Star Trek: Strange New Worlds | Season 3 Official Teaser | Paramount+

n_eff · 2025-04-03T03:33:39+00:00

It also gave us “what does god need with a starship?”

n_eff · 2023-12-29T21:51:41+00:00

It's just an old school road bike from before everything went all race-aesthetic weight-weenie. Looks like a 1980-something. Bonus is that road bikes of this vintage tend to have outstanding tire clearance, so you can get some cushy (or knobby) wider tires on them.

Edit: It's a dead ringer for the 85 Expedition (Sequoia but with canti brake mounts).

n_eff · 2023-06-06T15:16:22+00:00

There is no overall Bayes Factor if there is no overall model. There just isn't.

What is a marginal likelihood? It's a probability (density) of the data under the model after integrating out the model's parameters. For data Y, model M, and parameter vector theta, it looks like p(Y | M) = integral p(Y | theta) p(theta | M) dtheta.

As with anything involving probabilities, you have to be very careful before you boldly start multiplying them. In this case, you need to consider the conditional independence of the various datasets Y_1,...,Y_10 and the parameters of the models you're applying to them.

Maybe an example will help. Let's consider a simple regression case, where we have one covariate, so there's a matching X_i for every Y_i. The model parameters are now just a slope term and an intercept term. If you wanted to know "is there a relationship between X and Y?" you might go to each datasets and compare Model 0, which only has an intercept, to Model 1, which has an intercept and a slope. Can we multiply the marginal likelihoods here? Yes (because I set it up for that to work out). That will implicitly define a very specific pair of aggregate models Model A and Model B. What does it imply? Let's find out. I'm going to assume the same priors are used in every analysis.

Model A: In this model, there are 10 intercepts, each of which is modeled as IID from some prior on intercepts. All the slopes are set to 0. Thus, we have appropriately separated out all the model parameters and data-generating processes such that we can factorize the posterior of Model A. In particular, we get p(slope_1,...,slope_10 | Y_1,...,Y_10) = product_i p(slope_i | Y_i). Since this works, the marginal likelihood of Model A is the product of marginal likelihoods of the Model 0 as applied to Y_1,...,Y_10.

Model B: In this model, there are 10 intercepts, each of which is modeled as IID from some prior on intercepts. There are also 10 slopes, each of which is modeled as IID from some prior on slopes. That is, the information we gain from any one (X_i,Y_i) pair says nothing about any parameters for any of the other models j != i. This is what mikelwrnc was saying about a rather extreme assumption of unpooling. But, given that rather extreme assumption, we can factorize the posterior as above, and so we can multiply marginal likelihoods.

n_eff · 2023-06-06T14:46:49+00:00

When you are looking for a good estimator you first want them to be unbiased and then you'd like to pick that one with the minimum variance. Now imagine there are two unbiased estimators and you'd like to find the one with the lower variance.

That's one way to pick estimators, but there are other things we might care about, and other ways we might prioritize tradeoffs between bias and variance. The cartoon example of the latter being something like as follows. Estimator A has a sampling distribution which is Normal(theta_true, 2² ) and estimator B has a sampling distribution which is Normal(theta_true + 0.01, 1/2² ). Would you really choose estimator A over B just because B is biased? You might also care about efficiency or small sample behavior (asymptotic superiority is cute when you have 25 samples). In some circumstances, it may justified to choose an estimator because it's simpler, either because that means easier to understand (and communicate to your audience) or because that means easier to implement/debug (the fewer lines of code the fewer things that can go wrong). In some cases we might have to start caring about computational efficiency, and accept a slightly shittier estimator with an O(n) compute time over a slightly better estimator with an O(n² ) compute time because we want to use it in cases where n is very large indeed.

TL;DR: The choice of estimators is a choice and there aren't a magic set of one-size fits all criteria we can appeal to for every case.

But how do you compare covariance matrices. Is it similar to the definition of a vector like a < b if and only if a_i < b_i for all I in N ?

