We consider two-level models where a continuous response R and continuous covariates C are assumed missing at random. Inferences based on maximum likelihood or Bayes are routinely made by estimating their joint normal distribution from observed data R[subscript obs] and C[subscript obs]. However, if the model for R given C includes random…

Individuals draw conclusions about possibilities from assertions that make no explicit reference to them. The model theory postulates that assertions such as disjunctions refer to possibilities. Hence, a disjunction of the sort, "A or B or both," where "A" and "B" are sensible clauses, yields mental models of an…

Hinterecker, Knauff, and Johnson-Laird (2016) compared the adequacy of the probabilistic new paradigm in reasoning with the recent revision of mental models theory (MMT) for explaining a novel class of inferences containing the modal term "possibly." For example, "the door is closed or the window is open or both," therefore,…

Probabilities tend to become an integral part of early childhood mathematics curricula. Research has shown that at the age of 4, children indicate basics of probabilistic reasoning and can engage with probabilistic tasks and uncertainty. The aim of this study is to examine whether methodological and design alterations influence children's…

Like scientists, children seek ways to explain causal systems in the world. But are children scientists in the strict Bayesian tradition of maximizing posterior probability? Or do they attend to other explanatory considerations, as laypeople and scientists--such as Einstein--do? Four experiments support the latter possibility. In particular, we…

We report 3 experiments investigating novel sorts of inference, such as: A or B or both. Therefore, possibly (A and B). Where the contents were sensible assertions, for example, "Space tourism will achieve widespread popularity in the next 50 years or advances in material science will lead to the development of antigravity materials in the…

Two experiments tested how the "functional form" of the causal relations that link features of categories affects category-based inferences. Whereas "independent causes" can each bring about an effect by themselves, "conjunctive causes" all need to be present for an effect to occur. The causal model view of category…

Much of our real-life decision making is bounded by uncertain information, limitations in cognitive resources, and a lack of time to allocate to the decision process. It is thought that humans overcome these limitations through "satisficing," fast but "good-enough" heuristic decision making that prioritizes some sources of…

People consider alternative causes when deciding whether a cause is responsible for an effect (diagnostic inference) but appear to neglect them when deciding whether an effect will occur (predictive inference). Five experiments were conducted to test a 2-part explanation of this phenomenon: namely, (a) that people interpret standard predictive…

This dissertation deals with the theory of the phonetic component of grammar in a formal probabilistic inference framework: (1) it has been recognized since the beginning of generative phonology that some language-specific phonetic implementation is actually context-dependent, and thus it can be said that there are gradient "phonetic…

A rich tradition in developmental psychology explores physical reasoning in infancy. However, no research to date has investigated whether infants can reason about physical objects that behave probabilistically, rather than deterministically. Physical events are often quite variable, in that similar-looking objects can be placed in similar…

Children rely on both evidence and prior knowledge to make physical causal inferences; this study explores whether they make attributions about others' behavior in the same manner. A total of one hundred and fifty-nine 4- and 6-year-olds saw 2 dolls interacting with 2 activities, and explained the dolls' actions. In the person condition, each doll…

The study explores the development of 11-year-old students' informal inference about random bunny hops through student talk and use of computer simulation tools. Our aim in this paper is to draw on dialogic theory to explain how students make shifts in perspective, from intuition-based reasoning to more powerful, formal ways of using probabilistic…

According to Adams's Thesis, the acceptability of an indicative conditional sentence goes by the conditional probability of its consequent given its antecedent. We test, for the first time, whether this thesis is descriptively correct and show that it is not; in particular, we show that it yields the wrong predictions for people's judgments of the…

Two experiments investigated how people perform category-based induction for items that have uncertain categorization. Whereas normative considerations suggest that people should consider multiple relevant categories, much past research has argued that people focus on only the most likely category. A new method is introduced in which responses on…