The question of how we apply knowledge from biomedical science to medical and public health practice has been the subject of heated debates about generalizability and related concepts, such as applicability and inductive inference. In this essay, I interpret the term from the perspective of two causal models: determinism and indeterminism. I suggest that theories of generalizability can be formulated on the basis of both models and take the form of testable but unverifiable hypotheses, an attribute that is common to (...) all scientific theories. Nonetheless, there is one noteworthy difference between the two models: determinism allows one to rationalize a decision to treat a certain kind of patient but only indirectly a decision to treat any particular patient, whereas indeterminism accommodates both types of decisions. (shrink)

Despite the widespread use of key concepts of the Neyman–Pearson (N–P) statistical paradigm—type I and II errors, significance levels, power, confidence levels—they have been the subject of philosophical controversy and debate for over 60 years. Both current and long-standing problems of N–P tests stem from unclarity and confusion, even among N–P adherents, as to how a test's (pre-data) error probabilities are to be used for (post-data) inductive inference as opposed to inductive behavior. We argue that the relevance of error probabilities (...) is to ensure that only statistical hypotheses that have passed severe or probative tests are inferred from the data. The severity criterion supplies a meta-statistical principle for evaluating proposed statistical inferences, avoiding classic fallacies from tests that are overly sensitive, as well as those not sensitive enough to particular errors and discrepancies. Introduction and overview 1.1 Behavioristic and inferential rationales for Neyman–Pearson (N–P) tests 1.2 Severity rationale: induction as severe testing 1.3 Severity as a meta-statistical concept: three required restrictions on the N–P paradigm Error statistical tests from the severity perspective 2.1 N–P test T(): type I, II error probabilities and power 2.2 Specifying test T() using p-values Neyman's post-data use of power 3.1 Neyman: does failure to reject H warrant confirming H? Severe testing as a basic concept for an adequate post-data inference 4.1 The severity interpretation of acceptance (SIA) for test T() 4.2 The fallacy of acceptance (i.e., an insignificant difference): Ms Rosy 4.3 Severity and power Fallacy of rejection: statistical vs. substantive significance 5.1 Taking a rejection of H0 as evidence for a substantive claim or theory 5.2 A statistically significant difference from H0 may fail to indicate a substantively important magnitude 5.3 Principle for the severity interpretation of a rejection (SIR) 5.4 Comparing significant results with different sample sizes in T(): large n problem 5.5 General testing rules for T(), using the severe testing concept The severe testing concept and confidence intervals 6.1 Dualities between one and two-sided intervals and tests 6.2 Avoiding shortcomings of confidence intervals Beyond the N–P paradigm: pure significance, and misspecification tests Concluding comments: have we shown severity to be a basic concept in a N–P philosophy of induction? (shrink)

Many philosophers and statisticians argue that risk assessors are morally obligated to evaluate the probabilities and consequences of methodological error, and to base their decisions of whether to adopt a given parameter value, model, or hypothesis on those considerations. This argument is couched within the rubric of null hypothesis testing, which I suggest is a poor descriptive and normative model for risk assessment. Risk regulation is not primarily concerned with evaluating the probability of data conditional upon the null hypothesis, but (...) rather with measuring risks, estimating the consequences of available courses of action and inaction, formally characterising uncertainty, and deciding what to do based upon explicit values and decision criteria. In turn, I defend an ideal of value-neutrality, whereby the core inferential tasks of risk assessment – such as weighing evidence, estimating parameters, and model selection – should be guided by the aim of correspondence to reality. This is not to say that value-judgments be damned, but rather that they should be accounted for within a structured approach to decision analysis, rather than embedded within risk assessment in an informal manner. (shrink)

There have been many efforts to infer causation from association byusing statistical models. Algorithms for automating this processare a more recent innovation. In Humphreys and Freedman[(1996) British Journal for the Philosophy of Science 47, 113–123] we showed that one such approach, by Spirtes et al., was fatally flawed. Here we put our arguments in a broader context and reply to Korb and Wallace [(1997) British Journal for thePhilosophy of Science 48, 543–553] and to Spirtes et al.[(1997) British Journal for the (...) Philosophy of Science 48, 555–568]. Their arguments leave our position unchanged: claims to have developed a rigorous engine for inferring causation from association are premature at best, the theorems have no implications for samples of any realistic size, and the examples used to illustrate the algorithms are indicative of failure rather than success. The gap between association and causation has yet to be bridged. (shrink)

From the outside, Bayesian statistics may seem like a closed little corner of probability. Once a prior is specified you compute! From the inside the field is filled with problems, conceptual and otherwise. This paper surveys some of what remains to be done and gives examples of the work in progress via a Bayesian peek into Feller volume I.

This paper reconsider the fundamental de Finetti’s representation theorem. It is stressed its role at the front-line between Probability Theory and Inferential Statistics and its relation to the fundamental problem of relating past observations with future predictions i. e. the problem of induction.