Fundraising Update 1

TL;DR: We’re pretty much on track, though we also haven’t hit the goal of pushing the fund past $78,890.69. Donate and help put the fund over the line!

With the short version out of the way, let’s dive into the details. What’s changed in the past week and change?

import datetime as dt

import matplotlib.pyplot as pl

import pandas as pd
import pandas.tseries.offsets as pdto


cutoff_day = dt.datetime( 2020, 5, 27, tzinfo=dt.timezone(dt.timedelta(hours=-6)) )

donations = pd.read_csv('donations.cleaned.tsv',sep='\t')

donations['epoch'] = pd.to_datetime(donations['created_at'])
donations['delta_epoch'] = donations['epoch'] - cutoff_day
donations['delta_epoch_days'] = donations['delta_epoch'].apply(lambda x: x.days)

# some adjustment is necessary to line up with the current total
donations['culm'] = donations['amount'].cumsum() + 14723

new_donations_mask = donations['delta_epoch_days'] > 0
print( f"There have been {sum(new_donations_mask)} donations since {cutoff_day}." )
There have been 8 donations since 2020-05-27 00:00:00-06:00.

There’s been a reasonable number of donations after I published that original post. What does that look like, relative to the previous graph?

pl.figure(num=None, figsize=(8, 4), dpi=150, facecolor='w', edgecolor='k')

pl.plot( donations['delta_epoch_days'], donations['culm'], '-',c='#aaaaaa')
pl.plot( donations['delta_epoch_days'][new_donations_mask], \
        donations['culm'][new_donations_mask], '-',c='#0099ff')

pl.title("Defense against Carrier SLAPP Suit")

pl.xlabel("days since cutoff")
pl.ylabel("dollars")
pl.xlim( [-365.26,donations['delta_epoch_days'].max()] )
pl.ylim( [55000,82500] )
pl.show()

An updated chart from the past year. New donations are in blue.

That’s certainly an improvement in the short term, though the graph is much too zoomed out to say more. Let’s zoom in, and overlay the posterior.

# load the previously-fitted posterior
flat_chain = np.loadtxt('starting_posterior.csv')


pl.figure(num=None, figsize=(8, 4), dpi=150, facecolor='w', edgecolor='k')

x = np.array([0, donations['delta_epoch_days'].max()])
for m,_,_ in flat_chain:
    pl.plot( x, m*x + 78039, '-r', alpha=0.05 )
    
pl.plot( donations['delta_epoch_days'], donations['culm'], '-', c='#aaaaaa')
pl.plot( donations['delta_epoch_days'][new_donations_mask], \
        donations['culm'][new_donations_mask], '-', c='#0099ff')

pl.title("Defense against Carrier SLAPP Suit")

pl.xlabel("days since cutoff")
pl.ylabel("dollars")
pl.xlim( [-3,x[1]+1] )
pl.ylim( [77800,79000] )

pl.show()

A zoomed-in view of the new donations, with posteriors overlaid.

Hmm, looks like we’re right where the posterior predicted we’d be. My targets were pretty modest, though, consisting of an increase of 3% and 10%, so this doesn’t mean they’ve been missed. Let’s extend the chart to day 16, and explicitly overlay the two targets I set out.

low_target = 78890.69
high_target = 78948.57
target_day = dt.datetime( 2020, 6, 12, 23, 59, tzinfo=dt.timezone(dt.timedelta(hours=-6)) )
target_since_cutoff = (target_day - cutoff_day).days

pl.figure(num=None, figsize=(8, 4), dpi=150, facecolor='w', edgecolor='k')

x = np.array([0, target_since_cutoff])
pl.fill_between( x, [78039, low_target], [78039, high_target], color='#ccbbbb', label='blog post')
pl.fill_between( x, [78039, high_target], [high_target, high_target], color='#ffeeee', label='video')

pl.plot( donations['delta_epoch_days'], donations['culm'], '-',c='#aaaaaa')
pl.plot( donations['delta_epoch_days'][new_donations_mask], \
        donations['culm'][new_donations_mask], '-',c='#0099ff')

pl.title("Defense against Carrier SLAPP Suit")

pl.xlabel("days since cutoff")
pl.ylabel("dollars")
pl.xlim( [-3, target_since_cutoff] )
pl.ylim( [77800,high_target] )

pl.legend(loc='lower right')
pl.show()

The previous graph, this time with targets overlaid.

To earn a blog post and video on Bayes from me, we need the line to be in the pink zone by the time it reaches the end of the graph. For just the blog post, it need only be in the grayish- area. As you can see, it’s painfully close to being in line with the lower of two goals, though if nobody donates between now and Friday it’ll obviously fall quite short.