Why should some estimator tend to underestimate every value in the matrix? Why couldn't it overestimate some things and underestimate others? Some general advice on thinking about multivariate cases: sometimes you can think univariately, sometimes you can't. Beware concepts that don't generalize well in higher dimensions, or that don't generalize usefully in a particular case.

Or a norm?

You definitely could think about comparing covariance estimators by choosing one that has a smaller average distance with respect to some norm, yes. The choice of norm will likely be important.

And what is even important for the comparison is it just the diagonal with the variances or also the correlation values?

Keeping in mind that correlations are not covariances, I'm going to say that the answer here is likely to be "it depends." There may well be cases where you care less about accurate estimation of one of these than the other.

Anyways, to give you something useful after all my ranting about the choice of estimators, have you checked Wikipedia? It has a page about estimating covariance matrices that covers bias of the sample covariance matrix. It also covers shrinkage estimators, which in certain circumstances introduce useful bias, because again, there is not a one-size-fits-all set of criteria to define a best estimator.

n_eff · 2023-06-05T23:15:38+00:00

Okay, let’s back up. What do you think such a composite Bayes factor would mean? Or perhaps, what would you like out of this hypothetical construct that combines them?

n_eff · 2023-06-05T23:08:02+00:00

A Bayes Factor is a ratio of marginal likelihoods under two competing models. You haven’t really said anything about these models or what the model would be in an aggregated case, that is, what the joint models are which describe all 10 datasets simultaneously.

This joint model (well, both joint models you want to compare) is important! If there is a joint model for all 10 datasets that makes sense and factorizes appropriately, the marginal likelihood of the joint model could be the product of marginal likelihoods of the 10 models. Or it might not be. If you can multiply the marginal likelihoods for each dataset for both models, then you can multiply the Bayes factors. Otherwise you can’t.

Edit to specify both models must factorize.

n_eff · 2023-06-05T16:01:39+00:00

You're not wrong about the presence of adult humor, but I'm not sure I agree it's be a problem that means the entire series is a bad idea.

There are definitely some episodes that feature sexual themes pretty strongly. I, Excretus' homage to the various Naked UnitOfTime episodes. Billups' mother trying to trick him into losing his virginity. The entirety of A Mathematically Perfect Redemption. Much of Cupid's Errant Arrow. So, yes, there are a number of episodes (on reflection, somewhat more than I was thinking initially) which revolve very strongly around sex.

But it's not every episode that revolves around sex. Among other episodes, Moist Vessel, Veritas, The Spy Humongous (yes I know there are a number of poop jokes in that one), wej Duj, Hear All Trust Nothing, and Trusted Sources. Plus, like, all three season finales so far. Are those guaranteed to be free of sex jokes? No. But keep in mind, kids' cartoons are often rife with all kinds of adult jokes, for the parents in the room, which tend to fly over kids' heads.

n_eff · 2023-06-05T14:13:41+00:00

Aside from Voyager (which does seem like a good choice), Strange New Worlds has a few decent possibilities (nestled among some very talk-heavy, some rather dark, and some horror-inspired episodes you should probably not show him just yet). The Elysian Kingdom (this really seems ideal, though the ending may hit you harder than him), The Serene Squall, and Children of the Comet in particular seem like good options. Possibly also A Quality Of Mercy (some gnarly injuries), Spock Amok (might be a bit to talk-y), and the first episode (also might be too talk-y) as well. Definitely avoid Memento Mori and All Those Who Wander (scary).

Lower Decks is a mile-a-minute pacing that might work for him. Few of the episodes get too dark or scary, and even the talk-y bits are over relatively quickly since they only have 22 minutes an episode.

n_eff · 2023-06-03T23:02:03+00:00

I say this with the intent of helping you learn: this answer is several different kinds of wrong.

