A probability model for errors of classification. I. General considerations

This paper seeks to meet the need for a general treatment of the problem of error in classification. Within an m-attribute classificatory system, an object's typical subclass is that subclass to which it is most often allocated under repeated experimentally independent applications of the classificatory criteria. In these terms, an error of classification is an atypical subclass allocation. This leads to definition of probabilitiesO of occasional subclass membership, probabilitiesT of typical subclass membership, and probabilitiesE of error or, more generally, occasional subclass membership conditional upon typical subclass membership. In the relationshipf: (O, T, E) the relative incidence of independentO, T, andE values is such that generally one can specifyO values givenT andE, but one cannot generally specifyT andE values givenO. Under the restrictions of homogeneity ofE values for all members of a given typical subclass, mutual stochastic independence of errors of classification, and suitable conditions of replication, one can find particular systemsO =f(T, E) which are solvable forT andE givenO. A minimum of three replications of occasional classification is necessary for a solution of systems for marginal attributes, and a minimum of two replications is needed with any cross-classification. Although for such systems one can always specifyT andE values givenO values, the solution is unique for dichotomous systems only.With grateful acknowledgement to the Rockefeller Foundation; and to the United States Department of Health, Education, and Welfare, Public Health Service, for N. I. M. H. Grant M-3950.     

Stimulus probability and prediction outcome as determinants of choice reaction time: Some procedural considerations

Effects of stimulus probability and prediction outcome on two-choice reaction speed (CRS) were determined when a frequency imbalance was reversed half-way through 300 samples of a 70/30 stimulus distribution and when the same 70/30 distribution was sampled for 1200 trials. Prior to each presentation Ss made a prediction; following each presentation Ss identified the stimulus by pressing a right-hand or left-hand trigger. CRS was faster to correctly predicted stimuli, and faster to the more probable stimulus. Ss who were informed of the frequency imbalance reacted significantly faster than Ss who were not. Both practice and boredom effects were demonstrated by using the extended number of trials. CRS was faster during the second session of 300 trials than during the first; after two sessions, CRS was slower during the second half of two additional sessions.     

CS-dependent response probability in an auditory masked-detection task: considerations based on models of Pavlovian conditioning.

Experimental studies were performed using a Pavlovian-conditioned eyeblink response to measure detection of a variable-sound-level tone (T) in a fixed-sound-level masking noise (N) in rabbits. Results showed an increase in the asymptotic probability of conditioned responses (CRs) to the reinforced TN trials and a decrease in the asymptotic rate of eyeblink responses to the non-reinforced N presentations as a function of the sound level of the T. These observations are consistent with expected behaviour in an auditory masked detection task, but they are not consistent with predictions from a traditional application of the Rescorla-Wagner or Pearce models of associative learning. To implement these models, one typically considers only the actual stimuli and reinforcement on each trial. We found that by considering perceptual interactions and concepts from signal detection theory, these models could predict the CS dependence on the sound level of the T. In these alternative implementations, the animals response probabilities were used as a guide in making assumptions about the "effective stimuli".     

Possibility and probability

Conclusion De Finetti was a strong proponent of allowing 0 credal probabilities to be assigned to serious possibilities. I have sought to show that (pace Shimony) strict coherence can be obeyed provided that its scope of applicability is restricted to partitions into states generated by finitely many ultimate payoffs. When countable additivity is obeyed, a restricted version of ISC can be applied to partitions generated by countably many ultimate payoffs. Once this is appreciated, perhaps the compelling character of the Shimony argument will be less overwhelming and the attractiveness of de Finetti's more permissive attitude will become more apparent.I want to push the permissive tendency in de Finetti still further. It seems doubtful that RUIWC should be required as de Finetti apparently suggested. It is also excessively dogmatic and restrictive to require that the credal states of ideally situated rational agents be numerically definite (Levi 1974, 1980). And de Finetti's rejection of objectivism in statistics overreached itself when he dismissed objective probabilities as meaningless metaphysical artefacts (Levi 1986). In this respect, the philosophically most important lessons de Finetti has to teach us are to be found not in his celebrated representation theorem but in his discussions of the relations between 0-probability and possibility, conditional probability and countable additivity. Perhaps, the technical issues involved are remote and pedantic. But the attitude de Finetti sought to inculcate is of profound importance.Thanks are due to Teddy Seidenfeld whose comments have improved this paper substantially. He is not to blame for its lingering defects.     

Epistemology and probability

Probability is sometimes regarded as a universal panacea for epistemology. It has been supposed that the rationality of belief is almost entirely a matter of probabilities. Unfortunately, those philosophers who have thought about this most extensively have tended to be probability theorists first, and epistemologists only secondarily. In my estimation, this has tended to make them insensitive to the complexities exhibited by epistemic justification. In this paper I propose to turn the tables. I begin by laying out some rather simple and uncontroversial features of the structure of epistemic justification, and then go on to ask what we can conclude about the connection between epistemology and probability in the light of those features. My conclusion is that probability plays no central role in epistemology. This is not to say that probability plays no role at all. In the course of the investigation, I defend a pair of probabilistic acceptance rules which enable us, under some circumstances, to arrive at justified belief on the basis of high probability. But these rules are of quite limited scope. The effect of there being such rules is merely that probability provides one source for justified belief, on a par with perception, memory, etc. There is no way probability can provide a universal cure for all our epistemological ills.     