So if you want to see that blog post, get donating!

Fundraising Target Number 1

If our goal is to raise funds for a good cause, we should at least have an idea of where the funds are at.

(Click here to show the code)
created_at amount epoch delta_epoch culm
0 2017-01-24T07:27:51-06:00 10.0 2017-01-24 07:27:51-06:00 -1218 days +19:51:12 14733.0
1 2017-01-24T07:31:09-06:00 50.0 2017-01-24 07:31:09-06:00 -1218 days +19:54:30 14783.0
2 2017-01-24T07:41:20-06:00 100.0 2017-01-24 07:41:20-06:00 -1218 days +20:04:41 14883.0
3 2017-01-24T07:50:20-06:00 10.0 2017-01-24 07:50:20-06:00 -1218 days +20:13:41 14893.0
4 2017-01-24T08:03:26-06:00 25.0 2017-01-24 08:03:26-06:00 -1218 days +20:26:47 14918.0

Changing the dataset so the last donation happens at time zero makes it both easier to fit the data and easier to understand what’s happening. The first day after the last donation is now day one.

Donations from 2017 don’t tell us much about the current state of the fund, though, so let’s focus on just the last year.

(Click here to show the code)

The last year of donations, for the lawsuit fundraiser.

The donations seem to arrive in bursts, but there have been two quiet portions. One is thanks to the current pandemic, and the other was during last year’s late spring/early summer. It’s hard to tell what the donation rate is just by eye-ball, though. We need to smooth this out via a model.
The simplest such model is linear regression, aka. fitting a line. We want to incorporate uncertainty into the mix, which means a Bayesian fit. Now, what MCMC engine to use, hmmm…. emcee is my overall favourite, but I’m much too reliant on it. I’ve used PyMC3 a few times with success, but recently it’s been acting flaky. Time to pull out the big guns: Stan. I’ve been avoiding it because pystan‘s compilation times drove me nuts, but all the cool kids have switched to cmdstanpy when I looked away. Let’s give that a whirl.

(Click here to show the code)
CPU times: user 5.33 ms, sys: 7.33 ms, total: 12.7 ms
Wall time: 421 ms
CmdStan installed.

We can’t fit to the entire three-year time sequence, that just wouldn’t be fair given the recent slump in donations. How about the last six months? That covers both a few donation burts and a flat period, so it’s more in line with what we’d expect in future.

(Click here to show the code)
There were 117 donations over the last six months.

With the data prepped, we can shift to building the linear model.

(Click here to show the code)

I could have just gone with Stan’s basic model, but flat priors aren’t my style. My preferred prior for the slope is the inverse tangent, as it compensates for the tendency of large slope values to “bunch up” on one another. Stan doesn’t offer it by default, but the Cauchy distribution isn’t too far off.

We’d like the standard deviation to skew towards smaller values. It naturally tends to minimize itself when maximizing the likelihood, but an explicit skew will encourage this process along. Gelman and the Stan crew are drifting towards normal priors, but I still like a Cauchy prior for its weird properties.

Normally I’d plunk the Gaussian distribution in to handle divergence from the deterministic model, but I hear using Student’s T instead will cut down the influence of outliers. Thomas Wiecki recommends one degree of freedom, but Gelman and co. find that it leads to poor convergence in some cases. They recommend somewhere between three and seven degrees of freedom, but skew towards three, so I’ll go with the flow here.

The y-intercept could land pretty much anywhere, making its prior difficult to figure out. Yes, I’ve adjusted the time axis so that the last donation is at time zero, but the recent flat portion pretty much guarantees the y-intercept will be higher than the current amount of funds. The traditional approach is to use a flat prior for the intercept, and I can’t think of a good reason to ditch that.

Not convinced I picked good priors? That’s cool, there should be enough data here that the priors have minimal influence anyway. Moving on, let’s see how long compilation takes.

(Click here to show the code)
CPU times: user 4.91 ms, sys: 5.3 ms, total: 10.2 ms
Wall time: 20.2 s

This is one area where emcee really shines: as a pure python library, it has zero compilation time. Both PyMC3 and Stan need some time to fire up an external compiler, which adds overhead. Twenty seconds isn’t too bad, though, especially if it leads to quick sampling times.

(Click here to show the code)
CPU times: user 14.7 ms, sys: 24.7 ms, total: 39.4 ms
Wall time: 829 ms

And it does! emcee can be pretty zippy for a simple linear regression, but Stan is in another class altogether. PyMC3 floats somewhere between the two, in my experience.

