Nuclear will die. Solar will live.

In a recent article, I suggestedthat batteries might replace oil for many of our transportation needs within two decades. Batteries store energy, and we need a way to produce that energy in the form of electricity. Currently we produce most of our electricity from natural gas and coal. And while our use of natural gas and coal doesn’t feed the coffers of unsavory regimes like Russia and Saudi Arabia the way our use of oil does, it’s still the case that these energy sources are limited. They run out.  What will replace them?

                

The leading candidate is solar power. Cost is droppinglike a rock, including “balance of system” costs that include things like installation and land. For an update on the status of solar power, see this excellent article from The Economist. Of course, improvements in battery storage are very helpful for solar, since you need to store some energy for nighttime.

                

But there is still a strong contingent out there who is dead-set against the solar revolution – not because they want to keep using fossil fuels, but because they are convinced that only nuclear power can solve our energy crunch.

                

One example of this faction is the Breakthrough Institute, which regularly releases articlescomparing nuclear and solar, invariably supporting the former over the latter. Of course, solar costs continue to perform much, much better than they predict, but they continue to insist that nuclear – and only nuclear – must be the energy source of the future.

                

I’m always a bit puzzled by the anti-solar antipathy of the pro-nuclear crowd. Energy is energy, after all. Perhaps nuclear looks muscular and futuristic – an emblem of national greatness – while solar looks like wimpy hippie stuff.

                

But regardless of people’s feelings, the fact is that conventional nuclear power – by which I mean uranium fission, the kind of thing Mr. Burns produces on The Simpsons – is on the way out. This is not a cry of triumph on my part, but a lament. Nuclear power is cool. It’s just not the future.

                

For the most convincing evidence that uranium fission is on the way out, I again point you to The Economist. Their 2012 special report, called “The Dream That Failed,” shows how nuclear usage is flat, and expected to decline in rich countries.

                

There are three basic reasons conventional nuclear is dead: cost, safety risk, and obsolescence risk. These factors all interact.

                

First, cost. Unlike solar, which can be installed in small or large batches, a nuclear plant requires an absolutely huge investment. A single nuclear plant can cost on the order of $10 billion U.S. That is a big chunk of change to plunk down on one plant. Only very large companies, like General Electric or Hitachi, can afford to make that kind of investment, and it often relies on huge loans from governments or from giant megabanks. Where solar is being installed by nimble, gritty entrepreneurs, nuclear is still forced to follow the gigantic corporatist model of the 1950s.

                

Second, safety risk. In 1945, the U.S. military used nuclear weapons to destroy Hiroshima and Nagasaki, but a decade later, these were thriving, bustling cities again. Contrast that with Fukushima, site of the 2011 Japanese nuclear meltdown, where whole towns are still abandoned. Or look at Chernobyl, almost three decades after its meltdown. It will be many decades before anyone lives in those places again. Nuclear accidents are very rare, but they are also very catastrophic – if one happens, you lose an entire geographical region to human habitation.

                

Finally, there is the risk of obsolescence. Uranium fission is a mature technology – its costs are not going to change much in the future. Alternatives, like solar, are young technologies – the continued staggering drops in the cost of solar prove it. So if you plunk down $10 billion to build a nuclear plant, thinking that solar is too expensive to compete, the situation can easily reverse in a couple of years, before you’ve recouped your massive fixed costs.

                

If you want to see these forces at work on the largest possible scale, look at the example of Japan. Japan was a leader in solar when the technology first emerged, but the government bet big on nuclear. Now, with nuclear power suddenly…um…radioactive following Fukushima, Japan is struggling to catch up in solar. Meanwhile, huge losses by the Japanese nuclear industry are going to land in the lap of the government and the too-big-to-fail banks.

                

Oops.

Uranium fission was a great idea, but it hasn’t worked out. If nuclear fission is going to be viable in the future, it’s going to require thorium fuel (which is much safer than uranium) and much smaller, cheaper reactor designs. Those technologies are still in the research stage, not ready for immediate use. Meanwhile, solar power is racing ahead much faster than anyone expected, continuing to beat all the forecasts.

