ICES Training Programme recently offered Introduction to Bayesian Inference in Fisheries Science, conducted by Ray Hilborn and Samu Mäntyniemi. It was attended by 26 students from 17 countries.
Ray Hilborn, one of today’s leading experts on fisheries, is a professor in the School of Aquatic and Fishery Sciences, University of Washington, specializing in natural resource management and conservation. He serves as an advisor to several international fisheries commissions and agencies as well as teaching graduate and undergraduate courses in conservation, fishery stock assessment, and risk analysis. He is author of Quantitative Fisheries Stock Assessment, with Carl Walters, and The Ecological Detective: Confronting Models with Data, with Marc Mangel.
What is Bayesian statistics?
Bayesian statistics is one variety of statistics. Depending on how you divide it, you could say there are three primary schools. Beginning statistics courses centre on the concept of the null hypothesis and whether the data support rejection of the null hypothesis; usually, statistics are reported so that the probability of the null hypothesis is false. Then, there is the probability that you can reject the null hypothesis, and that’s often called Frequentive statistics. Finally, there’s another school, the Likelihoodist, that deals primarily with the extent to which the data support competing hypotheses. It’s a more interesting statistic because it realizes that you often have multiple different hypotheses, which is interesting to the extent that the data support the different hypotheses.
Bayesian statistics is, in a sense, much like the Likelihoodist, but it goes the additional step of actually assigning probabilities to competing hypotheses. The reason that’s so important is that, when you are giving advice to decision-makers, they want to know what’s the chance that something will happen. It turns out that Bayesian statistics is the only form of statistics that philosophically claims that they are probabilities. Going back – I guess I first ran into Bayesian statistics about 35 years ago – you find that Bayesian statistics really dominated business schools because they were built around decision-making.
Frequentive statistics dominated academic departments because they didn’t think in terms of decision-making. At the time, there was a strong divide between traditional statisticians and Bayesian statistics, almost like religions. More recently, statisticians play in both camps. They use one or the other, depending on the kind of problem they are solving or the questions they’re asking.
The most controversial element of Bayesian statistics is that it always begins with subjective probabilities. You start a Bayesian problem asking, what do I believe about the different hypotheses? Many people find this objectionable; they’re only interested in what the data tell us.
Decision-makers want to know probabilities, and Bayesian statistics is the only statistics that claim to do it. This makes sense because science is an incremental process. Isaac Newton said, “If I’ve seen farther, it’s by standing on the shoulders of giants”.
If you take the naive view that you’re only interested in what the data tell us, it means that you’ve learned nothing from all the previous experience of fisheries: every fishery is a new problem, and there is no accumulation of knowledge. The basic philosophy we’re teaching is that when you’re approaching any new problem in fisheries, you should be figuring out how to take all the cumulative knowledge that we’ve gained and apply it to this particular problem. Conceptually, it’s very straightforward.
When you get some data, that data updates your previous understanding, and if the data are very strong – that is, they’re very consistent and very informative – then your previous understanding will be completely pushed aside, and you’ll really be dominated by the data in front of you But if the data are very weak, then it’ll just move your previous beliefs a little bit, and that’s really how Bayesian statistics work. You’re nodding, so obviously I’ve completely convinced you that you’ll be a Bayesian statistician.
Absolutely. Can it be applied on a stock-by-stock basis or on a larger scale?
Both. The obvious application is to individual stock-by-stock problems, so let’s take the simple example of how many fish are there in a stock? What’s the population size? Bayesian statistics will give you a probability distribution. For example, there’s a 10 percent chance it’s in this range and a 20 percent chance…. No other form of statistics does that.
There are other methods that generate these distributions, and people often pretend that they are probability distributions, but they aren’t, and it’s really a perversion of those other approaches to call them probability distributions. The other approach people have taken is just to say, “our best guess is that there are 250 000 tons of fish, and we’re not going to consider the consequences of it being lower or higher”.