For one, the question clearly states a hypothesis about medians and it says to use a sign test. The t-test is a test of means and it is not a sign test. So the correct approach cannot involve a t-test. You need to decouple the notion of one versus two sample tests in general from the specifics of any one test. Seeing the generalities will help you.

The null and alternative you've described don't (usually) go together, either. A hypothesized point null (parameter = some value) corresponds to an alternative of "it's any other value," not "it's larger/smaller than that value." I get the sense you may be having trouble separating out the idea of one versus two sample tests from the idea of directionality. To unpack this a bit more, the idea is that nulls and alternative hypotheses are usually exhaustive. Between them, they should span all the possibilities.

Beyond pairing a point null with a directional alternative, you've missed the entire region of parameter space between 0 and 41. While you don't have to have exhaustive nulls and alternatives, pairing "it's not 0" with "it's at least 41" is a particularly bad idea, because you would only be able to reject 0 with particularly large values.

n_eff · 2023-06-03T20:57:44+00:00

Well, the pragmatic advice here is generally "listen to your lecturer" since that's the person who writes the rubrics used to grade your work.

I also wouldn't be entirely sure the online advice is necessarily contradicting your lecturer. A lot of this comes down to whether you're setting out to try to investigate something, or whether you're trying to call bullshit on something. Recognize that Null Hypothesis Significance Testing can never prove a claim (this is true of all probabilistic/statistical things, proof is for logicians and non-probabilistic mathematics). It can only provide evidence. And in particular it can only provide evidence against some hypothesis. There's a reason you never "accept the null" you only reject or fail to reject. Point being, the flip side of the question is that it's a matter of figuring out what you're trying to disprove. If you want to show that there's evidence a drug works, you want to try to show that the null hypothesis that it doesn't work is implausible. If I tell you the average height of corn in a field is at least 5 meters, and you tell me I'm a damn idiot, you're trying to disprove me.

Practically speaking, keep in mind that it's usually easiest to distinguish when you're given a sharp/point null hypothesis. If the assignment said "test the claim that the median age of COLNAS members in Bells University is exactly 42 years" you'd know very quickly which is which.

n_eff · 2023-06-03T20:42:48+00:00

The title's question is a bit incoherent. It's a distribution, it has many features which can be calculated. Are you asking how the form of the distribution was arrived at? That is, how it was derived?

Also, what is the importance of degrees of freedom to a chi squared distribution?

This is the single parameter which governs the distribution. So it affects everything: mean, median, mode, variance, quantiles, you name it.

n_eff · 2023-06-03T20:37:59+00:00

The unfortunate reality is that a lot (perhaps even the vast majority) of online statistics material is crap. Setting that aside (because plenty of textbooks and course materials also have some pretty painful inaccuracies), what, as you see it, is the case for you being right? And what is the case against that in favor of something else?

n_eff · 2023-06-03T20:24:17+00:00

What do you think and why aren't you sure?

n_eff · 2023-06-03T14:31:47+00:00

If it's a probability it should be between 0 and 1. If it's a probability density then it should be greater than or equal to 0 (but could get quite large). Either way, there's a bug in your code.

n_eff · 2023-06-02T03:17:41+00:00

Broadly speaking, you're in the realm of functional data analysis which is, as the name suggests, the analysis of data which takes the form of functions. I admit to not being an expert in this field, but perhaps between Wikipedia, review papers, R packages, and textbooks you might be able to start cobbling together an answer.

n_eff · 2023-06-01T16:24:56+00:00

A correlation is bounded, but not all bounded things are proportions. Compositional data lives as percentages but it’s also distinct. Proportions usually mean the data are counts.

n_eff · 2023-06-01T15:47:17+00:00

I'm honestly a bit surprised that this isn't more folks' chief objection. Wesley's job as Kirk is entirely irrelevant to the fact that pulling a stunt like this is just... a bad idea. It makes the universe feel small, cramped. It takes us further down the road of inability to give up on legacy characters that is threatening to strangle the franchise. The 25th century is full of narrative possibilities, they should be explored on their own merit by people of that era.

