Interpersonal comparison of subjective probabilities: Toward translating linguistic probabilities

Interpersonal variability in understanding linguistic probabilities can adversely affect decision making. Using the fact that everyone judges canonical probability events similarly in a manner consistent with axiom systems that yield a probability measure, we developed and tested a method for comparing the meanings of probability phrases across individuals. An experiment demonstrated that despite extreme heterogeneity in participants' linguistic probability lexicons, interpersonal similarity in phrase meaning is well predicted by phrase rank order within the lexicons. Thus, equally ranked phrases have similar meanings, and individual differences in linguistic probabilities may simply be explained by the phrases people use at each rank.     

MPTinR: Analysis of multinomial processing tree models in R

We introduce MPTinR, a software package developed for the analysis of multinomial processing tree (MPT) models. MPT models represent a prominent class of cognitive measurement models for categorical data with applications in a wide variety of fields. MPTinR is the first software for the analysis of MPT models in the statistical programming language R, providing a modeling framework that is more flexible than standalone software packages. MPTinR also introduces important features such as (1) the ability to calculate the Fisher information approximation measure of model complexity for MPT models, (2) the ability to fit models for categorical data outside the MPT model class, such as signal detection models, (3) a function for model selection across a set of nested and nonnested candidate models (using several model selection indices), and (4) multicore fitting. MPTinR is available from the Comprehensive R Archive Network at http://cran.r-project.org/web/packages/MPTinR/.     

The multinomial model of prospective memory: validity of ongoing-task parameters

The objective of this research was to provide additional experimental validation of the multinomial processing tree (MPT) model of event-based prospective memory (Smith & Bayen, 2004). In particular, the parameters that measure trial-type detection in the ongoing task were examined. In three experiments with different response instructions, event-based prospective memory tasks were embedded in ongoing color-matching tasks. The results support the validity of the MPT model, that is, manipulations of ongoing-task difficulty affected the ongoing-task parameters of the MPT model, while leaving the estimates for the prospective and the retrospective components of prospective memory unaffected.     

Indicative conditionals: probabilities and relevance

Philosophical Studies - We propose a new account of indicative conditionals, giving acceptability and logical closure conditions for them. We start from Adams’ Thesis: the claim that the...     

Verbal probabilities: An alternative approach

Previous studies of verbal probabilities have tried to place expressions like a chance, possible, and certain on 0–1 numerical probability scales. We ask instead, out of a range of outcomes, which outcome a verbal probability suggests. When, for instance, a sample of laptop batteries lasts from 1.5 to 3.5 hours, what is a certain and what is a possible duration? Experiment 1 showed that speakers associate certain with low values and possible with (unlikely) high or maximal values. In Experiment 2, this methodology was applied to several positive and negative verbal probability phrases, showing a preference for high rather than low or middle values in a distribution. Experiment 3 showed that such maxima are not universally described by large numbers. For instance, maximum speed is often described in terms of a small number of time units. What can (possibly) happen is accordingly sometimes described with very low and sometimes with very high values, depending upon focus of interest. Finally, participants in Experiment 4 were given the role of hearers rather than speakers and were asked to infer outcome ranges from verbal probabilities. Hearers appeared to be partly aware of speakers' tendencies to describe outcomes at the top of the range.     

Physical probabilities

A conception of probability as an irreducible feature of the physical world is outlined. Propensity analyses of probability are examined and rejected as both formally and conceptually inadequate. It is argued that probability is a non-dispositional property of trial-types; probabilities are attributed to outcomes as event-types. Brier's Rule in an objectivist guise is used to forge a connection between physical and subjective probabilities. In the light of this connection there are grounds for supposing physical probability to obey some standard set of axioms. However, there is no a priori reason why this should be the case.     

Prior probabilities

The theoretical construction and practical use of prior probabilities, in particular for systems having many degrees of freedom, are investigated. It becomes clear that it is operationally unsound to use mutually consistent priors if one wishes to draw sensible conclusions from practical experiments. The prior cannot usefully be identified with a state of knowledge, and indeed it is not so identified in common scientific practice. Rather, it can be identified with the question one asks. Accordingly, priors are free constructions. Their informal, ill-defined and subjective characteristics must carry over into the conclusions one chooses to draw from experiments or observations.     

Unknown probabilities

From a point of view like de Finetti's, what is the judgmental reality underlying the objectivistic claim that a physical magnitude X determines the objective probability that a hypothesis H is true? When you have definite conditional judgmental probabilities for H given the various unknown values of X, a plausible answer is sufficiency, i.e., invariance of those conditional probabilities as your probability distribution over the values of X varies. A different answer, in terms of conditional exchangeability, is offered for use when such definite conditional probabilities are absent.     

A multinomial model of event-based prospective memory

Prospective memory is remembering to perform an action in the future. The authors introduce the 1st formal model of event-based prospective memory, namely, a multinomial model that includes 2 separate parameters related to prospective memory processes. The 1st measures preparatory attentional processes, and the 2nd measures retrospective memory processes. The model was validated in 4 experiments. Manipulations of instructions to place importance on either the prospective memory task or the background task (Experiments 1 and 2) and manipulations of distinctiveness of prospective memory targets (Experiment 2) had expected effects on model parameters, as did a manipulation of the difficulty of prospective memory target encoding (Experiments 3 and 4). An alternative model was also evaluated.     

