ericjpedersen.bsky.social
Associate prof of biology prof Concordia University. Lost in the wilds between ecology, statistics, and dynamic systems. Always interested in chatting all things GAM- and and nonlinear-system related
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Yep, the coverage statements for CIs for GAMs in mgcv are averaged "across the function" (which is, confusingly, not the same thing as a simultaneous interval for the whole function; @gsimpson.bsky.social's got a nice post on the difference between these fromthebottomoftheheap.net/2016/12/15/s...)
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The coverage statements for CIs / p-values for penalized terms are averaged across the domain of the penalized regression function though; so e.g. individual CIs for specific random effect levels might be overly conservative or optimistic
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It is possible to calculate valid p-values with penalization by adjusting degrees of freedom for penalization; see Wood 2006 (onlinelibrary.wiley.com/doi/10.1111/...), and mgcv. It relies on some standard asymptotic arguments for calculating the values, but generally good small sample properties
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I found the cross-country comparisons of rise and fall in murder rates vs lead blood levels by Kevin Drum in Mother Jones to be some of the most convincing evidence for me
www.motherjones.com/kevin-drum/2...
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Strong argument that it's leaded gasoline driving a lot of that increase and decline
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The link function is actually the key part of GLM (and related frameworks), even though everyone focuses on the marginal distribution. It also allows for better modelling of dependency (via e.g. basis functions), on the link scale
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The fact that most of the frauds found are either in high profile journals or just really incompetent frauds makes me think this is a "only 10% of the iceberg is visible" situation
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I think GenAI is likely accelerating the issue, but even before chatGPT came out I received a lot of pushback from 2nd year undergrads about any writing or quantitative q's. In my first year of teaching I was amazed to hear that students thought a 3-5 sentence question was a "long answer question"
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I do have a bit of a hard time visualizing this as a dag though. Maybe:
Dice distribution -> Roll1
Roll1+->Decision to measure
Decision to measure+-> measurement 1
Roll1 +-> measurement 1
Dice distribution -> Roll2
Roll2 +-> measurement 2
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I haven't seen it framed like this, but regression to the mean seems like a good application of DAGs. Realized roll depends on average, and decision to measure depends on realized roll. Second measurement only depends on realized value.
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"Was Fëanor the Andrew Tate of the First Age? In this essay, I will..."
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And the HGAM paper only exists because of social media! It started when @noamross.net tweeted about tensoring random effects and smoothing splines and got us all curious what we could do with them
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Teaching in French was banned in Manitoba for more than 50 years, and the Quebec government at the time supported Manitoba banning it, because (from what I understand of it) it strengthened the case for Quebec's own language policies
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The Quebec act was declared one of the Intolerable Acts in part because it gave *too many* rights and freedoms (e.g. freedom to practice Catholicism) to the residents of Quebec after the Seven Years' War
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Good for me! I appreciate the discussion. Also, it's always nice to get to dig into matrix algebra as a break from grading :)
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But Julia's original point was that *just because X2 and X3 are strongly correlated, including them both does not necessarily impair the precision of our effect of interest*. I was trying to demonstrate that point.
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A couple quick corrections (I wrote this too fast):
the matrix should be:
M = n*[A B]
[B' C]
and
SE(b1)^2 = (SE(res)^2*M^{-1})[1,1]
(inverse of M times residual standard error)
so SE(b1)^2 = SE(res)^2*1/n(1-BC^{-1}B')^-1)
But the same argument still holds
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But I think that rough intuition is wrong here; just because (X'X)^-1 is hard to invert does not mean that the standard error for any specific parameter is large
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But if B / B' are "small", then BC^-1B' should be close to zero regardless unless C^-1 is very large (very poorly conditioned)
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(as a note: A,B, and C should all be multiplied by n above)
Inverse of a block matrix can be inverted blockwise (en.wikipedia.org/wiki/Block_m...) and the top left element of that inverse will have a value of:
(A - BC^-1B')^-1
3/n
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Since all variables have mean 0, SD of 1, then X'X is just the correlation matrix Cor(X). We can write it as a block matrix:
X'X = [A B]
[B'C]
(A=1, B = [cor(X1,X2), X1,X3], C = Cor(X2:X3))
SE(b) = (X'X)^-1[1,1], or the first diagonal element.
2/n
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Even if X'X is nearly non-invertible, that does not imply that the SE for any given parameter is large. To see this:
Fit Y ~ b1*X1 +b2*X2 + b3*X2, and we care about the SE(b1). [Y, X1:X3 are all centered and scaled] We assume that Cor(X2, X3) is "large", but Cor(X1, X2) and Cor(X1,X2) is "small"
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You could just compute moments for each dist and summarize the change in the first few moments
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A single distance measure might not be the best option here... We'd expect the posterior location (median, mode etc. ) to shift, but the posterior variance should also decrease. Diff distance measures will be sensitive to different components
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I knew there was a reason I'm holding on to those vga and mini usb cables...
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God I hate April Fools Day. The "now the internet is unreadable" day
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Yep. The way I think about it now is "the sample mean and se tell you about how certain you should be if your model is right. The rest of the data is there to explain to you why that assumption is wrong."
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I still find the idea of sufficiency to be slightly counter-intuitive. "What do you mean all that matters is the sample average? I collected 10,000 data points, should I just ignore them!?"
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This is not where I expected them to take the Ratatouille sequel
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He has a lot of practical experience at designing exploding rockets; that has to count for something
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In 1912, she moved to Berlin to begin working with Leonor Michaelis in enzyme kinetics. With him, she developed the Michaelis-Menten Equation.
The equation shows that the rate of reaction rate in enzymes increases to saturation as the substrate concentration increases.
🧵4/10
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I'd love to give it a try!
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The article does mention that these inconsistencies were at one point considered evidence of possible variation in the speed of light (I.e. a failure to replicate) rather than ignored systematic errors, which I think reinforces @devezer.bsky.social's original point re: lack of replication
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Thanks for tracking this down! I realized yesterday there was no reference in that doc for the CIs and I was going nuts trying to track down the source for the intervals
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By strict standards of replication, the estimated speed of light wasn't replicable based on highly inconsistent CIs, even though the initial estimates were within 1% of the modern value
(figure from www.olympus-lifescience.com/en/microscop...)
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Just to name a few ways: the Culture is deeply non hierarchical, fundamentally pro-trans, anarchist and anti-capitalist. Every member of the Culture would find Elon's day-to-day behavior completely inexplicable
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By strict standards of replication, the estimated speed of light wasn't replicable based on highly inconsistent CIs, even though the initial estimates were within 1% of the modern value
(figure from www.olympus-lifescience.com/en/microscop...)
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Also, the fact that Musk says he loves the Culture novels shows that he has the reading comprehension of a rock. The books couldn't be more antithetical to everything he's done than if they were written with him in mind
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This is a great idea! I'd love to be added too
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