ABSTRACT: The Likelihood Principle has been defended on Bayesian grounds, on the grounds that it coincides with and systematizes intuitive judgments about example problems, and by appeal to the fact that it generalizes what is true when hypotheses have deductive consequences about observations. Here we divide the Principle into two parts-- one qualitative, the other quantitative-- and evaluate each in the light of the Akaike information criterion. Both turn out to be correct in a special case (when the competing hypotheses have the same number of adjustable parameters), but not otherwise.

Akaike's framework for thinking about model selection in terms of the goal of predictive accuracy and his criterion for model selection have important philosophical implications. Scientists sometimes test models whose truth values they already know, and then sometimes choose models that they know full well are false. Instrumentalism helps explain this pervasive feature of scientific practice, and Akaike's framework provides instrumentalism with the epistemology it needs. Akaike's criterion for model selection also throws light on the role of parsimony considerations in hypothesis evaluation. I explain the basic ideas behind Akaike's framework and criterion; several biological examples, including the use of maximum likelihood methods in phylogenetic inference, are considered. Philosophers of science usually agree that the point of testing theories -- indeed, the point of doing science -- is to try to determine which theories are true. Of course, we all recognize that scientists never have access to all possible theories on a given subject; they are limited by the theories they have at hand. But given a set of competing theories, the point of theory assessment is to ascertain which of these competitors is one's best guess as to what the truth is. Bayesians tend to see things this way, so do scientists who use orthodox Neyman-Pearson methods, and likelihoodists tend to fall into this pattern as well. To be sure, there are deep differences among these outlooks. Bayesians assess which hypotheses are most probable, frequentists evaluate which hypotheses should be rejected, and likelihoodists say which hypotheses are best supported. But these assessments typically invoke the concept of truth; the question is which hypotheses are most probably true, or should be rejected as ...

Does evolutionary theory have implications about the existence of supernatural entities? This question concerns the logical relationships that hold between the theory of evolution and different bits of metaphysics. There is a distinct question that I also want to address; it is epistemological in character. Does the evidence we have for evolutionary theory also provide evidence concerning the existence of supernatural entities? An affirmative answer to the logical question would entail an affirmative answer to the epistemological question if the principle in confirmation theory that Hempel (1965, p. 31) called the special consequence condition were true: The special consequence condition: If an observation report confirms a hypothesis H, then it also confirms every consequence of H. According to this principle, if evolutionary theory has metaphysical implications, then whatever confirms evolutionary theory also must confirm those metaphysical implications. But the special consequence is false. Here‟s a simple example that illustrates why. You are playing poker and would dearly like to know whether the card you are about to be dealt will be the Jack of Hearts. The dealer is a bit careless and so you catch a glimpse of the card on top of the deck before it is dealt to you. You see that it is red. The fact that it is red confirms the hypothesis that the card is the Jack of Hearts, and the hypothesis that it is the Jack of Hearts entails that the card will be a Jack. However, the fact that the card is red does not confirm the hypothesis that the card will be a Jack. 2 Bayesians gloss these facts by understanding confirmation in terms of probability raising: The Bayesian theory of confirmation: O confirms H if and only if Pr(H│O)> Pr(H). The general reason why Bayesianism is incompatible with the special consequence

Abstract: ―Absence of evidence isn’t evidence of absence ‖ is a slogan that is popular among scientists and nonscientists alike. This paper assesses its truth by using a probabilistic tool, the Law of Likelihood. Qualitative questions (―Is E evidence about H?‖) and quantitative questions (―How much evidence does E provide about H?‖) are both considered. The paper discusses the example of fossil intermediates. If finding a fossil that is phenotypically intermediate between two extant species provides evidence that those species have a common ancestor, does failing to find such a fossil constitute evidence that there was no common ancestor? Or should the failure merely be chalked up to the imperfection of the fossil record? The transitivity of the evidence relation in simple causal chains provides a broader context, which leads to discussion of the finetuning argument, the anthropic principle, and observation selection effects.

Abstract: Bayesians often reject the Akaike Information Criterion (AIC) because it introduces ideas that do not fit into their philosophy of statistical inference. Here we show that a difference in the AIC scores that two models receive is evidence that they differ in their degrees of predictive accuracy, where evidence is understood in terms of the Law of Likelihood. Since the Law of Likelihood is a central Bayesian principle,

We analyze four general signal detection models for recognition memory that differ in their distributional assumptions. Our analyses show that a basic assumption of signal detection theory, the likelihood ratio decision axis, implies three regularities in recognition memory: (1) the mirror effect, (2) the variance effect, and (3) the z-ROC length effect. For each model, we present the equations that produce the three regularities and show, in computed examples, how they do so. We then show that the regularities appear in data from a range of recognition studies. The analyses and data in our study support the following generalization: Individuals make efficient recognition decisions on the basis of likelihood ratios. In a typical recognition memory test, individuals consider a series of test items presented in random order. Some of the test items have been seen previously (old), others are new, and the prior probability that an item is old is �. In the simplest case, the individuals are asked to classify each item as “old ” or “new, ” and their performance is measured by the proportion of correct classifications. Signal detection models of the recognition process assume that the information available on a single trial can be represented by a random variable X. The distribution of this variable is fO(x) when the item is old (O) and fN(x) when it is new (N). If X is a continuous random variable, fO(x) and fN(x) are probability density functions, whereas if X is discrete, they are probability mass functions. 1 Given X, the likelihood ratio (LR) for “old ” over “new” responses is f ( X)

We analyze four general signal detection theory models for recognition memory. The models differ in distributional assumptions. The analyses show that a basic assumption of signal detection theory, the likelihood ratio decision axis, implies three regularities in recognition memory. 1. The mirror effect 2. The variance effect 3. The z-ROC length effect. We present the equations that produce the three regularities in each model and show how they do so in computed examples. We then show that the three regularities appear in the data of a range of recognition studies. The analyses and the data support the following generalization: individuals make efficient recognition decisions on the basis of likelihood ratios. 3 In a typical recognition memory test, individuals consider a series of test items some of which have been seen previously and others of which are new. The items are presented in random order. The prior probability that an item is “old ” is π. In the simplest case, the individuals are asked to classify each item as “old ” or “new ” and their performance is measured by the proportion of correct classifications. Signal detection models of the recognition process assume that the information available on a single trial can be represented by a random variable X. The distribution of the variable X is fO ( x) when the item is old (O) and fN ( x) when the item is new (N). If X is a continuous random variable then fO ( x) and fN ( x) are probability density functions while if is discrete, they are probability mass functions. 1 Given X, the likelihood ratio (LR) in favor of “old ” over “new ” is,