Another great feature of Stan are the built-in diagnostics. These are really handy for confirming the posterior converged, and if not it can give you tips on what’s wrong with the model.

(Click here to show the code)
Processing csv files: /tmp/tmpyfx91ua9/linear_regression-202005262238-1-e393mc6t.csv, /tmp/tmpyfx91ua9/linear_regression-202005262238-2-8u_r8umk.csv, /tmp/tmpyfx91ua9/linear_regression-202005262238-3-m36dbylo.csv, /tmp/tmpyfx91ua9/linear_regression-202005262238-4-hxjnszfe.csv

Checking sampler transitions treedepth.
Treedepth satisfactory for all transitions.

Checking sampler transitions for divergences.
No divergent transitions found.

Checking E-BFMI - sampler transitions HMC potential energy.
E-BFMI satisfactory for all transitions.

Effective sample size satisfactory.

Split R-hat values satisfactory all parameters.

Processing complete, no problems detected.

The odds of a simple model with plenty of datapoints going sideways are pretty small, so this is another non-surprise. Enough waiting, though, let’s see the fit in action. First, we need to extract the posterior from the stored variables …

(Click here to show the code)
There are 256 samples in the posterior.

… and now free of its prison, we can plot the posterior against the original data. I’ll narrow the time window slightly, to make it easier to focus on the fit.

(Click here to show the code)

The same graph as before, but now slightly zoomed in on and with trendlines visible.

Looks like a decent fit to me, so we can start using it to answer a few questions. How much money is flowing into the fund each day, on average? How many years will it be until all those legal bills are paid off? Since humans aren’t good at counting in years, let’s also translate that number into a specific date.

(Click here to show the code)
mean/std/median slope = $51.62/1.65/51.76 per day

mean/std/median years to pay off the legal fees, relative to 2020-05-25 12:36:39-05:00 =
	1.962/0.063/1.955

mean/median estimate for paying off debt =
	2022-05-12 07:49:55.274942-05:00 / 2022-05-09 13:57:13.461426-05:00

Mid-May 2022, eh? That’s… not ideal. How much time can we shave off, if we increase the donation rate? Let’s play out a few scenarios.

(Click here to show the code)
median estimate for paying off debt, increasing rate by   1% = 2022-05-02 17:16:37.476652800
median estimate for paying off debt, increasing rate by   3% = 2022-04-18 23:48:28.185868800
median estimate for paying off debt, increasing rate by  10% = 2022-03-05 21:00:48.510403200
median estimate for paying off debt, increasing rate by  30% = 2021-11-26 00:10:56.277984
median estimate for paying off debt, increasing rate by 100% = 2021-05-17 18:16:56.230752

Bumping up the donation rate by one percent is pitiful. A three percent increase will almost shave off a month, which is just barely worthwhile, and a ten percent increase will roll the date forward by two. Those sound like good starting points, so let’s make them official: increase the current donation rate by three percent, and I’ll start pumping out the aforementioned blog posts on Bayesian statistics. Manage to increase it by 10%, and I’ll also record them as videos.

As implied, I don’t intend to keep the same rate throughout this entire process. If you surprise me with your generosity, I’ll bump up the rate. By the same token, though, if we go through a dry spell I’ll decrease the rate so the targets are easier to hit. My goal is to have at least a 50% success rate on that lower bar. Wouldn’t that make it impossible to hit the video target? Remember, though, it’ll take some time to determine the success rate. That lag should make it possible to blow past the target, and by the time this becomes an issue I’ll have thought of a better fix.

Ah, but over what timeframe should this rate increase? We could easily blow past the three percent target if someone donates a hundred bucks tomorrow, after all, and it’s no fair to announce this and hope your wallets are ready to go in an instant. How about… sixteen days. You’ve got sixteen days to hit one of those rate targets. That’s a nice round number, for a computer scientist, and it should (hopefully!) give me just enough time to whip up the first post. What does that goal translate to, in absolute numbers?

(Click here to show the code)
a   3% increase over 16 days translates to $851.69 + $78039.00 = $78890.69

Right, if you want those blog posts to start flowing you’ve got to get that fundraiser total to $78,890.69 before June 12th. As for the video…

(Click here to show the code)
a  10% increase over 16 days translates to $909.57 + $78039.00 = $78948.57

… you’ve got to hit $78,948.57 by the same date.

Ready? Set? Get donating!

It’s Payback Time

I’m back! Yay! Sorry about all that, but my workload was just ridiculous. Things should be a lot more slack for the next few months, so it’s time I got back blogging. This also means I can finally put into action something I’ve been sitting on for months.