Our government should continue to fund research into next-generation nuclear power. But what next-generation energy source should we be installing, right now? It’s not even a contest. Solar beats nuclear.

Priors and posteriors

A really wonderful blog post by Stephen Senn, head of the Methodology and Statistics Group at the Competence Center for Methodology and Statistics in Luxembourg, sums up the philosophical problem I've always had with Bayesian inference in scientific studies. Basically, the question is: Where does the prior come from? Senn argues that it can't be your real prior, since you can't quantify your real prior.

Where else could your prior come from? Here's the list I thought of:

1. You could use a "standard" prior that a bunch of other people use because it's "noninformative" in some sense (e.g. a Jeffreys prior). See this Larry Wasserman blog post on some of the potential problems with that approach.

2. You could use some prior that comes from empirical data. This is the foundation of the "empirical Bayes" approach.

3. You could choose a bunch of different priors and see how sensitive the posterior is to the choice of prior. This could be done in a haphazard or a systematic way, and it's not immediately clear if one of those is always better than the other. The drawback of this approach is that it's a bit cumbersome, and hard to interpret.

4. You could choose a prior that is close to the answer you want to get. The less informative your data is, the closer your prior will be to your posterior. This seems a bit scientifically dishonest. But I bet someone out there has tried it.

5. You can choose an "adversarial prior" that is similar to what you think someone who disagrees with your conclusion would say. (Thanks to Sean J. Taylor of Twitter for pointing this out.)

Have I missed any big ones?

Anyway, as always in stats, there's some element of intuition that can't be incorporated into the estimation in a systematic way.

Anyway, Andrew Gelman, one of the high priests of Bayesianism, so to speak, had this to say about Senn's post:

I agree with Senn’s comments on the impossibility of the de Finetti subjective Bayesian approach. As I wrote in 2008, if you could really construct a subjective prior you believe in, why not just look at the data and write down your subjective posterior. The immense practical difficulties with any serious system of inference render it absurd to think that it would be possible to just write down a probability distribution to represent uncertainty. I wish, however, that Senn would recognize “my” Bayesian approach (which is also that of John Carlin, Hal Stern, Don Rubin, and, I believe, others). De Finetti is no longer around, but we are! 

I have to admit that my own Bayesian views and practices have changed. In particular, I resonate with Senn’s point that conventional flat priors miss a lot and that Bayesian inference can work better when real prior information is used. Here I’m not talking about a subjective prior that is meant to express a personal belief but rather a distribution that represents a summary of prior scientific knowledge. Such an expression can only be approximate (as, indeed, assumptions such as logistic regressions, additive treatment effects, and all the rest, are only approximations too), and I agree with Senn that it would be rash to let philosophical foundations be a justification for using Bayesian methods. Rather, my work on the philosophy of statistics is intended to demonstrate how Bayesian inference can fit into a falsificationist philosophy that I am comfortable with on general grounds.

Cool.

Update: Thinking about it a little more, I don't think Senn's point really has any implications for study design. But it does seem to have implications for how a "client" (or reader of a paper) should treat a "Bayesian" researcher's results. Basically, a researcher doing Bayesian inference is not the same as a Bayesian agent in a model. A Bayesian agent in a model always uses her own prior, and thus always uses information optimally. A researcher doing Bayesian inference cannot use his own prior, and so may not be using information optimally. So using Bayesian inference shouldn't be a free ticket to respectability for research results.

Postwar vs. New Gilded Age: How did the middle class do?

Here's another point in the ongoing debate over the fate of the American middle class in recent decades (installment 1 here, installment 2 here).

In his original post, Brad DeLong wrote:

Across most of the income distribution Americans today are little if any better off than their predecessors back in 1979...For 150 years before 1979 Americans had confidently expected that each generation would live roughly twice as well in a material sense as its predecessor, not find itself struggling against the current to stay in the same place.