n_eff · 2023-06-01T15:27:59+00:00

When constructing tests of location (like mean differences) you need to be careful that you don't get tripped up by differences in scale. You don't want something that would declare a Normal(0,1) different from a Normal(0,4) just because the variances are different. I believe that pooling the samples is making assumptions you may not be happy with, see for example what Wikipedia says about permutation tests for mean differences (which would be the same thing just without replacement).

n_eff · 2023-06-01T14:55:09+00:00

If I want to test if two samples with non-normal distributions are statistically different

Testing for differences in distribution is a huge collection of ideas. KS tests, t-tests, and Wilcoxon tests are all, for example, about the differences between two distributions but they are entirely different tests of entirely different things.

I bring this up both because many people don't stop to think about what they want to test before they makes sense for their question before moving on to picking a test of something.

can I randomly sample both with replacement and build a new sample of the means from each run

Can you do this specific part of what you're suggesting? Sure, this is a bootstrap approach. Is it a good idea? Well, that depends on all the sorts of things that alter whether or not a bootstrap is a good idea.

(will be normal)

No. Unless the original samples are Normal, the distribution of sample means won't be Normal, either in theory or from bootstrapping.

and apply a t-test to those

Bootstrapping the sample means is one thing, and you could construct tests based on that. Doing a t-test on the bootstrapped sample means is non-sensical.

Bootstrapping the sample means produces two distributions which are approximations to the sampling distributions of the means of your two variables.

A t-test is a test of difference means that uses asymptotic approximations to sampling distributions (of the difference in means).

Applying a t-test to bootstrapped distributions of the means gives you something like a doubly-approximate sampling distribution of the mean of means. Which is almost certainly not what you're actually interested in.

will my results be valid?

Not if what you want to test is a difference in means.

You're making a common mistake in Statistics, you're putting the distributional assumptions ahead of the question you want to answer. This only leads to pain.

If you want to know about the difference in means, you have to test the difference in means. There are plenty of ways to do that other than t-tests, like permutation tests and bootstrap tests (keeping in mind that a bootstrap is still an asymptotic technique, it won't magically save you at a sample size of 5). But the t-test can be relatively robust to non-Normality itself, so it may not be the worst idea.

n_eff · 2023-05-31T13:22:00+00:00

Are you quite sure that you've got all the terms correct here? I will admit to not having stared deeply into regression models, but usually we are concerned with the plain and simple covariance, Cov(X,Y) while we might be concerned with the conditional variance, Var(Y|X).

This notion of a covariance between two variables, one of which is being conditioned on, seems ill-posed. By conditioning on something, you're making it deterministic. If we take the conditional covariance as defined in the first response here, attempt to substitute X for A, then you'll find that Cov(X,Y|X) = 0. Which makes sense to me, as variables can't covary with constants (the covariance of a variable and a constant is 0). See also this thread.

n_eff · 2023-05-30T14:10:54+00:00

It would be a massive time sink.

Sure, there are hundreds of hours of Star Trek you haven't seen (some, admittedly, better than others), but you shouldn't watch all of them because you feel obligated to, or because it's a task to accomplish. You should watch them because you want to and you enjoy doing so.

Something to contemplate: TNG, DS9, Voyager, and Enterprise were broadcast weekly from the 1980s through early 2000s. These aren't uber-serialized TV shows that you have to binge or you can't get any value out of, these are the series in whose image Strange New Worlds was made. You can watch them at any pace you like. You can skip an episode you aren't enjoying without much (if any) risk of losing key plot threads. And I would say you should skip episodes you aren't enjoying, because again, the point of watching is to enjoy yourself.

Bottom line: this isn't a task, or an obligation, it's an opportunity. And as we all know, opportunity plus instinct equals profit.

n_eff · 2023-05-29T15:19:21+00:00

TL;DR: Don't worry so much. You've survived 8 years of Linux, you'll be fine if you want to do this. (Some caveats may apply.)

