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Citing a spike in new coronavirus cases Governor Newsom yesterday announced new CA restrictions. In his press conference last Friday he encouraged listeners to download the state’s raw data and play with it, so I did.
Wanting to understand the spike, I grouped the data for each county (it’s reported by county in their files) into totals per day for the state. Heeding a cautionary note about irregularities in daily reporting, I calculated 7-day averages for new daily cases and new daily deaths. It should go without saying that “new daily cases” means new cases known among people tested, and therefore says nothing about the base rate in the population. The number of daily tests in CA grows roughly exponentially. Each day we do more tests than we did the previous day. This increase in daily testing is apparent in the blue line in the below chart. On the same chart I plotted 7-day averages of daily reported deaths. 7-day-averaged daily new deaths peaked on Apr 24 and have declined roughly steadily since.
In the next chart I plotted total tests (not daily new tests) and total cases vs. time. The left vertical axis and the red line indicate total known cases. The blue line, which rises similarly, indicates the total test count.
The conditions of people tested has likely changed over time. Initially, tests were only available to sick people. Therefore we should expect a change in the ratio of deaths per person tested, and that is the case. To make the numbers more understandable, I plotted deaths per 1000 known cases over time (red line below). That rate peaks at about May 1, stays roughly even for three weeks, then drops by 50% at the end of June.
Another look at the change in nature of people being tested is the plot of cases per test (blue line below), or, as plotted here for easier reading, cases per 1000 tests. Note this plot is of a daily ratio. For the first two weeks of the plot (the last two weeks of March) both the numerator and denominator of the values forming the plotted values are small. So the first few weeks of data are unreliable. On Apr 3, CA performed three times as many tests as on the previous day (113687 vs. 35267) but the increase in positive tests between Apr 3 and 4 was small. Therefore there is an abrupt drop in the cases (positive tests) per 1000 tests on Apr 3.
I see nothing in these plots that I would describe as a spike. I’ll leave any further interpretation to readers. The data plotted here is exactly as taken from data.ca.gov with the exception of one data point. The total test count in the ca.gov data for May 27 is obviously wrong. It is much higher than the total at May 28, and totals (as opposed to daily new values) cannot decrease. The value used in my plots is interpolated from the preceding and following days. Email me or leave a comment if you’d like a copy of my Excel file that combines data from several of the ca.gov files, groups the county data together, calculates the 7-day averages for smoothing, and shows the source of the plots shown here.
Many friends report an astounding improvement in air quality across the country over the past few weeks, an unexpected silver lining to coronavirus lockdown. They can breathe better and see distant mountains previously obscured by haze. The Washington Post, The Guardian, and NPR have covered the phenomenon. “Anyone walking, biking or driving outdoors can see the blue skies,” says The Mercury News. They were unclear as to whether the blue skies could be seen by those confined with only window views.
AirNow, developed by the EPA, makes its archives available online. Here is what the first Monday in April has looked like for the previous five years. 2020 is at the bottom.
Playing poker online is far more addictive than gambling in a casino. Online poker, and other online gambling that involves a lot of skill, is engineered for addiction. Online poker allows multiple simultaneous tables. Laptops, tablets, and mobile phones provide faster play than in casinos. Setup time, for an efficient addict, can be seconds per game. Better still, you can rapidly switch between different online games to get just enough variety to eliminate any opportunity for boredom that has not been engineered out of the gaming experience. Completing a hand of Texas Holdem in 45 seconds online increases your chances of fast wins, fast losses, and addiction.
Tilt is what poker players call it when a particular run of bad luck, an opponent’s skill, or that same opponent’s obnoxious communications put you into a mental state where you’re playing emotionally and not rationally. Anger, disgust, frustration and distress is precipitated by bad beats, bluffs gone awry, a run of dead cards, losing to a lower ranked opponent, fatigue, or letting the opponent’s offensive demeanor get under your skin.
