rnburn's comments

> By this metric, we can see that the states where it’s easiest to find housing include Utah (2.83 units per capita), California (2.75), Hawaii (2.57), and Texas (2.57). Overall, in the United States, there are approximately 2.35 housing units available per capita

I don't know how deedclaim computed those numbers, or the reliability of the source; but California most definitely has a shortage of housing. The numbers I quoted come from the McKinsey Global institute study: https://web.archive.org/web/20161105022549/https://www.mckin...

And local policy is very much a problem. Briefly as described in https://www.youtube.com/watch?v=0IHEMHc2yfY, California has a lot of housing restrictions, a high cost of construction, and processes that make it easy for housing opponents to block new developments.

And your statement "you will see fewer homeless people moving to California to camp in a tent and then finding it tough to get back into housing." is not an accurate characterization. Most of the homeless in California are Californians. Quoting from 2023 UCSF homeless study (https://homelessness.ucsf.edu/sites/default/files/2023-06/CA...): "People experiencing homelessness in California are Californians. Nine out of ten participants lost their last housing in California; 75% of participants lived in the same county as their last housing"

California has close to the worst per capita housing supply of any state in the US. From https://www.vox.com/cities-and-urbanism/2018/2/23/17011154/s...: "The state’s population has steadily grown, but it hasn’t been building new places for people to live at anything close to the same rate. It now ranks 49th in housing units per capita." There's a lot that can be done locally to improve homelessness.

Where are you getting that 90% number from? That doesn't match with any source I'm familiar with. For example, the 2023 statewide homeless study from UCSF (https://homelessness.ucsf.edu/sites/default/files/2023-06/CA...) reported these numbers: "We describe current regular use of cocaine, amphetamines, and non-prescribed opioids as use three times a week or more. By this definition, one third (35%) of participants reported currently using cocaine, amphetamines, or non-prescription opioids regularly (Figure 31). Thirty-one percent of participants report current regular use of methamphetamines; 3% cocaine, and 11% non-prescribed opioids. In the prior six months, 13% of all participants report using injection drugs."

That's a good book. I'd also recommend John Tukey's classic paper "Some Graphic and Semigraphic Displays", https://www.edwardtufte.com/tufte/tukey

Tukey was one of Tufte's mentors.

One other rule I've found helpful is banking to 45 degrees -- it's an easy way to rmake elationships easier to perceive: http://vis.stanford.edu/files/2006-Banking-InfoVis.pdf

The paper gives the rate of convergence you get with Polynomial interpolants in Chebyshev nodes:

> If f has v derivatives, with the vth derivative being of bounded variation V, then ||f - p_n|| = O(V n^{-v}) as n -> ∞

and

> If f is analytic, the convergence is geometric, with ||f - p_n|| = O(p^{-n}) for some p > 1

You will not get that good of a rate of convergence with cubic splines. See https://www.researchgate.net/publication/243095286_On_the_Or...

This is further explained in Trefethen's book https://www.amazon.com/Approximation-Theory-Practice-Applied...

Quoting from Ch 14

> In fact, polynomial interpolants in Chebyshev points are problem-free when evaluated by the barycentric interpolation formula. They have the same behavior as discrete Fourier series for period functions, whose reliability nobody worries about. The introduction of splines is a red herring: the true advantage of splines is not that they converge where polynomials fail to do so, but that they are more easility adapted to irregular point distributions and more localized.

You can see also the software package https://www.chebfun.org/ for Chebyshev interpolations with Matlab and https://github.com/rnburn/bbai for Chebyshev interpolation of arbitrary dimension functions with sparse grids for Python. And here is a quick notebook for an experiment you can run that will compare Chebyshev interpolants to cubic splines: https://github.com/rnburn/bbai/blob/master/example/13-sparse...

> There are many techniques to interpolate between a given set of points. Polynomial interpolation can perfectly fit N points with an N-1 degree polynomial, but this approach can be problematic for large a N; high-degree polynomials tend to overfit their data, and suffer from other numerical issues like Runge's phenomenon.

This is a misconception that's often repeated. High degree polynomial interpolations are problematic if you use equispaced points. If you use Chebyshev points, they are highly accurate and in general perform much better than cubic splines. See myth 1 from Lloyd Trefethen's paper: https://people.maths.ox.ac.uk/trefethen/mythspaper.pdf

> "A reasonable model for the “blowup factor” (actual time divided by estimated time) would be something like a log-normal distribution.

Research has shown a power-law distribution to be a better fit.

See "The Empirical Reality of IT Project Cost Overruns: Discovering a Power-Law Distribution" https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4204819

> "it is estimated that 75% of SF’s homeless are from outside of the city" -- Where are you getting that 75% number from? The latest survey I'm familiar with showed nearly exactly the opposite (71% of homeless in SF had a prior place of residence in SF). See https://sfstandard.com/2023/05/22/san-francisco-homeless-peo...