Archive for January, 2016
My Trouble with Bayes
Posted by Bill Storage in Philosophy of Science, Probability and Risk, Uncategorized on January 21, 2016
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.
Science, God, and the White House
Posted by Bill Storage in Philosophy of Science on January 9, 2016
Back in the 80s I stumbled upon the book, Scientific Proof of the Existence of God Will Soon Be Announced by the White House!, by Franklin Jones, aka Frederick Jenkins, later Da Free John, later Adi Da Samraj. I bought it on the spot. Likely a typical 70s mystic charlatan, Jones nonetheless saw clearly our poor grasp of tools for seeking truth and saw how deep and misguided is our deference to authority. At least that’s how I took it.
Who’d expect a hippie mystic to be a keen philosopher of science. The book’s title, connecting science, church and state, shrewdly wraps four challenging ideas:
- That there can be such a thing as scientific proof of anything
- That there could be new findings about the existence of God
- That evidence for God could be in the realm of science
- That government should or could accredit a scientific theory
On the first point, few but the uneducated, TIME magazine, and the FDA think that proof is in the domain of science. Proof is deductive. It belongs to math, logic and analytic philosophy. Science uses evidence and induction to make inferences to the best explanation.
Accepting that strong evidence would suffice as proof, point number 2 is a bit trickier. Evidence of God’s existence can’t be ruled out a priori. God could be observable or detectable; we might see him or his consequences. An almighty god could easily have chosen to regularly show himself or to present unambiguous evidence. But Yahweh, at least in modern times, doesn’t play like that (A wicked and adulterous generation demands a sign but none will be given – Matthew 16:4). While believers often say no evidence would satisfy the atheist, I think a focused team could come up with rules for a demonstration that at least some nonbelievers would accept as sufficient evidence.
Barring any new observations that would constitute evidence, point number 3 is tough to tackle without wading deep into philosophy of science. To see why, consider the theory that God exists. Is it even a candidate for a scientific theory, as one WSJ writer thinks (Science Increasingly Makes the Case for God)? I.e., is it the content of a theory or the way it is handled by its advocates that makes the theory scientific? If the latter, it can be surprisingly hard to draw the line between scientific investigations and philosophical ones. Few scientists admit this line is so blurred, but how do string theorists, who make no confirmable or falsifiable predictions, defend that they are scientists? Their fondness for non-empirical theory confirmation puts them squarely in the ranks of the enlightenment empiricist, Bishop Berkeley of Cloyne (namesake of our fair university) who maintained that matter does not exist. Further, do social scientists make falsifiable predictions, or do they just continually adjust their theory to accommodate disconfirming evidence?
That aside, those who work in the God-theory space somehow just don’t seem to qualify as scientific – even the young-earth creationists trained in biology and geology. Their primary theory doesn’t seem to generate research and secondary theories to confirm or falsify. Their papers are aimed at the public, not peers – and mainly aim at disproving evolution. Can a scientific theory be primarily negative? Could plate-tectonics-is-wrong count as a proper scientific endeavor?
Gould held that God was simply outside the realm of science. But if we accept that the existence of God could be a valid topic of science, is it a good theory? Following Karl Popper, a scientific theory can withstand only a few false predictions. On that view the repeated failures of end-of-days predictions by Harold Camping and Herbert Armstrong might be sufficient to kill the theory of God’s existence. Or does their predictive failures simply exclude them from the community of competent practitioners?
Would NASA engineer, Edgar Whisenant be more credible at making predictions based on the theory of God’s existence? All his predictions of rapture also failed. He was accepted by the relevant community (“…in paradigm choice there is no standard higher than the assent of the relevant community” – Thomas Kuhn) since the Trinity Broadcast Network interrupted its normal programming to help watchers prepare. If a NASA engineer has insufficient scientific clout, how about our first scientist? Isaac Newton predicted, in Observations upon the Prophecies of Daniel and the Apocalypse of St. John, that the end would come in 2000 CE. Maybe Newton’s calculator had the millennium bug.