Tilt is so important to online poker that many products and commitment devices have emerged to deal with it. Tilt Breaker provides services like monitoring your performance to detect fatigue and automated stop-loss protection that restricts betting or table count after a run of losses.
A few years back, some friends and I demonstrated biometric tilt detection using inexpensive heart rate sensors. We used machine learning with principal dynamic modes (PDM) analysis running in a mobile app to predict sympathetic (stress-inducing, cortisol, epinephrine) and parasympathetic (relaxation, oxytocin) nervous system activity. We then differentiated mental and physical stress using the mobile phone’s accelerometer and location functions. We could ring an alarm to force a player to face being at risk of tilt or ragequit, even if he was ignoring the obvious physical cues. Maybe it’s time to repurpose this technology.
In past crises, the flow of bad news and peer communications were limited by technology. You could not scroll through radio programs or scan through TV shows. You could click between the three news stations, and then you were stuck. Now you can consume all of what could be home work and family time with up to the minute Covid death tolls while blasting your former friends on Twitter and Facebook for their appalling politicization of the crisis.
You yourself are of course innocent of that sort of politicizing. As a seasoned poker player, you know that the more you let emotions take control your game, the farther your judgments will stray from rational ones.
Still yet, what kind of utter moron could think that the whole response to Covid is a media hoax? Or that none of it is.
Philosophy can get you into trouble.
I don’t get many responses to blog posts; and for some reason, most of those I get come as email. A good number of those I have received fall into two categories – proclamations and condemnations of philosophy.
The former consist of a final word offered on a matter that I wrote about having two sides and warranting some investigation. The respondents, whose signatures always include a three-letter suffix, set me straight, apparently discounting the possibility of an opposing PhD. Regarding argumentum ad verecundiam, John Locke’s 1689 Essay Concerning Human Understanding is apparently passé in the era where nonscientists feel no shame for their science illiteracy and “my scientist can beat up your scientist.” For one blog post where I questioned whether fault tree analysis was, as commonly claimed, a deductive process, I received two emails in perfect opposition, both suitably credentialed but unimpressively defended.
More surprising is hostility to endorsement of philosophy in general or philosophy of science (as in last post). It seems that for most scientist, engineers and Silicon Valley tech folk, “philosophy” conjures up guys in wool sportscoats with elbow patches wondering what to doubt next or French neoliberals congratulating themselves on having simultaneously confuted Freud, Marx, Mao, Hamilton, Rawls and Cato the Elder.
When I invoke philosophy here I’m talking about how to think well, not how to live right. And philosophy of science is a thing (hint: Google); I didn’t make it up. Philosophy of science is not about ethics. It has to do with that fact that most of us agree that science yields useful knowledge, but we don’t all agree about what makes good scientific thinking. I.e., what counts as evidence, what truth and proof mean, and being honest about what questions science can’t answer.
Philosophy is not, as some still maintain, a framework or ground on which science rests. The failure of logical positivism in the 1960s ended that notion. But the failure of positivism did not render science immune to philosophy. Willard Van Orman Quine is known for having put the nail in the coffin of logical positivism. Quine introduced a phrase I discussed in my last post – underdetermination of theory by data – in his 1951 “Two Dogmas of Empiricism,” often called the most important philosophical article of the 20th century. Quine’s article isn’t about ethics; it’s about scientific method. As Quine later said in Ontological Relativity and Other Essays (1969):
I see philosophy not as groundwork for science, but as continuous with science. I see philosophy and science as in the same boat – a boat which we can rebuild only at sea while staying afloat in it. There is no external vantage point, no first philosophy. All scientific findings, all scientific conjectures that are at present plausible, are therefore in my view as welcome for use in philosophy as elsewhere.
Philosophy helps us to know what science is. But then, what is philosophy, you might ask. If so, you’re halfway there.
