this is kinda hard because it’s really dependent on the particular context. One approach that’s been suggested to me is to find the smallest value that’s practically meaningful, i.e. maybe a 20% increase in the response rate. From there you can increase it slightly to define medium and large effects, but at least the small size is pegged to something that would matter in the real world
One major issue with frequentist statistics is that it only considers the total count of events and not their more detailed order. It would consider a coin that did 1000 heads in a row and then 1000 tails to have the same behavior as a regular coin even though that is clearly wrong.
I take offense at that remark against statisticians on their incapacity for violence. I'd have you know, Sir, that statisticians are just as likely to commit violent crimes but have less probability of being caught because they know how not to become a statistic.
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Thanks for your video! I’m by no means a statistician, but I find Bayesian inference to be interesting and valuable in and of itself when you look at statistical learning. When you need to examine and theorize about the process of learning, viewing probability in terms of a belief updating process is extremely useful. So many people get stuck on the “Bayesian stats is subjective”, but if you’re looking at a machine learning model, the point is that over time it can learn and reduce its error over a training process using belief update rules. Is there a frequentist interpretation of machine learning?
The problem with a lot of the current faddish enthusiasm for Bayesian analysis is that soms people are pretending to have very specific, numerical priors that are OBVIOUSLY just pulled out of thin air, at which point, it is unclear what point there is to hearing out the rest of their alleged "analysis".
@very-normal It's no doubt not a fad amongst actual statisticians but it seems to have become a mostly rhetorical gimmick in other fields, including debates over the historicity of religious figures, of all ridiculous things.
I’m coming into this vid from having freshly covered Quantum Mechanics content. I’m still confused if P(A|B) is a similar operation to the inner product, <A|B> 😂💀💀 9:30 Also Bayesian statistics does seem better. Generally in statistics, when it comes to something like sociology & politics, you need to understand how datasets may be biased inherently. Any data set could have an implicit bias based on how it was measured. So if Bayesian statistics incorporates biases in the datasets, it would make a lot more sense. For example in the 2020 election, polls predicted a landslide win for Biden. But the actual election was a lot closer than polls predicted. Thank the heavens Biden won. I understand I’m a Brit and don’t have a horse in the race, but Biden was obviously the more reasonable candidate. However, the externality of covid was overlooked in the polls. And the actual election results were much closer than polls predicted. Republican voters usually disrespected the lockdown, so this meant that democratic voters were more likely to stay inside and answer polling calls. This bias actually DID lead to polls being wildly off at the time. Datasets cannot be trusted on their own. Bias in measurement of data must be taken into account. If Bayesian statistics incorporates biases in how datasets were measured, than that explicitly makes it better. This is frequently how “scientific” racists make arguments. They will show a dataset, and say “x race commits more crime, because x dataset says so” And without cross-referencing other factors like wealth inequality, institutional racism, racist bias in policing, lead poisoning being common in poorer communities, education differences, etc… The statement “x race commits more crime” might be true… in a vacuum. But the actual truth is that “x race” are more heavily policed than “y race”. They might commit more crimes in the data, but they are also more focused by police. Which then creates a bias in the crime statistics. And the actual truth is likely that there is little difference between “x race” & “y race” when it comes to average amount of crimes committed. For example more people belonging to “y race” openly admit to smoking an illegal substance. And the rate that “x race” admit to smoking the same illicit substance, is actually far smaller than “y race” However, even though less people of group “x race” smoke this illicit substance… They get arrested and charged for possession drastically more often by police. Despite the real rate of drug abuse being lower among “x race” When I was a teenager I’d walk by police with class A drugs in my bag. Actively looking suspicious no less 😂 I’m “y race” btw. I never got stopped once. However I have friends from “x race” that would get regularly stopped and searched. Despite the fact that they were straight edge types, and never done an illicit activity in their life 😂 Bias in statistics is important. Anyway imma go back to studying quantum mechanics for now. I’m enjoying the module at university.