If we can’t reject the theory for any number of wrong predictions, might there be another basis for rejecting it? Some say absence of a clear mechanism is a good reason to reject theories. In the God theory, no one seems to have proposed a mechanism by which such a God could have arisen. Aquinas’s tortured teleology and Anselm’s ontological arguments still fail on this count. But it seems unfair to dismiss the theory of God’s existence on grounds of no clear mechanism, because we have long tolerated other theories deemed scientific with the same weakness. Gravity, for example.
Does assent of the relevant community grant scientific status to a theory, as Kuhn would have it? If so, who decides which community is the right one? Theologians spend far more time on Armageddon than do biologists and astrophysicists – and theologians are credentialed by their institutions. So why should Hawking and Dawkins get much air time on the matter? Once we’ve identified a relevant community, who gets to participate in its consensus?
This draws in point number 4, above. Should government or the White House have any more claim to a scientific pronouncement than the Council of Bishops? If not, what are we to think of the pronouncements by Al Gore and Jerry Brown that the science of climate is settled? Should they have more clout on the matter than Pope Francis (who, interestingly, has now made similar pronouncements)?
If God is outside the realm of science, should science be outside the jurisdiction of government? What do we make of President Obama’s endorsement of “calling out climate change deniers, one by one”? You don’t have to be Franklin Jones or Da Free John to see signs here of government using the tools of religion (persecution, systematic effort to censure and alienate dissenters) in the name of science. Is it a stretch to see a connection to Jean Bodin, late 16th century French jurist, who argued that only witches deny the existence of witches?
Can you make a meaningful distinction between our government’s pronouncements on the truth or settledness of the climate theory (as opposed to government’s role in addressing it) and the Kremlin’s 1948 pronouncement that only Lamarckian inheritance would be taught, and their call for all geneticists to denounce Mendelian inheritance? Is it scientific behavior for a majority in a relevant community to coerce dissenters?
In trying to draw a distinction between UN and US coercion on climate science and Lysenkoism, some might offer that we (we moderns or we Americans) are somehow different – that only under regimes like Lenin’s and Hitler’s does science get so distorted. In thinking this, it’s probably good to remember that Hitler’s eugenics was born right here, and flourished in the 20th century. It had nearly full academic support in America, including Stanford and Harvard. That is, to use Al Gore’s words, the science was settled. California, always a trendsetter, by the early 1920s, claimed 80% of America’s forced sterilizations. Charles Goethe, founder of Sacramento State University, after visiting Hitler’s Germany in 1934 bragged to a fellow California eugenicist about their program’s influence on Hitler.
If the era of eugenics seems too distant to be relevant to the issue of climate science/politics, consider that living Stanford scientist, Paul Ehrlich, who endorsed compulsory abortion in the 70s, has had a foot in both camps.
As crackpots go, Da Free John was rather harmless.
________
“Indeed, it has been concluded that compulsory population-control laws, even including laws requiring compulsory abortion, could be sustained under the existing Constitution if the population crisis became sufficiently severe to endanger the society.” – Ehrlich, Holdren and Ehrlich, EcoScience, 3rd edn, 1977, p. 837
“You will be interested to know that your work has played a powerful part in shaping the opinions of the group of intellectuals who are behind Hitler in this epoch-making program.” – Charles Goethe, letter to Edwin Black, 1934
Fine Tuned Fibs for the Cause
Posted by Bill Storage in Philosophy of Science on January 7, 2016
In my last post I compared our self-policing of facts that might chip away at our beliefs about environmental religion to lying for God in medieval and ancient times – something the writer of the epistles seems to boast of doing. Lying for God, on matters of science, may still be with us today.
William Lane Craig argues, in a line of thinking he calls reasonable faith (see his video), that the apparent fine tuning of the universe allowing life in it to exist can only be explained as the work a designer. For Craig that designer happens to be the God of evangelical Protestantism.
Fine tuning has two different but related meanings in physics. The first deals mainly with theory, the second mainly with observation – something for Descartes, and something for Bacon.