Philosophy is the art of asking questions that come naturally to children, using methods that come naturally to lawyers. – David Hills in Jeffrey Kasser’s The Philosophy of Science lectures
The aim of philosophy, abstractly formulated, is to understand how things in the broadest possible sense of the term hang together in the broadest possible sense of the term. – Wilfrid Sellars, “Philosophy and the Scientific Image of Man,” 1962
This familiar desk manifests its presence by resisting my pressures and by deflecting light to my eyes. – WVO Quine, Word and Object, 1960
In past consulting work I’ve wrestled with subjective probability values derived from expert opinion. Subjective probability is an interpretation of probability based on a degree of belief (i.e., hypothetical willingness to bet on a position) as opposed a value derived from measured frequencies of occurrences (related posts: Belief in Probability, More Philosophy for Engineers). Subjective probability is of interest when failure data is sparse or nonexistent, as was the data on catastrophic loss of a space shuttle due to seal failure. Bayesianism is one form of inductive logic aimed at refining subjective beliefs based on Bayes Theorem and the idea of rational coherence of beliefs. A NASA handbook explains Bayesian inference as the process of obtaining a conclusion based on evidence, “Information about a hypothesis beyond the observable empirical data about that hypothesis is included in the inference.” Easier said than done, for reasons listed below.
Bayes Theorem itself is uncontroversial. It is a mathematical expression relating the probability of A given that B is true to the probability of B given that A is true and the individual probabilities of A and B:
P(A|B) = P(B|A) x P(A) / P(B)
If we’re trying to confirm a hypothesis (H) based on evidence (E), we can substitute H and E for A and B:
P(H|E) = P(E|H) x P(H) / P(E)
To be rationally coherent, you’re not allowed to believe the probability of heads to be .6 while believing the probability of tails to be .5; the sum of chances of all possible outcomes must sum to exactly one. Further, for Bayesians, the logical coherence just mentioned (i.e., avoidance of Dutch book arguments) must hold across time (synchronic coherence) such that once new evidence E on a hypothesis H is found, your believed probability for H given E should equal your prior conditional probability for H given E.
Plenty of good sources explain Bayesian epistemology and practice far better than I could do here. Bayesianism is controversial in science and engineering circles, for some good reasons. Bayesianism’s critics refer to it as a religion. This is unfair. Bayesianism is, however, like most religions, a belief system. My concern for this post is the problems with Bayesianism that I personally encounter in risk analyses. Adherents might rightly claim that problems I encounter with Bayes stem from poor implementation rather than from flaws in the underlying program. Good horse, bad jockey? Perhaps.
Problem 1. Subjectively objective
Bayesianism is an interesting mix of subjectivity and objectivity. It imposes no constraints on the subject of belief and very few constraints on the prior probability values. Hypothesis confirmation, for a Bayesian, is inherently quantitative, but initial hypotheses probabilities and the evaluation of evidence is purely subjective. For Bayesians, evidence E confirms or disconfirms hypothesis H only after we establish how probable H was in the first place. That is, we start with a prior probability for H. After the evidence, confirmation has occurred if the probability of H given E is higher than the prior probability of H, i.e., P(H|E) > P(H). Conversely, E disconfirms H when P(H|E) < P(H). These equations and their math leave business executives impressed with the rigor of objective calculation while directing their attention away from the subjectivity of both the hypothesis and its initial prior.
2. Rational formulation of the prior
Problem 2 follows from the above. Paranoid, crackpot hypotheses can still maintain perfect probabilistic coherence. Excluding crackpots, rational thinkers – more accurately, those with whom we agree – still may have an extremely difficult time distilling their beliefs, observations and observed facts of the world into a prior.
3. Conditionalization and old evidence
This is on everyone’s short list of problems with Bayes. In the simplest interpretation of Bayes, old evidence has zero confirming power. If evidence E was on the books long ago and it suddenly comes to light that H entails E, no change in the value of H follows. This seems odd – to most outsiders anyway. This problem gives rise to the game where we are expected to pretend we never knew about E and then judge how surprising (confirming) E would have been to H had we not know about it. As with the general matter of maintaining logical coherence required for the Bayesian program, it is extremely difficult to detach your knowledge of E from the rest of your knowing about the world. In engineering problem solving, discovering that H implies E is very common.