Here is a simple egghead detector: engaged in the frequentist-Bayesian feud? yes => egghead detected, not worth my time no => congrats, you have a functioning right hemisphere
I got lost. With the coffee shop exercise, "The probability it receives a 4 or 5 star review". Receive from whom? Does it mean it 'has' received by past customers or is it ideally about the coffee shop's track record at the end of time by its reviewers?
Frequentist approch looks like a neutral pragmatic approach to statistics while the bayesian approach is more flexible and adaptive approach. I'm sure each have their own strengths in different situations. I believe frequentist approach is good as an first value estimation when you know nothing about the data you're studying while bayesian approach allows you to get more precise results as your understanding gets better. I know what I'm saying isn't mathematically rigorous but it mathematics is always derived from "desired properties" and it very much look like these approaches are developed for the desired properties they offer. If you have any objections, let me know I'm very interested in learning more about what you think.
Heyo, I send you a mail some time ago asking for a full rez pic of the "map of statistics" you made, would you mind responding to it? I really wanna hang it up and gradually cross it out :3
There is a mechanics anologue to this: Do you use classical mechanics or include relativistic effects? Depends. If classical is good enough you use that because relativism reduces to classical for simple and slow systems. Frequentist or Bayesian? Same reasoning. Depends. If your problem is described well enough (or perfectly) by frequentist approaches you use that, otheise Bayesian. Because why would you shoot yourself in the foot intentionally just to do it the more complicated way?
So, in short: 1) Governor et al show gross invompetence and broadcast private information of their employees. 2) Governor et al misuse their power in order to cover up their mistakes and silence the witnesses with threats and false accusations. 3) governor et al attempt to influence the legal process they falsely instigated in order to get at an innocent journalist that did them a favor. 4) After being publicly proven wrong, the governor et al persist in their defamation and malicious prosecution of the journalist. ... Hold on. Doesn't this exact playbook resemble the actions of a certain yellow gorilla? It seems the societal rot does spread from the top down.
they're both completely full of shit. real world systems are known to be chaotic in the general case. we cherrypick the hell out of descriptions of things in mathematics to make it not appear this way, but that's wrong. as such the 'outliers' can never be discounted in the way that statistical methods, under any school of statistics, assume they can be. so, if your raw data has 500 data points that sort of cluster around some nice linear or logarithmic or whatever curve, but there are a few outlier points way above and below that curve that you're going to ignore, you don't actually know that the curve describes the system you're measuring and those outliers you're throwing out aren't just as validly part of the correct description of the system. you're making an assumption that your simple-minded continuous function oriented view of mathematics is correct, and forcing that onto the data. but that's a horseshit assumption that we already know is wrong in general. the universe doesn't care about continuous functions, we made that up because we're terrible at math.
To me this seems like the frequentist approach starts with "the experiments is all we know" and therefore you can calculate the probability directly from definition, while bayesian starts with some belief about what we expect and we try to use not just the experiment data but also other knowledge we may have. Wouldn't then bayesian approach with uninformative prior always reproduce (correctly done) frequentist approach? The frequentist approach is based on the implicit assumption that every possibility is equally likely, with bayesian you don't necessarily have that assumption, you may provide it explicitly though.
I still don't understand why the Bayesian method is not susceptible to manipulation and subjectivity. You claim that even if I arbitrarily choose the initial probability, it only makes sense if it is supported by evidence. But where does that evidence come from? From the frequentist method, right? Because if it's from the Bayesian method, then I'm stuck in a circular argument... am I not?
