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Introduction to Modern Statistics

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Re: Introduction to Modern Statistics

#61

Post by begemotz »

epgui wrote: post #53

As much as I appreciate and love all pedagogical endeavours in the field, especially in the form of open texts, I really, really, really dislike this overall approach to teaching introductory statistics. I'm hoping to see, over time, a shift away from ad-hoc null hypothesis testing in favour of linear models (yes, in introductory courses, from the start-- see link below) and Bayesian-by-default approaches. https://li…

I agree about teaching from a unified GLM basis. The 'bayesian-by-default' approach seems to going out on a more tenuous limb, imo.

Re: Introduction to Modern Statistics

#62

Post by JHonaker »

begemotz wrote: post #61
epgui wrote: post #53

As much as I appreciate and love all pedagogical endeavours in the field, especially in the form of open texts, I really, really, really dislike this overall approach to teaching introductory statistics. I'm hoping to see, over time, a shift away from ad-hoc null hypothesis testing in favour of linear models (yes, in introductory courses, from the start-- see link below) and Bayesian-by-default approaches. https://li…

I agree about teaching from a unified GLM basis. The 'bayesian-by-default' approach seems to going out on a more tenuous limb, imo.

It's only appears tenuous because the subjective choices you have to make when using frequentist methods are made for you by the developer of the method.

It's less comfortable to use Bayesian methods because you have to be explicit about your assumptions as the user, which opens your assumptions up for easier inspection. There's also way less specific information implied by priors than most people think. Informative priors should try to make distinctions between something that's reasonable-ish and something that's essentially infinity (take pharmacokinetics for example, the diffusion velocity of a molecule in your blood stream shouldn't have a velocity near the speed of light in a vacuum should it?). They should not be forcing your model to achieve a particular result. Luckily, because of the need to explicitly state them in a Bayesian analysis, it's much easier to determine if they were properly set.

Prior specification is essentially problem domain-informed regularization where you can actually hope to understand if the hyperparameter is going to work or not.

Re: Introduction to Modern Statistics

#63

Post by growingkittens »

ndr wrote: post #47
growingkittens wrote: post #46

Is there a "pre-statistics" book that teaches the thinking skills and concepts needed to understand statistics?

This book seems to start where you need it to start. You don't need much beyond basic calculus. Most suffer from some mental block they got installed at a young age akin those that say "I'm bad at math" because their teacher sucked. Dive in and you won't regret it.

My mental block is a brain injury that went undiagnosed until I was 30. I can't really hold more than two numbers in my head at a time. I struggled through math in school because it was lecture based, and the books were written to accompany a lecture.

I can learn math fairly well if I have the right written material and the right direction. However, I do not retain math skills: without active practice, I revert back to "how do fractions work?"

For example, I did extremely well in a college algebra course that was partially online (combined with Khan Academy to catch up). I could do my tests perfectly in pen, much to the amusement of the assistants. I could make connections and see the implications and applications of the math. Roughly three to six months later, I was back to forgetting fractions.

I can't learn these things over time, but I can learn them all at once. I'm collecting resources for my next math adventure.

Re: Introduction to Modern Statistics

#64

Post by usgroup »

mkl wrote: post #36
usgroup wrote: post #31

Earlier quoted context omitted.

These things are great if they add value for you, but I would be very skeptical of any non-mathematical approach to statistics. I think statistics is only made clear by mathematics, much the same as Physics. And one cannot grasp statistics without being able to understand the maths. I think that still the best way to understand statistics is to start with the mathematical theory and to grind 1000+ textbook problems.

> I think that still the best way to understand statistics is to start with the mathematical theory and to grind 1000+ textbook problems. Are there any books you'd recommend for this approach?

My grind was "Mathematical Statistics with Applications" by Wackerly et al. There are PDF versions if you Google for it. I can't say it was quick, easy or intuitive; but it works.

I also liked "In all Likelihood" by Pawitan for a "likelihoodist" foundational approach.

Re: Introduction to Modern Statistics

#65

Post by 0xDEAFBEAD »

mjburgess wrote: post #30

What's often missing from these introductions is when statistics will not work; and what it even means when it "works". The amount of data needed to tell between two normal is about 30 data points -- between two power-law distributions, >trillion. (And this basically scuppers the central limit theorem, on which a lot of cargo-cult stats is justified). Stats, imv, should be taught simulation-first: code up your hypoth…

>The amount of data needed to tell between two normal is about 30 data points

What are you trying to say here? If there are two normal distributions, both with variance one, one having mean 0 and the other having mean 100, and I get a single sample from one of the distributions, I can guess which distribution it came from with very high confidence. Where did the number 30 come from?

Re: Introduction to Modern Statistics

#66

Post by usgroup »

ImaCake wrote: post #34
usgroup wrote: post #29

Earlier quoted context omitted.

I've had similar thoughts, but I think its more to do with what is in your head at the time you hear about it. I found permutation tests satisfying to learn about because they somehow helped consolidate what I knew from distribution theory. If I didn't know any distribution theory prior, I'm not sure they could have that effect. If you study mathematical statistics, it is not taught as a cookbook. At the elementary l…

I think those short courses would be more effective if they didn't bother with ANOVA and instead taught intro probability and distributions and then jumped straight to regression. ANOVA is just a really specific way of doing a regression. In R, and python::statsmodels you get the answer to (essentially) an ANOVA any time you run an LM or GLM; its the Z-statistic for your whole model. I know there is more nuance to th…

I agree with the sentiment although I'm not sure there is the time for all of it. At least when I took them, probability theory and distribution theory were separate semester long courses, and the former was a prerequisite for the latter.

Re: Introduction to Modern Statistics

#67

Post by brutusborn »

2devnull wrote: post #59
mjburgess wrote: post #37

Earlier quoted context omitted.

The comment is addressed to the informed reader who is the only one with a hope of being persuaded on this point. To teach this, from scratch, I think is fairly easy -- but there's few with any incentive to do it. Many in academia wouldnt know how, and if they did, would discover that much of their research can be shown a priori to not be worthwhile (rather than after a decade of 'debate'). All you really need is to…

“ that much of their research can be shown a priori to not be worthwhile” Bingo. Cargo cult stats all the way down. It’s not just personal interest, it’s the entire field, it’s their colleagues, mentors, and students. Good luck getting somebody to see the light when not just their own income depends on not seeing it, their whole world depends on the “stat recipes” handed down from granny.

I think the egotistical aspect is the most powerful: many researchers have built an identity based on the fact that they “know” something, so to propose better alternatives to their pet theories is tantamount to proposing their life is a lie. To change their mind they need to admit they didn’t “know”.

The better the alternatives, the more fierce the passion with which they will be rejected by the mainstream.

Re: Introduction to Modern Statistics

#68

Post by ndr »

obscurette wrote: post #60
ndr wrote: post #47

Earlier quoted context omitted.

This book seems to start where you need it to start. You don't need much beyond basic calculus. Most suffer from some mental block they got installed at a young age akin those that say "I'm bad at math" because their teacher sucked. Dive in and you won't regret it.

I have been a math teacher and although I can't guarantee that I didn't suck, I can say that most of kids don't develop this attitude because of teachers, but because of their parents. "My mum says that she sucked at math/music/whatever as well, so do I!" is far too common. As a teacher I just didn't have resources to influence this attitude either.

Yes, parents can be horrible too. Unfortunately it's somehow socially acceptable and even worthy of pride in some circles, to be "bad at math". It's seems very rare for someone to openly say "I'm bad at [my native language]" or "writing".

I feel stats is has a somewhat similar effect even among those with math education. Several friends who have a degree in math recoil at the first mention of stats concepts.

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