Reference Class Problem Research Articles

Simpson’s Paradox in Natural Resource Evaluation

Reversals of statistical relationships, when two or more groups of data in a cross tabulation are aggregated, were first revealed more than a century ago. The reversal was later named Simpson’s paradox after his reversal examples in a seminal paper drew the attention of the statistical community. However, almost all the published cases have been in sociology and biomedical statistics. Does Simpson’s reversal occur in geosciences? Various examples from petroleum geology and reservoir modeling will be shown in this paper. Boundary conditions for such a reversal will be discussed under a broader framework of sampling analysis. Ecological inference bias, change of support problem, modifiable areal unit problem, and reference class problem will be discussed in relation to the Simpson’s paradox in the framework of spatial statistics. It will be demonstrated that the traditional interpretation of the paradox as a result of disproportional sampling based on a contingency table is not always true in the framework of spatial statistics, and the reversal while theoretically benign is inferentially treacherous. Therefore, emphasis will be on the discussion of combining statistical and scientific inferences in geologic modeling and hydrocarbon resource evaluation under various sampling schemes or support effect with or without a Simpson’s reversal.

The Reference Class Problem and Mathematical Models of Inference

The Reference Class Problem and Mathematical Models of Inference

Legal Decisions and the Reference Class Problem

There has been a long history of discussion on the usefulness of formal methods in legal settings. Some of the recent debate has focussed on foundational issues in statistics, in particular, how the reference-class problem affects legal decisions based on certain types of statistical evidence. Here we examine aspects of this debate, stressing why the reference-class problem presents serious difficulties for the kinds of statistical inferences under consideration and the relevance of this for the use of statistics in the courtroom. We also consider the relevance of foundational statistical issues in the broader context of

Probability, Explanation and Inference: A Reply

This essay, published in a symposium issue on the “reference class problem” and legal evidence, replies to articles by Dale Nance, Mark Colyvan and Helen Regan, Robert Rhee, and Larry Laudan. We discuss the limits of probabilistic modeling of evidence and the relationship between such modeling and explanatory accounts of legal proof.

From Theory into Practice: Introducing the Reference Class Problem

From Theory into Practice: Introducing the Reference Class Problem

The reference class problem is your problem too

The reference class problem arises when we want to assign a probability to a proposition (or sentence, or event) X, which may be classified in various ways, yet its probability can change depending on how it is classified. The problem is usually regarded as one specifically for the frequentist interpretation of probability and is often considered fatal to it. I argue that versions of the classical, logical, propensity and subjectivist interpretations also fall prey to their own variants of the reference class problem. Other versions of these interpretations apparently evade the problem. But I contend that they are all "no-theory" theories of probability - accounts that leave quite obscure why probability should function as a guide to life, a suitable basis for rational inference and action. The reference class problem besets those theories that are genuinely informative and that plausibly constrain our inductive reasonings and decisions. I distinguish a "metaphysical" and an "epistemological" reference class problem. I submit that we can dissolve the former problem by recognizing that probability is fundamentally a two-place notion: conditional probability is the proper primitive of probability theory. However, I concede that the epistemological problem remains.

The Difference Between Selection and Drift: A Reply to Millstein

Millstein [Bio. Philos. 17 (2002) 33] correctly identies a serious problem with the view that natural selection and random drift are not conceptually distinct. She offers a solution to this problem purely in terms of differences between the processes of selection and drift. I show that this solution does not work, that it leaves the vast majority of real biological cases uncategorized. However, I do think there is a solution to the problem she raises, and I offer it here. My solution depends on solving the biological analogue of the reference class problem in probability theory and on the reality of individual fitnesses.

Causal Generalizations and Good Advice

In this essay, I focus on the convergence of two problems. The first is our old nemesis, the reference-class problem. The second is the problem of interpreting causal generalizations such as 'smoking causes lung cancer'. This problem has been with us since the time of Hume. Within the framework of the probabilistic theory of causation (which I have been exploring since the early '90s), this problem takes on a very precise form. All parties to the dispute agree that the truth of such a generalization depends upon certain conditional probabilities; they disagree about the configuration of these probabilities that must obtain in order for the claim to be true. The key to solving this second problem rests in the observation that causal generalizations can serve as guides to life: if I know that smoking causes lung cancer, that gives me a good reason not to smoke. Here is where the two problems converge. One way to formulate the reference-class problem is as follows: which objective, conditional probabilities should guide my decisions? I answer that one should be (partly) guided by the conditional probabilities that figure in the probabilistic theory of causation. This, in turn, helps us to solve the second problem. 'Smoking causes lung cancer' describes a configuration of objective, conditional probabilities, such that if the agent were guided by those probabilities, it would be rational for her to refrain from smoking. Like Hume, I conclude that the truth of a causal generalization is partly a subjective matter.

REFERENCE CLASSES AND MULTIPLE INHERITANCES

The reference class problem in probability theory and the multiple inheritances (extensions) problem in non-monotonic logics are special cases of conflicting beliefs. One popular solution accepted in the two domains is the specificity principle. By analyzing an example, several factors beyond specificity are found to be relevant to the priority of a reference class. A new approach, Non-Axiomatic Reasoning System (NARS), is discussed, where these factors are all taken into account. It is argued that the solution provided by NARS is better than the solutions provided by probability theory and non-monotonic logics.