Richard Carrier has been a sore spot for me. He was one of the reasons I got interested in Bayesian statistics, and for a while there I thought he was a cool progressive. Alas, when it was revealed he was instead a vindictive creepy asshole, it shook me a bit. I promised myself I’d help out somehow, but I’d already done the obsessive analysis thing and in hindsight I’m not convinced it did more good than harm. I was at a loss for what I could do, beyond sharing links to the fundraiser.

Now, I think I know. The lawsuits may be long over, thanks to Carrier coincidentally dropping them at roughly the same time he came under threat of a counter-suit, but the legal bill are still there and not going away anytime soon. Worse, with the removal of the threat people are starting to forget about those debts. There have been only five donations this month, and four in April. It’s time to bring a little attention back that way.

One nasty side-effect of Carrier’s lawsuits is that Bayesian statistics has become a punchline in the atheist/skeptic community. The reasoning is understandable, if flawed: Carrier is a crank, he promotes Bayesian statistics, ergo Bayesian statistics must be the tool of crackpots. This has been surreal for me to witness, as Bayes has become a critical tool in my kit over the last three years. I suppose I could survive without it, if I had to, but every alternative I’m aware of is worse. I’m not the only one in this camp, either.

Following the emergence of a novel coronavirus (SARS-CoV-2) and its spread outside of China, Europe is now experiencing large epidemics. In response, many European countries have implemented unprecedented non-pharmaceutical interventions including case isolation, the closure of schools and universities, banning of mass gatherings and/or public events, and most recently, widescale social distancing including local and national lockdowns. In this report, we use a semi-mechanistic Bayesian hierarchical model to attempt to infer the impact of these interventions across 11 European countries.

Flaxman, Seth, Swapnil Mishra, Axel Gandy, H Juliette T Unwin, Helen Coupland, Thomas A Mellan, Tresnia Berah, et al. “Estimating the Number of Infections and the Impact of Non- Pharmaceutical Interventions on COVID-19 in 11 European Countries,” 2020, 35.

In estimating time intervals between symptom onset and outcome, it was necessary to account for the fact that, during a growing epidemic, a higher proportion of the cases will have been infected recently (…). Therefore, we re-parameterised a gamma model to account for exponential growth using a growth rate of 0·14 per day, obtained from the early case onset data (…). Using Bayesian methods, we fitted gamma distributions to the data on time from onset to death and onset to recovery, conditional on having observed the final outcome.

Verity, Robert, Lucy C. Okell, Ilaria Dorigatti, Peter Winskill, Charles Whittaker, Natsuko Imai, Gina Cuomo-Dannenburg, et al. “Estimates of the Severity of Coronavirus Disease 2019: A Model-Based Analysis.” The Lancet Infectious Diseases 0, no. 0 (March 30, 2020). https://doi.org/10.1016/S1473-3099(20)30243-7.

we used Bayesian methods to infer parameter estimates and obtain credible intervals.

Linton, Natalie M., Tetsuro Kobayashi, Yichi Yang, Katsuma Hayashi, Andrei R. Akhmetzhanov, Sung-mok Jung, Baoyin Yuan, Ryo Kinoshita, and Hiroshi Nishiura. “Incubation Period and Other Epidemiological Characteristics of 2019 Novel Coronavirus Infections with Right Truncation: A Statistical Analysis of Publicly Available Case Data.” Journal of Clinical Medicine 9, no. 2 (February 2020): 538. https://doi.org/10.3390/jcm9020538.

A significant chunk of our understanding of COVID-19 depends on Bayesian statistics. I’ll go further and argue that you cannot fully understand this pandemic without it. And yet thanks to Richard Carrier, the atheist/skeptic community is primed to dismiss Bayesian statistics.

So let’s catch two stones with one bird. If enough people donate to this fundraiser, I’ll start blogging a course on Bayesian statistics. I think I’ve got a novel angle on the subject, one that’s easier to slip into than my 201-level stuff and yet more rigorous. If y’all really start tossing in the funds, I’ll make it a video series. Yes yes, there’s a pandemic and potential global depression going on, but that just means I’ll work for cheap! I’ll release the milestones and course outline over the next few days, but there’s no harm in an early start.

Help me help the people Richard Carrier hurt. I’ll try to make it worth your while.

Case Dismissed

Just over two years ago, Richard Carrier filed a lawsuit against Freethought Blogs, The Orbit, Skepticon, and a few individuals. Strangely, his choice of venue was Ohio, well away from anyone involved

It’s worth noting that Ohio lacks any anti-SLAPP protections — making it easier to sue people who may not have the money to fight back — while California, Minnesota, and Missouri have at least some protections.