In my previous posts, I pointed out that median household income had increased. But let's just look at median individual income. Was 1979-2000 really worse than the postwar period, for the average person?

Let's look at the relative performance of the period, not its absolute performance.

I found this cool graph from the Russell Sage Foundation. Using Census data, it shows inflation-adjusted median and mean household and individual income, starting in 1947:

Median individual income in constant 2012 dollars is the green time series. I drew three horizontal lines, corresponding to 1947, 1979, and 2000. 

From 1947 to 1979, real median individual income went from around $16,000 to around $21,000 - a total increase of about 32%. That is a compound annual growth rate of about 0.8%.

From 1979 to 2000, real median individual income went from around $21,000 to around $28,000 - a total increase of about 33%. That is a compound annual growth rate of about 1.38%.

Let's do a comparison that's a little more favorable to DeLong and Thomas' argument, and a little less favorable to mine. Let's use 1972 as the end of the "good" times and 1972-2012 as the "bad" times.

From 1947 to 1972,  real median individual income went from around $16,000 to around $23,000 - a total increase of about 48%. That is a compound annual growth rate of about 1.46%.

From 1972 to 2012,  real median individual income went from around $23,000 to around $27,000 - a total increase of about 17%. That is a compound annual growth rate of about 0.4%.

Finally, From 1979 to 2012,  real median individual income went from around $21,000 to around $27,000 - a total increase of about 28%. That is a compound annual growth rate of about 0.76%.

You can play around with these numbers more, but several conclusions emerge:

Conclusion 1: If you go by personal rather than household income, it is not true, as Brad asserts, that the average American saw his or her material standard of living double in the Postwar period.

Conclusion 2: The period from 1979-2000 - the Late 20th Century Boom - was about as good for the average American's income as the Postwar Boom period from 1947-1972. The Postwar Boom wins, but only slightly, since both booms have fairly high compound growth rates.

Conclusion 3: The Total Postwar period, from 1947 through 1979, is almost exactly the same as the Total New Gilded Age from 1979-2012, although both have fairly low compound growth rates.

Conclusion 4: The Late 20th Century Boom thoroughly thumps the Total Postwar Period (1947-1979) in terms of the growth in the material standard of living of the average American.

Conclusion 5: The 1970s was bad, but was over quickly. The Post-2000 period has also been bad, and is stretching out for longer than the 1970s.

In other words, Brad DeLong's contention that the average American saw a dramatic slowdown or reversal in the rate of growth of his or her material standard of living in 1979 is not supported by this evidence. And his contention that the Postwar rate of growth in material standard of living represented a generational doubling is not correct, if you exclude the effects of technological improvements. It was more like a 33%-50% increase.

And my contention that the period from 1979-2000 was a great time for the average American's material standard of living is correct, if you compare it to the period from 1947 -1979, and even looks pretty good if you compare it only to the best Postwar decades.

Again, this is not accounting for leisure and home production. But observe that the Postwar period, just like the period from 1980-2000, saw a steady increase in the percent of women in the labor force:

Therefore, hours spent on home production were decreasing at about the same rate in the Postwar period as in 1979-2000. In other words, although women's workforce entry contributed more to rising income in 1979-2000 (because women's wages had converged somewhat with men's by then), the rate at which household production hours were sacrificed - the rate at which women exited the home and went into the workforce - was roughly the same in both periods.

So as I see it, the entire case that 1979-2000 represented a dramatic slowdown in the growth of material living standards relative to the Postwar period rests on the fact that leisure increased during the Postwar but flatlined during 1979-2000:

If you want to make the case that the American economy did dramatically worse for the average American in 1979-2000 than in 1947-1979, this is the most convincing case I can think of. 

(Note: I still think the Postwar period represented a much bigger jump in the welfare of Americans, since marginal utility of consumption is concave. Getting food on the table, warm clothes, and a roof over your head is vastly more important than getting a bigger house, a second car, etc.)