Translation of first order formulas into ground formulas via a completion theory

A translation technique is presented which transforms a class of First Order Logic formulas, called Restricted formulas, into ground formulas. For the formulas in this class the range of quantified variables is restricted by Domain formulas.If we have a complete knowledge of the predicates involved in the Domain formulas their extensions can be evaluated with the Relational Algebra and these extensions are used to transform universal (respectively existential) quantifiers into finite conjunctions (respectively disjunctions).It is assumed that the complete knowledge is represented by Completion Axioms and Unique Name Axioms à la Reiter. These axioms involve the equality predicate. However, the translation allows to remove the equality in the ground formulas and for a large class of formulas their consequences are the same as the initial First Order formulas. This result open the door for the design of efficient deduction techniques.     

Role-Playing Effects on Rorschach Scoring and Interpretation

Female Rorschach examinees role-played hostile, sexy, and neutral accompaniments to their own standard, abbreviated protocols. In response to these roles, male examiners made modest scoring errors of a magnitude consistent with experimenter-bias effects but were unaffected in their report writing. Ratings made by the examinees suggested that the examiners were perceived as reacting to the role-playing.     

On simplicity of formulas

Simple formula should contain only few quantifiers. In the paper the methods to estimate quantity and quality of quantifiers needed to express a sentence equivalent to given one.     

MCMI-II Scoring: Weighted and Unweighted Algorithms

This brief report examines the relationship between the scale scores derived through weighted and unweighted item scoring on the Millon Clinical Multiaxial Inventory-II (MCMI-II). The inventories of 356 subjects across three Samples were scored using weighted and unweighted algorithms. Correlations between the weighted and unweighted MCMI-II scales were found to approach unity. This casts doubt on whether the weighting system has substantial effect on the profiles that are generated or on reducing interscale correlations.     

Accuracy,Verisimilitude, and Scoring Rules

Suppose that beliefs come in degrees. How should we then measure the accuracy of these degrees of belief? Scoring rules are usually thought to be the mathematical tool appropriate for this job. But there are many scoring rules, which lead to different ordinal accuracy rankings. Recently, Fallis and Lewis [2016] have given an argument that, if sound, rules out many popular scoring rules, including the Brier score, as genuine measures of accuracy. I respond to this argument, in part by noting that the argument fails to account for verisimilitude—that certain false hypotheses might be closer to the truth than other false hypotheses are. Oddie [forthcoming], however, has argued that no member of a very wide class of scoring rules (the so-called proper scores) can appropriately handle verisimilitude. I explain how to respond to Oddie's argument, and I recommend a class of weighted scoring rules that, I argue, genuinely measure accuracy while escaping the arguments of Fallis and Lewis as well as Oddie.     

Personality Variables in Rorschach Scoring

Twenty-three clinical trainees scored a standardized list of 150 Rorschach responses and were administered the EPPS. Ten directional hypotheses were advanced which predicted certain personality attributes of those making scoring errors in various determinant categories. Results showed significant differences between high and low error groups on scores on several EPPS scales, supporting four of the ten hypotheses. Scoring errors in the color, human movement, texture, and vista determinant categories were related to scores on the Exhibition, Affiliation, Autonomy, and Abasement scales, respectively. Implications of these results are discussed regarding the reliability of Rorschach interpretations.     

Suggested Refinement of Rorschach Scoring

Eighty-three undergraduate subjects (58 women and 25 men) participated in a prospective study in which they (a) completed widely used objective and projective measures of dependency, and then (b) provided monthly reports of the frequency and impact of various types of life events during a 1-semester (3-month) period. As expected, subjects' projective dependency scores predicted their frequency estimates and impact ratings of interpersonal life events but were unrelated to frequency estimates and impact ratings of other types of life events (e.g., achievement-related, legal). Objective dependency scores were unrelated to all life event frequency estimates and impact ratings. Findings are discussed in the context of recent theoretical frameworks that distinguish implicit dependency needs (which are assessed via projective measures) from self-attributed dependency needs (which are assessed via self-report tests). The importance of the type of dependency measure used in studies of the dependency-life events relationship is emphasized.     

Representativeness and conjoint probability

People commonly violate a basic rule of probability, judging a conjunction of events to be more probable than at least 1 of its component events. Many manifestations of this conjunction fallacy have been ascribed to people's reliance on the representativeness heuristic for judging probability. Some conjunction fallacies, however, have been ascribed to the incorrect rules people use to combine probabilities. In 2 experiments, representativeness was pitted against probability combination to determine the contributions of each to the fallacy. Even for exemplar representativeness problems, the fallacy stemmed primarily from the application of incorrect combination rules. Representativeness seemed to be involved only insofar as it influenced the probabilities of a conjunction's component events. Implications of these findings are discussed for the representativeness account of judgmental errors and the relation between similarity and probability.     

Free will and probability

The chance objection to incompatibilist accounts of free action maintains that undetermined actions are not under the agent's control. Some attempts to circumvent this objection locate chance in events posterior to the action. Indeterministic-causation theories locate chance in events prior to the action. However, neither type of response gives an account of free action which avoids the chance objection. Chance must be located at the act of will if actions are to be both undetermined and under the agent's control. This dissolves the apparent paradox of Frankfurt-type cases as well as the chance objection to incompatibilist free will.