It was a crafty move, but in the end it bit Carrier in the ass.

Defendants made allegedly defamatory statements outside of Ohio, relating to conduct that occurred outside of Ohio, about an individual who moved to Ohio a few weeks before the statements were made. In sum, there is no sufficiently substantial connection between any of the Defendants and Ohio to make the exercise of personal jurisdiction reasonable.

The Court declines to hold an evidentiary hearing because even if all of Plaintiff’s assertions of fact are true, there is still an insufficient basis for personal jurisdiction. Weighing the evidence in the light most favorable to Plaintiff, the Court holds that Plaintiff has not made a prima facie showing of personal jurisdiction over any of the Defendants.

PZ Myers is already celebrating, quite understandably, so I’ll play the grump.

For the foregoing reasons, the Court GRANTS Defendents’ motion to dismiss for lack of personal jurisdiction and DISMISSES Plaintiff’s Complaint WITHOUT PREJUDICE.

WITHOUT PREJUDICE” is the troublesome bit, as that means Carrier can re-file his lawsuit in another state. He appears to be an independent scholar that earns most of his money from online courses, yet his legal bills must be substantial, which suggests one or more people are subsidizing his lawsuit. Even if he didn’t have a sponsor at the start, he likely has one now. How much money are those people willing to sink into griefing FtB/The Orbit/Skepticon? If Carrier’s move was to set up this lawsuit, that suggests he or his possible backers know the legal system, know how expensive it can be, and hold a substantial grudge.

I’d recommend tossing some cash at the defendants; if my pessimism is accurate they’ll need the cash, and if not it’s a good guess that their legal bills are more than what they fundraised. Don’t dump all your cash in there, though. Save a bit for champagne, as this is still a celebration.


HJH 2018-11-14: Two things. James Hammond on Pharyngula pointed out that I wasn’t considering the statute of limitations. It turns out both Minnesota and Missouri only allow libel claims within the two years, and California within one; two of Carrier’s original five claims were for libel, so he can’t re-file those. Minnesota and California also limit personal injury claims to two years after the incident, which I think block his claims of emotional distress there. “Tortious interference with a business expectancy” is going to be very difficult to prove, even in civil court, as the allegations of misbehavior against him haven’t prevented Carrier from offering online courses, being invited to speak at conferences, and give lectures.

In sum, there isn’t much to re-file on, which deflates a lot of my pessimism.

PZ Myers, meanwhile, confirms what I suspected.

The donations don’t yet fully cover our legal costs, so no, we’re still in the hole.

If Carrier’s intention was to punish his accusers via the legal system, he’s partly succeeded. One way to soften the blow is by donating to Skepticon or the rest of the defendants. They’ll all be grateful for the support.

It’s Time

I finally gave in and set up a public Patreon account. My financial situation isn’t as good as it once was, and I could use the pocket change. It’s on a per-work basis, as my posting schedule is erratic and goes through long dry spells. I only intend to ding patrons for my larger, more analytic posts; those “hey look at this cool thing” posts are too easy to charge for. If you’re worried about a posting spree draining your bank account, no problem: Patreon allows you to set up a monthly cap, so you’ll never be caught with a surprise bill.

Why the reluctance to hop on this bandwagon? The main reason why I never became an artist is that I have no appetite for self-promotion. Long-time friends and family members have no idea about my blog, because I know their interests and know it’s not their cup. Running a successful Patreon demands a pro-active social media presence, and that’s just not my thing. I’m not anti-social so much as a-social, which leads to all sorts of confusion when people meet me in person.

Having said that, I do have a few special things planned.

Some people dropped out of the hike, due to the lousy conditions. There is no such thing at O'Hara.

I used to be an avid photographer, and I’ve still got a tonne of unprocessed photos sitting on my hard drive. So let’s say that if you contribute at least $5 in any given month, then if you send me an address I’ll send you a photo postcard. I’ll track which ones you receive so you’ll never get the same one twice. I also have a lot of old ideas kicking around that were never fully completed, so a members-only poll of which ones to revive might encourage me to finish one of them. Even if not, it at least gives you some insight into where my head is at.

So if that sort of thing is appealing to you, or you just like the stuff I write enough to donate some pocket change, sign up. If you don’t or can’t, no problem! I don’t plan on going anywhere.

Help A Brother Out

Tony Thompson Jr. has been around the social justice side of atheism/skepticism for a long while; I mean, just check the page count on his blog. He’s a great guy, but his personality can’t stop hurricanes. Tony escaped the worst, but he’s still had to deal with no electricity or running water, a lack of food and other essentials, and his funds are running dry.

If you’ve got a few extra dollars, send them his way.