Assessing automatic activation of valence: a multinomial model of EAST performance

The Extrinsic Affective Simon Task (EAST; De Houwer, 2003) has been introduced as an indirect measure of automatic activation of valence. EAST effects provide nonrelative valence measures of single stimuli compared to relative measures (e.g., Implicit Association Test) that imply a comparison between two stimuli or concepts. However, EAST effects can be biased by response tendencies. A multinomial process dissociation model of EAST performance is proposed and successfully validated in four experiments. Its parameters provide pure and unbiased measures of automatic valence activation, controlled processing of task-relevant features, and response tendency. A first application of latent-class hierarchical multinomial models reveals a significant amount of parameter heterogeneity resulting from interindividual differences in accuracy motivation.     

Correction to: The structure of epistemic probabilities

Philosophical Studies - The original version of this article was published with an error in the final equation in this sentence on page 20 (section 3.6.1).     

Analysis of multinomial models under inequality constraints: Applications to measurement theory

Multinomial random variables are used across many disciplines to model categorical outcomes. Under this framework, investigators often use a likelihood ratio test to determine goodness-of-fit. If the permissible parameter space of such models is defined by inequality constraints, then the maximum likelihood estimator may lie on the boundary of the parameter space. Under this condition, the asymptotic distribution of the likelihood ratio test is no longer a simple χ² distribution. This article summarizes recent developments in the constrained inference literature as they pertain to the testing of multinomial random variables, and extends existing results by considering the case of jointly independent mutinomial random variables of varying categorical size. This article provides an application of this methodology to axiomatic measurement theory as a means of evaluating properly operationalized measurement axioms. This article generalizes Iverson and Falmagne’s [Iverson, G. J. & Falmagne, J. C. (1985). Statistical issues in measurement. Mathematical Social Sciences, 10, 131-153] seminal work on the empirical evaluation of measurement axioms and provides a classical counterpart to Myung, Karabatsos, and Iverson’s [Myung, J. I., Karabatsos, G. & Iverson, G. J. (2005). A Bayesian approach to testing decision making axioms. Journal of Mathematical Psychology, 49, 205-225] Bayesian methodology on the same topic.     

Appletree: A multinomial processing tree modeling program for macintosh computers

Multinomial processing tree (MPT) models are statistical models that allow for the prediction of categorical frequency data by sets of unobservable (cognitive) states. In MPT models, the probability that an event belongs to a certain category is a sum of products of state probabilities. AppleTree is a computer program for Macintosh for testing user-defined MPT models. It can fit model parameters to empirical frequency data, provide confidence intervals for the parameters, generate tree graphs for the models, and perform identifiability checks. In this article, the algorithms used by AppleTree and the handling of the program are described.     

New multinomial models for the Chechile-Meyer task

This paper provides a critique of the Chechile and Meyer (J. Math. Psychol. 13 (1976) 269) multinomial processing tree (MPT) models that were generated for the measurement of storage and retrieval components of the correct recall rate. These models were developed for a specific test procedure that involved the random mixing of recall and recognition trials. A key problem with the Chechile and Meyer (J. Math. Psychol. 13 (1976) 269) models is the validity of an assumption made for foil recognition test trials. Three new MPT models for obtaining separate storage and retrieval measures are provided. These new models circumvent the difficulties of the Chechile and Meyer (J. Math. Psychol. 13 (1976) 269) models. Both maximum likelihood estimates (MLE) and population-parameter mapping (PPM) estimates (discussed in Chechile (J. Math. Psychol. 42 (1998) 432)) are provided for the model parameters. Monte Carlo studies were conducted to compare the relative accuracy of the MLE and PPM storage estimates. Both methods have the same average error rate for samples that are very large in size; however, for all the more practical sample sizes, the PPM estimates were more accurate. Statistical methods for model selection were also developed and tested. Finally, the new models were used to reanalyze some existing data. The new analyses provide strong validation evidence for the new models.     

Overestimation of subjective probabilities

Abstract.— When asked to estimate the probability of outcomes of draws from a binomial population, student subjects tend to report p values that clearly exceed the objective ones. The probability of specific binomial sequences was found to be even more overestimated, while the answers became much more conservative when the outcomes were grouped into a few categories. These findings were replicated in a second experiment, where the probability of heights in a male and a female student population was estimated. When the task was to estimate frequency of occurrence, instead of probability, the answers became more realistic. The conclusion is drawn that the direct p estimates are relatively independent of frequency judgments, the chief determinant being the properties of the particular sample to be evaluated, irrespective of the number and probabilities of other possible samples.     

Underdetermination of infinitesimal probabilities

Synthese - A number of philosophers have attempted to solve the problem of null-probability possible events in Bayesian epistemology by proposing that there are infinitesimal probabilities....     

Archimedean qualitative probabilities

Necessary and sufficient conditions for the existence of a probability measure agreeing with a weak order on an algebra of events are given. In the case of a countable algebra they consist of an extension of Kraft, Pratt, and Seidenberg's (1959. Annals of Mathematical Statistics, 38, 780–786) additivity condition through the requirement of an Archimedean property. In the case of a σ-algebra and a σ-additive agreeing probability, Villegas' (1964. Annals of Mathematical Statistics, 35, 1787–1796) monotone continuity condition, which becomes necessary, is merely added to them.