Deborah Mayo

Despite its widespread use in science, the Neyman-Pearson Theory of Statistics (NPT) has been rejected as inadequate by most philosophers of induction and statistics. They base their rejection largely upon what the author refers to as after-trial criticisms of NPT. Such criticisms attempt to show that NPT fails to provide an adequate analysis of specific inferences after the trial is made, and the data is known. In this paper, the key types of after-trial criticisms are considered and it is argued that each fails to demonstrate the inadequacy of NPT because each is based on judging NPT on the grounds of a criterion that is fundamentally alien to NPT. As such, each may be seen to either misconstrue the aims of NPT, or to beg the question against it.

In a recent discussion note Sober (1985) elaborates on the argument given in Sober (1982) to show the inadequacy of Ronald Giere's (1979, 1980) causal model for cases of frequency-dependent causation, and denies that Giere's (1984) response avoids the problem he raises. I argue that frequency-dependent effects do not pose a problem for Giere's original causal model, and that all parties in this dispute have been guity of misinterpreting the counterfactual populations involved in applying Giere's model

Although both philosophers and scientists are interested in how to obtain reliable knowledge in the face of error, there is a gap between their perspectives that has been an obstacle to progress. By means of a series of exchanges between the editors and leaders from the philosophy of science, statistics and economics, this volume offers a cumulative introduction connecting problems of traditional philosophy of science to problems of inference in statistical and empirical modelling practice. Philosophers of science and scientific practitioners are challenged to reevaluate the assumptions of their own theories - philosophical or methodological. Practitioners may better appreciate the foundational issues around which their questions revolve and thereby become better 'applied philosophers'. Conversely, new avenues emerge for finally solving recalcitrant philosophical problems of induction, explanation and theory testing.

In empirical modeling, an important desiderata for deeming theoretical entities and processes as real is that they can be reproducible in a statistical sense. Current day crises regarding replicability in science intertwines with the question of how statistical methods link data to statistical and substantive theories and models. Different answers to this question have important methodological consequences for inference, which are intertwined with a contrast between the ontological commitments of the two types of models. The key to untangling them is the realization that behind every substantive model there is a statistical model that pertains exclusively to the probabilistic assumptions imposed on the data. It is not that the methodology determines whether to be a realist about entities and processes in a substantive field. It is rather that the substantive and statistical models refer to different entities and processes, and therefore call for different criteria of adequacy.

I argue that although the judgments required to reach statistical risk assessments may reflect policy values, it does not follow that the task of evaluating whether a given risk assessment is warranted by the evidence need also be imbued with policy values. What has led many to conclude otherwise, I claim, stems from misuses of the statistical testing methods involved. I set out rules for interpreting what specific test results do and do not say about the extent of a given risk. By providing a more objective understanding of the evidence, such rules help in adjudicating conflicting risk assessments. To illustrate, I consider the risk assessment conflict at the EPA concerning the carcinogenicity of formaldehyde.

We argue that a responsible analysis of today's evidence-based risk assessments and risk debates in biology demands a critical or metascientific scrutiny of the uncertainties, assumptions, and threats of error along the manifold steps in risk analysis. Without an accompanying methodological critique, neither sensitivity to social and ethical values, nor conceptual clarification alone, suffices. In this view, restricting the invitation for philosophical involvement to those wearing a "bioethicist" label precludes the vitally important role philosophers of science may be able to play as bioevidentialists. The goal of this paper is to give a brief and partial sketch of how a metascientific scrutiny of risk evidence might work.