comp sci major and this was all our last test was about, good to know that me being super confused was normal.

Isn't it interesting that P(A|B) is directly proportional to P(B|A)? This seems to imply that when one finds a sequence running one direction, they are likely to also find it running in the opposite direction. Everything is an oscillator.

So I should frequently use Bayesian statistics? 🤔

I still dont quite follow, does the prior significantly affect the results? if so, what qualifies a good guess? is it how close it is to the posterior distribution?, also what kinda data is good to use in bayesian statistics? I often work with rats so data hardly achieves double digits, but the quality of it is really good since there is little noise in it, is that type of data fit for bayesian methods?, are there "equivalents" of frequentist statistic tests in bayesian statistics? like test that do the same function of a t students or anova?, I have a lot of questions and they are kinda hard to answer by reading because in my bachelor degree I only recieved basic training in biostatistics.

Aspiring Biostatistician here, my target school has some current PhD students specializing in Bayesian inference so I came here to learn what I might be in for. A part of me worries that specializing in Bayesian techniques could downsize my potential job pool, is there any validity to this concern?

are bayesian just a generalization of frequentist approach where conclusions will match for bayesian and frequentist methodologies if you choose a completely uninformative prior?

Am I correct that frequentist just set P(θ) = 1, which probably also makes the integral easy?

Can you recommend me a good book for learning bayesian statistics? I am a master degree student in statistics and I have done an exam in Bayesian statistics and other exams about markov chains and also computational statistics.

How do you read the notation in min 7:14? In which you have the estimate through MLE, the true parameter over an arrow and the parameter set

Bayesian stats is cool in theory but I’ve never found anything on how to deal with cofounders with it. Do they just deal with univariate data?

Updating my priors right now 🤖

This video could be a nice kick-off to a series where you explain each of the layers and the related methods. As is, it is too packed for me. The assumptions and limitations of the methods would need explanation, as to my experience this is where even Profs get sloppy.

I clearly missed something ... if P(D) is just a number, and we know that the posterior must be normalized over some range of theta, then isn't P(D) just the normalization constant?

Portable Document Format. After ten years, I still have no idea of how to do this. I suppose that I need to take a class. Unless I have no real use for it

I think Reverend Bayes came a little before 1963. Still a great video!

10:40 - Animal Crossing background music :O

Isn't the "post" in "Bayesian posterior" pronounced like "fence post"? In any case, Bayes published his paper in 1763, not 1963. ;-) Love the videos!

I wonder if Marilyn vos Savant used Bayesian statistics for her infamous solution to the "Monty Hall Problem"? People who disagreed with her solution were probably frequentists. That would include me.

TRIGGERED! Frequentist for life 😤 nice video though, as usual

As head of experimentation at a tech company, we have to disabuse frequentist-only interpretation of A/B test results Turns out once you care about being right and predictive, rather than academically accurate, you have to become Bayesian

baysian vs frequentist is kinda like Newtonian vs Hamiltonian

Very normal is the chad bayesian doge