Research

My research over the past few years has focused on several connected strands in formal epistemology, decision theory, statistical inference, and general philosophy of science, and in particular on Bayesian approaches within these fields. Listed below are four projects that I find interesting and would like to work on in the next few years. The first two projects spring from work done in my dissertation, whereas the second two are projects unrelated to my dissertation.

Probability and verisimilitude

According to Bayesians, the probability of a hypothesis is supposed to represent the probability that the hypothesis is true. However, many of the models studied in the sciences – including models studied by Bayesian statisticians – include idealizations and approximations that render the models strictly speaking false. Nevertheless, even though many scientific models are strictly speaking false, some models are clearly better than others, and, intuitively, evidence can be used to discriminate in a principled way between multiple false models. However, Bayesian confirmation theory apparently cannot account for this. For, presumably, a scientist who knows a model M to be false should assign M a probability of 0. But in that case no evidence can ever either confirm or disconfirm M, since a model that is assigned a prior probability of 0 will also have a posterior probability of 0, regardless of the evidence. I call this problem the “interpretive problem.”

In my dissertation, I investigate whether the Bayesian framework can accommodate the idea that some false hypotheses can be closer to the truth (i.e. have a higher "verisimilitude") than others. Implicitly, I think scientists must operate with some, indeed several, tacit notions of verisimilitude. The interesting thing about the Bayesian framework is that scientists who use Bayesian methods with false hypotheses are apparently forced to rank hypotheses implicitly by their verisimilitude. Several questions now arise. For example, how may scientists use their background knowledge to rank hypotheses by their verisimilitude in a principled way? What measures of verisimilitude are compatible with the Bayesian framework?

In my dissertation, I argue that predictive accuracy is one kind of verisimilitude that Bayesians can take on board, provided Bayesian probabilities are interpreted as something other than degrees of belief. Moreover, I argue that scientists have background information regarding which hypotheses are more predictively accurate than others, and that they can sometimes use this background knowledge in a principled way to construct reasonable prior probabilities (i.e., probabilities one assigns to a set of hypotheses prior to any observations). However, I need to do more research in order to figure out what other goals can be accommodated in the Bayesian framework, aside from discovering the truth or the most predictively accurate hypothesis. I am also interested in exploring how foundational Bayesian evidential principles like the Likelihood Principle and the Law of Likelihood change when the Bayesian framework is reinterpreted in different ways. According to preliminary work I have done, there is also an interesting connection between reinterpretations of probability and Bayesian versions of Ockham’s razor. In future research, I wish to explore this further.

Interpreting the Bayesian framework and other formal frameworks

How to interpret properly the Bayesian framework, and other formal frameworks, has potentially large implications for our understanding of epistemic and practical rationality. For example, in my dissertation I argue that the Bayesian probability that it is rational for an agent to assign to a hypothesis depends on the goals of the agent. If the standard Bayesian interpretation of probability is correct, and the probability that an agent assigns to a hypothesis represents the agent’s degree of belief in the hypothesis, then the implication is that whether an agent’s degree of belief in a hypothesis is rational depends on the goals of the agent. That is a startling implication. For example, whether your degrees of belief concerning the current barometric pressure are rational depends on whether your goal is to have correct beliefs about the barometric pressure or whether your goal is to avoid getting caught in the rain.

However, an alternative stance is that the Bayesian framework should not be interpreted as applying directly to agent’s degrees of belief at all. Indeed, there are several ways in which the Bayesian framework seems descriptively inaccurate as a framework for rational human reasoning. This motivates interpreting the Bayesian framework in general, and Bayesian probabilities specifically, as pragmatic tools that agents can use to accomplish certain goals. The idea here is that Bayesian probabilities are a convenient way of keeping track of how well hypotheses are doing with respect to evidence, and that Bayesian probabilities and utilities can be a useful fiction for making and evaluating decisions.

I find myself vacillating between the preceding two ways of understanding the Bayesian framework. Similar concerns come up with other quantitative frameworks of rationality. The bigger-picture questions here are, among others: do epistemic and practical rationality have particular quantitative structures? If so, are the structures unified and how do we know what the structures are? If not, then what is the normative force of a quantitative framework such as Bayesianism?

Causal assumptions behind prior probabilities

In the sciences, a prior probability distribution over a set of hypotheses should ideally be (and is often) constructed by taking into account relevant background. For example, a scientist who wants a prior distribution over the possible historical rates of sound change in Tagalog may consult languages that he or she has more historical information about, such as German. In this case setting up a prior involves extrapolating information from one language to another. I believe that the construction of a reasonable prior distribution can often be viewed as a kind of extrapolation problem. There are good reasons for thinking that any extrapolation explicitly relies on certain causal assumptions. What kinds of causal assumptions are required in order to set up a prior distribution in a reasonable way? Is there anything sensible and general that can be said about this problem? I am particularly interested in using the causal diagram framework of Pearl and Spirtes/Glymour/Scheines to shed light on these questions.

Science as data compression

Solomonoff’s ideal theory of induction and the Minimum Description Length principle in statistical inference are both based on the idea that induction is the discovery of patterns in data, and that any pattern found in a data set can be used to compress the data (i.e. describe the data in way that is more succinct than simply reiterating the data). The idea that science can be viewed as a kind of data-compression enterprise presents an intriguing picture, but it is clearly a bit inaccurate. In particular, science usually aims at going beyond any particular data set, and often the goal is counterfactual inference. Can the science-as-data-compression picture be reconciled with these facts about scientific inquiry?