4. Equating increased probability with hypothesis confirmation.
My having once met Hillary Clinton arguably increases the probability that I may someday be her running mate; but few would agree that it is confirming evidence that I will do so. See Hempel’s raven paradox.
5. Stubborn stains in the priors
Bayesians, often citing success in the business of establishing and adjusting insurance premiums, report that the initial subjectivity (discussed in 1, above) fades away as evidence accumulates. They call this washing-out of priors. The frequentist might respond that with sufficient evidence your belief becomes irrelevant. With historical data (i.e., abundant evidence) they can calculate P of an unwanted event in a frequentist way: P = 1-e to the power -RT, roughly, P=RT for small products of exposure time T and failure rate R (exponential distribution). When our ability to find new evidence is limited, i.e., for modeling unprecedented failures, the prior does not get washed out.
6. The catch-all hypothesis
The denominator of Bayes Theorem, P(E), in practice, must be calculated as the sum of the probability of the evidence given the hypothesis plus the probability of the evidence given not the hypothesis:
P(E) = [P(E|H) x p(H)] + [P(E|~H) x P(~H)]
But ~H (“not H”) is not itself a valid hypothesis. It is a family of hypotheses likely containing what Donald Rumsfeld famously called unknown unknowns. Thus calculating the denominator P(E) forces you to pretend you’ve considered all contributors to ~H. So Bayesians can be lured into a state of false choice. The famous example of such a false choice in the history of science is Newton’s particle theory of light vs. Huygens’ wave theory of light. Hint: they are both wrong.
7. Deference to the loudmouth
This problem is related to no. 1 above, but has a much more corporate, organizational component. It can’t be blamed on Bayesianism but nevertheless plagues Bayesian implementations within teams. In the group formulation of any subjective probability, normal corporate dynamics govern the outcome. The most senior or deepest-voiced actor in the room drives all assignments of subjective probability. Social influence rules and the wisdom of the crowd succumbs to a consensus building exercise, precisely where consensus is unwanted. Seidenfeld, Kadane and Schervish begin “On the Shared Preferences of Two Bayesian Decision Makers” with the scholarly observation that an outstanding challenge for Bayesian decision theory is to extend its norms of rationality from individuals to groups. Their paper might have been illustrated with the famous photo of the exploding Challenger space shuttle. Bayesianism’s tolerance of subjective probabilities combined with organizational dynamics and the shyness of engineers can be a recipe for disaster of the Challenger sort.
All opinions welcome.
Arianna Huffington spoke at The Commonwealth Club in San Francisco last week. Interviewed by Facebook CEO Sheryl Sandberg, Huffington spoke mainly on topics in her recently published Thrive: The Third Metric to Redefining Success and Creating a Life of Well-Being, Wisdom, and Wonder. 2500 attendees packed Davies Symphony Hall. Several of us were men.
Huffington began with the story of her wake-up call to the idea that success is killing us. She told of collapsing from exhaustion, hitting the corner of her desk on the way down, gashing her forehead and breaking her cheek bone.
She later realized that “by any sane definition of success, if you are lying in a pool of blood on the floor of your office you’re not a success.”
After this epiphany Huffington began an inquiry into the meaning of success. The first big change was realizing that she needed much more sleep. She joked that she now advises women to sleep their way to the top. Sleep is a wonder drug.
Her reexamination of success also included personal values. She referred to ancient philosophers who asked what is a good life. She explicitly identified her current doctrine with that of the Stoics (not to be confused with modern use of the term stoic). “Put joy back in our everyday lives,” she says. She finds that we have shrunken the definition of success down to money and power, and now we need to expand it again. Each of us needs to define success by our own criteria, hence the name of her latest book. The third metric in her book’s title includes focus on well-being, wisdom, wonder, and giving.
