A problem for the alternative difference measure of confirmation

Among Bayesian confirmation theorists, several quantitative measures of the degree to which an evidential proposition E confirms a hypothesis H have been proposed. According to one popular recent measure, s, the degree to which E confirms H is a function of the equation P(H|E) ? P(H|~E). A consequence of s is that when we have two evidential propositions, E1 and E2, such that P(H|E1) = P(H|E2), and P(H|~E1) ≠ P(H|~E2), the confirmation afforded to H by E1 does not equal the confirmation afforded to H by E2. I present several examples that demonstrate the unacceptability of this result, and conclude that we should reject s (and other measures that share this feature) as a measure of confirmation.     

The threat of nuclear war: Some responses

The possibility of nuclear holocaust threatens the very existence of the world community. Biologists, earth scientists, educators, lawyers, philosophers, physicists, physicians, and social scientists have addressed the problem from their special perspectives, and have had substantial impact on the public. Behavior analysts, however, have not as a whole contributed a great deal to the goal of preventing nuclear catastrophe. We argue that the threat of nuclear war is primarily a behavioral problem, and present an analysis of that problem. In addition, we address the difficulty of implementing behavioral interventions that would contribute to the survival of the World.     

Behavioral economics and behavioral momentum

Some relations between elasticity of demand and the conditions of reinforcement are reanalyzed in terms of resistance to change, in ways suggested by the metaphor of behavioral momentum; some relations between resistance to change and the conditions of reinforcement are reanalyzed in terms of elasticity of demand, in ways suggested by behavioral economics. In addition, some data on labor supply in relation to variable-ratio schedules and alternative reinforcement are reanalyzed in terms of resistance to change and compared with steady-state resistance data for performance on multiple and concurrent interval schedules. The results of these studies can be summarized by two functions based on the behavioral momentum approach, relating relative behavioral mass to relative reinforcement per response or per unit time. The former is a relation between relative unit price and relative behavioral mass, suggesting the possibility of convergent measurement of a theoretical construct common to both approaches. However, the momentum and economic approaches differ fundamentally on whether it is preferable to construe discriminated operant behavior as selected and strengthened by its consequences or as part of a behavior–consequence bundle that maximizes utility.     

Reinforcement contingencies and signal detection.

Pigeons were trained to discriminate temporal stimuli in a discrete-trial signal-detection procedure. Pecks to one side key were reinforced intermittently after exposure to one duration, and pecks to the other side key were reinforced intermittently after exposure to a different duration. In Experiment I, the allocation of reinforcers was varied systematically for correct responses and for errors, using a procedure that controlled the obtained numbers of reinforcers. When reinforcers were allocated symmetrically, the level of discrimination decreased as the proportion of reinforcers for errors increased. When reinforcers were allocated asymmetrically, the decrease in discrimination was less systematic. Bias toward one or the other side key roughly matched the ratio of reinforcers obtained by pecks at those keys, independent of the level of discrimination. In Experiment II, the overall rate of reinforcement for correct responses was varied both within and between experimental conditions. The level of discrimination was positively related to the overall rate of reinforcement. The discrimination data of both experiments were interpreted in relation to the contingencies of reinforcement and nonreinforcement, characterized by the average difference in reinforcement probability for correct responses and errors.     

Feedback functions for variable-interval reinforcement

On a given variable-interval schedule, the average obtained rate of reinforcement depends on the average rate of responding. An expression for this feedback effect is derived from the assumptions that free-operant responding occurs in bursts with a constant tempo, alternating with periods of engagement in other activities; that the durations of bursts and other activities are exponentially distributed; and that the rates of initiating and terminating bursts are inversely related. The expression provides a satisfactory account of the data of three experiments.     

Causal Inference from Noise

Correlation is not causation is one of the mantras of the sciences—a cautionary warning especially to fields like epidemiology and pharmacology where the seduction of compelling correlations naturally leads to causal hypotheses. The standard view from the epistemology of causation is that to tell whether one correlated variable is causing the other, one needs to intervene on the system—the best sort of intervention being a trial that is both randomized and controlled. In this paper, we argue that some purely correlational data contains information that allows us to draw causal inferences: statistical noise. Methods for extracting causal knowledge from noise provide us with an alternative to randomized controlled trials that allows us to reach causal conclusions from purely correlational data.