If a past study uses a frequentist method to analyze the data, then a new prior should be formed to reflect what that finding found. For example if a past study found the probability to be 70%, then my new study should probably make the prior on and around 70% more likely. If past studies use a Bayesian analysis, then it’s even easier. The posterior from the past study becomes the prior in the new study. The past data helps inform the prior, not so much the method was frequentist or Bayesian. You’re right that it can be hard and arbitrary to choose a prior, but that’s not a reason to abandon the method in the first place. Classic frequentist methods don’t work well with smaller sample size, yet people are taught to do it anyway
What is probability? : one also needs to compare and contrast that with 'statistics' as either synonyms or distinctions to help with discussion. The frequentist 'close enough for practical purposes' get out also isn't great from an engineering perspective either ('when will the bridge fall down?', 'tracking a radar blip', etc.). I feel that the Bayes formula starts as a 'complicated' (tricky to visualise) formula, and that P(A & B) = P(A|B).P(B) = P(B|A).P(A) is an easier starting point that is just as simple as frequentist counting with the same underlying assumptions (Belief: identically and consistency of the independent events)...
Interesting video. I'm a little bit surprised, though. I'm fairly confident (let's say 0.80) that the uninformative prior for the binomial distribution in a beta distribution with parameters alpha=beta=1/2. I'm using Jeffrey's priors. If there's something I'm missing, I'd like to know.
It doesn’t matter much in this context because there’s so much data that it dominates the posterior. From my perspective, the prior parameters can represent “past” successes and failures, and Beta(1,1) just says we saw only one of both. Having 0.5 of a success doesn’t make as much sense, but it still works in the end. In a paper, we might justify our priors slightly differently
@@very-normal, I concur that the alpha and beta parameters are directly linked to the numbers of successes and failures. Jeffrey 's priors are proportional to the square root of the determinant of Fisher's information matrix, it cannot be as readily interpreted. If other methods for uninformative priors exist, I'm interested. Thanks and thanks for the video!
I have trouble when you say "you can have strange priors, but you're gonna need to justify them with evidence". There is no rigorous method of assessing whether verbal statements such as "I have a heavy prejudice against cafes like mostra" produce valid or invalid priors. If we cannot have rigor in determining the validity of priors presented in a Bayesian analysis, then we are no longer considering logic and are instead considering rhetoric and argumentation, which the frequentists are very right to point out as being a major flaw.
You are offered a pair of loaded dice with an assertion of their 'loading'. Can you believe them, and how much should you pay to test them before buying. Should you start by assuming the dice are unweighted (and the sale is a confidence trick), or that the dice are weighted as offered. PS the con artist (?) did a single dice throw, to show you, before stating the weighting...
A lot of it is hammers vs wrenches. There are plenty of cases where subjective Bayesian isn't appropriate at all. If a drug company did a clinical trial, and proved that their drugs works, based on an analysis that involved their own subjective prior which assumed that the drug works, would you believe them? If someone is trying to prove that climate change affects x, and they use their own prior which assumes that climate change affects x, would you believe them? These examples illustrate that objectivity is sometimes really important (where objectivity means: reducing arbitrary decisions as much as possible...clearly nothing can be completely objective). On the other hand, there are plenty of situations where you should be including subjective prior information. There is also a whole field of statistics which is frequentist Bayesian methods, which to some extent takes the best of both worlds. It uses Bayesian methods, but has the objectivity of frequentism. The real problem in statistics is over-use of maxlik, which is neither frequentist nor Bayesian.
That’s fair, but to clear something up: priors in clinical trials are often done with past studies in mind and with input from field experts, they’re not often made purely from the beliefs and feelings of a sole statistician
good video, i was just confused with the expected table numbers, I thought to caculate this by hand any of the tables you displayed were good. I ended up learning to multiply the margins and applying the Yate's correction and that was enough replicate the result you got from R
In my opinion, these two philosophies can be reconciled by thinking of frequentist statistics as just approaching the problem with a specific prior that is asking "am I X percent confident in posterior outcome A?"