Refreshingly (for me at least) Huffington drew repeatedly on ancient western philosophy, mostly that of the Stoics. In keeping with the Stoic style, her pearls often seem self-evident only after the fact:
“The essence of what we are is greater than whatever we are in the world.”
Take risk. See failure as part of the journey, not the opposite of success. (paraphrased)
I do not try to dance better than anyone else. I only try to dance better than myself.
“We may not be able to witness our own eulogy, but we’re actually writing it all the time, every day.”
“It’s not ‘What do I want to do?’, it’s ‘What kind of life do I want to have?”
“Being connected in a shallow way to the entire world can prevent us from being deeply connected to those closest to us, including ourselves.”
“‘My life has been full of terrible misfortunes, most of which never happened.'” (citing Montaigne)
As you’d expect, Huffington and Sandberg suggested that male-dominated corporate culture betrays a dearth of several of the qualities embodied in Huffington’s third metric. Huffington said the most popular book among CEOs is the Chinese military treatise, The Art of War. She said CEOs might do better to read children’s books like Silverstein’s The Giving Tree or maybe Make Way for Ducklings. Fair enough; there are no female Bernie Madoffs.
I was pleasantly surprised by Huffington. I found her earlier environmental pronouncements to be poorly conceived. But in this talk on success, wisdom, and values, she shone. Huffington plays the part of a Stoic well, though some of the audience seemed to judge her more of a sophist. One attendee asked her if she really believed that living the life she identified in Thrive could have possibly led to her current success. Huffington replied yes, of course, adding that she, like Bill Clinton, found they’d made all their biggest mistakes while tired.
Huffington’s quotes above align well with the ancients. Consider these from Marcus Aurelius, one of the last of the great Stoics:
Everything we hear is an opinion, not a fact. Everything we see is a perspective, not the truth.
Very little is needed to make a happy life; it is all within yourself, in your way of thinking.
Confine yourself to the present.
Be content to seem what you really are.
The object of life is not to be on the side of the majority, but to escape finding oneself in the ranks of the insane.
I particularly enjoyed Huffington’s association of sense-of-now, inner calm, and wisdom with Stoicism, rather than, as is common in Silicon Valley, with a misinformed and fetishized understanding of Buddhism. Further, her fare was free of the intellectualization of mysticism that’s starting to plague Wisdom 2.0. It was a great performance.
Preach not to others what they should eat, but eat as becomes you, and be silent. – Epictetus
In a recent post I mentioned that probabilistic failure models are highly vulnerable to wrong assumptions of independence of failures, especially in redundant system designs. Common-mode failures in multiple channels defeats the purpose of redundancy in fault-tolerant designs. Likewise, if probability of non-function is modeled (roughly) as historical rate of a specific component failure times the length of time we’re exposed to the failure, we need to establish that exposure time with great care. If only one channel is in control at a time, failure of the other channel can go undetected. Monitoring systems can detect such latent failures. But then failures of the monitoring system tend to be latent.
For example, your car’s dashboard has an engine oil warning light. That light ties to a monitor that detects oil leaks from worn gaskets or loose connections before the oil level drops enough to cause engine damage. Without that dashboard warning light, the exposure time to an undetected slow leak is months – the time between oil changes. The oil warning light alerts you to the condition, giving you time to deal with it before your engine seizes.
But what if the light is burned out? This failure mode is why the warning lights flash on for a short time when you start your car. In theory, you’d notice a burnt-out warning light during the startup monitor test. If you don’t notice it, the exposure time for an oil leak becomes the exposure time for failure of the warning light. Assuming you change your engine oil every 9 months, loss of the monitor potentially increases the exposure time from minutes to months, multiplying the probability of an engine problem by several orders of magnitude. Aircraft and nuclear reactors contain many such monitoring systems. They need periodic maintenance to ensure they’re able to detect failures. The monitoring systems rarely show problems in the check-ups; and this fact often lures operations managers, perceiving that inspections aren’t productive, into increasing maintenance intervals. Oops. Those maintenance intervals were actually part of the system design, derived from some quantified level of acceptable risk.