In theory selection, fine tuning refers to how the details of a theory might need to be tweaked to make them fit observations. For example, in Ptolemaic astronomy, as used prior to Copernicus, the model only matched measurements if the planets’ epicycles stayed put in comparison to the straight line connecting the earth and sun and if the periods of the epicycles were exactly one year. Given those restrictions, the Ptolemaic model made good predictions. But why would those particular quantities have such relations? No reason could be found other than that they needed to be that way for the model to work. In Ptolemy’s defense, he did not believe the model represented reality; it merely gave right predictions. But the church believed it; and they forbade the teaching of the Copernican model. Copernicus’s model gave no better predictions; and it didn’t explain the lack of parallax in star positions or why a rotating earth didn’t suffer from great winds. But, Copernicus didn’t rely on fine tuning of his theory. What criterion is most important in theory selection – absence of fine tuning, predictive success, or explanatory power? That’s a topic for another time I guess. Read Paul Feyerabend on the matter if it grabs you.
In modern physics, fine tuning more commonly refers to our observation that many of the measured values that are, to our knowledge, constant across the universe have values that, were they even slightly different, would prevent life from being possible anywhere. Martin Rees, perhaps the first scientist to delve deep into the matter, identified six dimensionless constants (ratios of things we measure in physics, basically) on which life as we know it depends. These include the ratio of electromagnetic strength to the strength of gravity, the ratio of the mass density of the universe to the density required to halt expansion, and the so-called cosmological constant, the ratio of dark energy density in the universe to the density that would be needed to halt its expansion.
Popular examples of such fine tuning include the claim that if the electromagnetism/gravity ratio differed by an almost infinitesimal amount – say 1 part in 10 to the 40th power (1E-40) – things would be very quiet indeed. With a bit more gravity, stars would be too small and would burn out far too fast. Tweaking the other constants makes things even worse. Adjusting the cosmological constant to a few parts in ten to the 120 in either direction would make the universe either expand too fast for galaxies and stars to form or to collapse upon itself just after the big bang. These are unimaginably large/small numbers. A few scientists argue that our thinking is wrong here – again a topic for later. If interested, see Why the Universe Is Not Designed for Us by Victor J. Stenger.
William Lane Craig accepts that fine tuning exists, giving three possible explanations: physical necessity, chance, or design. Craig rules out necessity because a life-prohibiting universe is easily imaginable. He notes that the probabilities for these incredibly fine-tuned values to occur by chance is ridiculously remote, thus leaving design as the only alternative.
Now I can’t know Craig’s motives or his state of mind, but his argument here is consistent with someone who knows more than he’s telling. That is, Craig is clearly highly intelligent; he has command of analytic philosophy, mathematics and at least a decent knowledge of physics. Yet he starts his fine tuning evangel with an egregious example of privileged hypothesis on top of false choice – just to start. Is he sure the given alternatives are the only live options? And can chance be ruled out in a multiverse model? I.e., in a model with 10 to the 500 instances of what we call our universe, you’re pretty much bound to get a few that look like ours with randomized values for the physical constants.
But we need not start with an exotic option. Did Craig rule out combinations of necessity and chance? Did he challenge the problem statement from the beginning? Many other have – questioning the notion that these measure values aren’t environmental constants at all; perhaps we’ve misconceived an underlying relationship that ties the values together in the same way pi is tied to 3.141592. Part of Stenger’s work is along these lines.
Having given his rationale for preferring the designer hypothesis to an artificially restricted set of alternatives, Craig then takes the leap from designer to the God of evangelical Christianity. That is, Krishna, Zeus, Ahura Mazda and the spaghetti monster are off the table. Craig holds that a being with unlimited cosmic power – who could construct any universe of his choosing – used his infinite powers to fine tune that universe to the precise values of constants that would allow that universe to support galaxies, stars and life. It’s hard for me to believe Craig doesn’t see the contradiction in an argument involving a God of ultimate power being bound by laws of physics. That is, Craig’s God is praiseworthy for essentially outwitting – by a tiny margin – physical laws that are nearly out of his control. This seems a better argument for the religion of the Assyrians than for evangelical Christianity; it recalls Marduk’s narrow defeat over Tiamat.
In Reasonable Faith, Craig deals often with the concept of insincere arguments. Do his religious convictions cause him to be blind to elementary fallacies and contradictions in his own doctrine? Or is he simply lying for the cause?