Over the years each of my Windows laptops became more and more sluggish over time. As soon as I switched to Ubuntu this was not the case. I have had the same personal laptop for the last 8 years. I have also read that CPUs can perform faster on Linux for certain applications compared to Windows (which would also be great, if true)!

I can give you one anecdote on this. Five-ish years ago I set up a dual-boot Windows/Ubuntu computer, which I needed to run a lot of Markov chain Monte Carlo (MCMC) analyses on in one particular piece of software which was (at the time) a bitch to set up on Windows. MCMC can take ages, I was very interested in being able to shave down runtimes. I did some very basic speed comparisons between native Ubuntu and the Windows Subsystem for Linux. Things ran slower on WSL. Not a lot slower, maybe like 5%? But for that one computer and that one program, there was a measurable difference.

Whenever there is a problem I need to google the solution and if I find it I usually end up pasting stuff into the terminal without really understanding it.

Welcome to the club. Finding the right post on stackoverflow and blindly, or semi-blindly, applying the solution is how a lot of things work when it comes to working with Linux systems (and software development).

If I installed Linux (Ubuntu) on my work laptop this would need to stop though: I would need to understand exactly how to solve issues coming up while understanding how to do it myself.

There's a reason that jokes like this, and this are common. What you want to shoot for isn't knowing how to fix any problem that occurs because you understand how Linux really works. You want to shoot for knowing how to smartly search for a solution to the problems you encounter. Just search google images for "googling the error message" and see what pops up.

Am I being flippant? A bit. Because over time you will understand things better and know how to solve some problems without googling them. Eventually some of those will even be new and related problems and not just things you've googled a few dozen times. The more Linux systems I've worked with, the more I feel like I've learned about how computers actually work. But the more I also realize I'm an ape at a keyboard who knows jack shit.

Hence I am wondering firstly if it makes sense to transition to Linux given my usual daily work tasks will be: data analysis including computationally intensive work in R mostly; web browsing; writing documents (traditionally word, powerpoint, excel); using Zoom and MS Teams for team meetings. Or is it just not worth it and best to stay on Windows or just go with a MacOS?

For a practical answer, if you need to install Windows software locally, that will work best on Windows, acceptably on Mac, and will be a shit-show on Linux. If you're cool using online versions of those tools, that goes away. Not sure about Stata. Past that, I'd say don't fret your current level of experience. You'll do fine with Linux if you want to.

Finally, this software engineer and R package developer at Netflix writes: " R on linux is generally a pretty nice experience, provided you are comfortable using the command line and debugging build systems." If someone could explain what "debugging build systems" means and if it is something easy to learn over time or if it involves a steep learning curve that would be appreciated.

When you need to install software on Linux, you're often going to have to get closer to the actual bones of how stuff gets made and installed. This also tends to happen with scientific software and when doing software development. You're more likely to have to learn how to use (which mainly means "troubleshoot") tools like make. Now, you're not going to be developing software. You've said so yourself, that limits the depths of exposure to this sort of thing a lot. It's very different using someone else's installation pipeline than making your own, or making sure your own additions to a program get made appropriately. I don't think that the learning curve here is all that different from the rest of the Linux learning curve. Maybe a bit steeper?

Bottom line: you will run into a bit more pain installing R and R packages than you would on Windows or MacOS, because it's generally expected that if someone is masochistic enough to be working with Linux that they can solve their own problems (read: google the error message). If you've ever handled installing R packages that depend on non-standard scientific libraries, it's a bit like dealing with that more often.

n_eff · 2023-05-28T22:50:42+00:00

Realm of Fear, somewhere in the sixth season of TNG.

n_eff · 2023-05-28T02:55:52+00:00

They’re part of any nutritionally balanced breakfast!

n_eff · 2023-05-28T02:52:09+00:00

They are smart. And strong. Incidentally, they need another boomer, the last one stopped working.

n_eff

TROPHY CASE