Common-mode failures get a lot press when they’re dramatic. They’re often used by risk managers as evidence that quantitative risk analysis of all types doesn’t work. Fukushima is the current poster child of bad quantitative risk analysis. Despite everyone’s agreement that any frequencies or probabilities used in Fukushima analyses prior to the tsunami were complete garbage, the result for many was to conclude that probability theory failed us. Opponents of risk analysis also regularly cite the Tacoma Narrows Bridge collapse, the Chicago DC-10 engine-loss disaster, and the Mount Osutaka 747 crash as examples. But none of the affected systems in these disasters had been justified by probabilistic risk modeling. Finally, common-mode failure is often cited in cases where it isn’t the whole story, as with the Sioux City DC-10 crash. More on Sioux City later.
On the lighter side, I’d like to relate two incidents – one personal experience, one from a neighbor – that exemplify common-mode failure and erroneous assumptions of exposure time in everyday life, to drive the point home with no mathematical rigor.
I often ride my bicycle through affluent Marin County. Last year I stopped at the Molly Stone grocery in Sausalito, a popular biker stop, to grab some junk food. I locked my bike to the bike rack, entered the store, grabbed a bag of chips and checked out through the fast lane with no waiting. Ninety seconds at most. I emerged to find no bike, no lock and no thief.
I suspect that, as a risk man, I unconsciously model all risk as the combination of some numerical rate (occurrence per hour) times some exposure time. In this mental model, the exposure time to bike theft was 90 seconds. I likely judged the rate to be more than zero but still pretty low, given broad daylight, the busy location with lots of witnesses, and the affluent community. Not that I built such a mental model explicitly of course, but I must have used some unconscious process of that sort. Thinking like a crook would have served me better.
If you were planning to steal an expensive bike, where would you go to do it? Probably a place with a lot of expensive bikes. You might go there and sit in your pickup truck with a friend waiting for a good opportunity. You’d bring a 3-foot long set of chain link cutters to make quick work of the 10 mm diameter stem of a bike lock. Your friend might follow the victim into the store to ensure you were done cutting the lock and throwing the bike into the bed of your pickup to speed away before the victim bought his snacks.
After the fact, I had much different thought thoughts about this specific failure rate. More important, what is the exposure time when the thief is already there waiting for me, or when I’m being stalked?
My neighbor just experienced a nerve-racking common mode failure. He lives in a San Francisco high-rise and drives a Range Rover. His wife drives a Mercedes. He takes the Range Rover to work, using the same valet parking-lot service every day. He’s known the attendant for years. He takes his house key from the ring of vehicle keys, leaving the rest on the visor for the attendant. He waves to the attendant as he leaves the lot on way to the office.
One day last year he erred in thinking the attendant had seen him. Someone else, now quite familiar with his arrival time and habits, got to his Range Rover while the attendant was moving another car. The thief drove out of the lot without the attendant noticing. Neither my neighbor nor the attendant had reason for concern. This gave the enterprising thief plenty of time. He explored the glove box, finding the registration, which includes my neighbor’s address. He also noticed the electronic keys for the Mercedes.
The thief enlisted a trusted colleague, and drove the stolen car to my neighbor’s home, where they used the electronic garage entry key tucked neatly into its slot in the visor to open the gate. They methodically spiraled through the garage, periodically clicking the button on the Mercedes key. Eventually they saw the car lights flash and they split up, each driving one vehicle out of the garage using the provided electronic key fobs. My neighbor lost two cars though common-mode failures. Fortunately, the whole thing was on tape and the law men were effective; no vehicle damage.
Should I hide my vehicle registration, or move to Michigan?
In theory, there’s no difference between theory and practice. In practice, there is.