“…unbelief is at root a spiritual, not an intellectual, problem.” – William Lane Craig, Reasonable Faith: Christian Truth and Apologetics, 3rd edn., p.59
But You Need the Data
Posted by Bill Storage in Multidisciplinarians on January 4, 2016
In my last post, But We Need the Rain, I suggested that environmentalist animism in San Francisco may fill the role once filled by religious belief, and may suffuse daily life as Christian belief did in medieval Europe. As the phrase “God be with ye” once reminded countrymen of correct thinking, so too might acknowledgment that we need the rain.
Medieval institutions – social and governmental – exerted constant pressure steering people away from wrong thinking; and the church dissuaded its flock from asking the wrong questions. Telling a lie to save a soul was OK; deceiving heathens into Christianity was just fine. I wonder if a weaker form of this sentiment remains in my fair city – in the form of failing to mention relevant facts about an issue and through the use of deceptive and selective truths. As theologian Thomas Burnet put it in the early 18th century, too much light is hurtful to weak eyes.
The San Francisco Chronicle, according to Google data, has published over 50 articles in the last two years mentioning the Shasta and Oroville reservoirs in connection with California’s four-year-old drought. Many of these pieces call attention to low levels of these reservoirs, e.g., Shasta was at 53% of normal level in January 2014.
None mention that Shasta and Oroville were, despite the drought, at 108% and 101% of normal level in April 2013, two years into the drought. Climate is mentioned in nearly all sfgate.com articles on the drought, but mismanagement of water resources by governments is mentioned in only one. Digging a bit deeper – with other sources – you’ll find bitter disputes between farmers saying water is wasted on environmental restoration and environmentalists asking why desert farmers want to grow thirsty crops like rice and cotton. I’d think Northern California citizens, asked by the governor to bathe less, might be interested in why so much of the Shasta and Oroville water left the reservoirs – whether they want to blame Sacramento, farmers, or environmentalists – and in the details of the dispute.
Is the Chronicle part of a conspiracy to get liberals in power by linking the water shortage to climate change rather than poor governance? I doubt it. There are no conservatives to displace. More likely, it seems to me, the Chronicle simply mirrors the values and beliefs held by its readers, an unusually monolithic community with a strong uniformity of views. The sense of identification with a community here somewhat resembles that of a religious group, where there’s a tendency for beliefs to be held as true by individuals because they are widely believed by the group – and to select or reject evidence based on whether it supports a preexisting belief.
“Being crafty, I caught you with guile.” – 2 Corinthians, 12:16
But We Need the Rain
Posted by Bill Storage in Multidisciplinarians on January 1, 2016
Chance outdoor meetings on recent damp days in San Francisco tend to start or finish (or both) with the statement, “but we need the rain.” No information is conveyed by these words. Their recipient already knows we need the rain. And the speaker knows the recipient knows it. Perhaps it is said aloud to be sure the nature gods hear it and continue to pour forth the blessings. Perhaps it reveals competitive piety – a race to first claim awareness of our climate-change sins. Or maybe it has just become a pleasant closing of a street encounter along the lines of “good bye.”
Of course, we don’t need the rain. San Francisco’s water supply falls 200 miles east of here and is collected in Hetch Hetchy Reservoir, eternally under attack from activists who insist their motive is environmental restoration, not anti-capitalism. We don’t pump water that falls at sea level up into our reservoirs, nor do we collect water that falls on the coast. A coastal system that dumps rain in San Francisco does not mean it’s raining in the Sierras.
So California’s High Sierras need the rain, not us. But saying “but we need the rain” does little harm. Saying it lets the gods know we are grateful; and saying it reminds each other to be thankful.
“We need the rain” may have more in common with “good bye” than is apparent to most. Etymologists tell us that “God be with ye” became “God b’wy” by the mid-1600s, and a few decades later was “good b’wy,” well on its way to our “good bye,” which retains the ending “ye” as a reminder of its genesis
In the homogenous cultures of pre-enlightenment Europe, God was a fact of the world, not a belief of religion. “God be with ye” wasn’t seen as a religious sentiment. It was an expression of hopefulness about a universe that was powered by God almighty, the first cause and prime mover, who might just be a providential God hearing our pleas that He be with ye. Am I overly cynical in seeing a connection?
Rain be with ye.
The Multidisciplinarian 