Idealists will not stop to debate which approach is more valid, pragmatists will just use one or the other depending which one fits best in any given situation.
a few years ago I was at a gas station, and a guy was tinkering w/ the engine on his drag car. he couldn't get it to quite reach peak power, so he was adjusting the timing w/ a timing light. I was there about 5 minutes, fueling up my car, and watching him, before I went over to offer help. frustrated, he let me fiddle w/ it a little bit, and when he looked away I turned off the timing light and just tuned it by sound. when he heard how great it was running where I set it he got excited, but then looked at it with the timing light and saw it was off about a degree from where he thought it should be, so he immediately tried to correct it, and the engine went back to the reduced power that he'd been fighting to get rid of that whole time. eventually I just left, letting him be wrong, because it's his car and his problem, not mine. sometimes relying on your tools and expectations too much is why you fail. that's why claiming that science isn't based on dogma is absolutely ludicrous.
I am not a mathematician but I have knowledge on biostatistics. The frequentist approach falls short in regards of rare diseases because: 1 - The definition of rare disease is both arbitrary and normative. (less than 1 in 2 thousand). 2 - Most medics, even doctors, are not sufficiently informed about rare diseases. 3 - Differential diagnosis typically is symptom informed and not revolving on the investigation of prevalence of specific causes. (Example: when you go do the medic with a sore throat the medic doesn't ask for a swab before looking for bacterial plaque. However only a subset of individuals with bacterial infection and sore throat will have bacterial plaque when seeing a doctor.) 4 - All these not only create sub notification, typically above 40%, but also the samples of control and unhealthy individuals will not approach infinity. 5 - Complex-Adaptative Natural Entities often behave like Loaded Dice. Not only in prevalence but in appearance/aspect, aggravating the Item 3 problem. -- Mathematicians need to understand these are not transcendental matters and that tools are instrumental, not necessary. This battle is not a first principles contention.
Bayesan probability still has the same definition as frequentist probability!!! What you are showing is not a "definition" of probability, it is just Bayes' rule, which says NOTHING of P(A), only of P(B|A). The law of large numbers gives the definition of probability, regardless of what field of maths you study. I feel like this was really misrepresented in the video.
Finally I have the vocabulary to describe my philosophical objections to the way that the topic of statistics is often discussed. Probabilities have no place in a world of perfect knowledge; to a hypothetical god, all probabilities would be either 1 or 0, and nothing in between. It is only our ignorance of outcomes that gives meaning to statistics. FWIW the Bayesian approach is what I studied in signal analysis. I just didn't realize that the whole of statistics was bifurcated like this.
It's not actually bifurcated. Bayesian statistics produces useful methods, while frequentist statistics is an aspiration. They are not mutually exclusive. There are plenty of methods that are neither, and plenty of methods that are both.
When I use machine learning algorithm to predict stuff, is it the bayesian way or the frequentist way ? or something between both or does it really depends on the data distribution or depend of the specific machine learning algorithm ?
I think it depends on the model. For prediction, I don’t think the distinction matters all that much. I don’t work a lot with prediction but this has been my experience But for inference, it changes how you do statistics and interpret results
Not a statistician, but I do have a take on this... The Bayesian method relies on priors which hamstrings the whole practical purpose of analysis. Instead of debating results, people instead debate priors. It just shifts the whole thing from one frying pan to the other. The simplistic frequentist approach you described is utterly naive. You completely missed the whole concept of random walk. In practice, the most reliable approach to probability is the non-naive version with a large dataset, or a large set of datasets. Random walk is critical to understand for the frequentist approach to make any sense. For example, imagine flipping a balanced coin 4 times (small example, easier to explain) The naive approach would assume that larger datasets tend towards 50% heads, but this doesn't make sense. The probabilities are: 0% heads -> 1/16 25% heads -> 4/16 50% heads -> 6/16 75% heads -> 4/16 100% heads -> 1/16 It's a bell curve centered at 50%. With large data sets, your chance of getting the expected 50% result is only around 6/16, but your chances of getting either 25% or 75% is 8/16... Which means the naive approach is more likely to give an inaccurate result! Random Walk (results steering away) is a huge topic in itself and definitely needs to be accounted for to rely on the frequentist method.
