This study presents a probabilistic model of melody perception, which infers the key of a melody and also judges the probability of the melody itself. The model uses Bayesian reasoning: For any “surface” pattern and underlying “structure,” we can infer the structure maximizing P(structure|surface) based on knowledge of P(surface, structure). The probability of the surface can then be calculated as ∑ P(surface, structure), summed over all structures. In this case, the surface is a pattern of notes; the structure is a (...) key. A generative model is proposed, based on three principles: (a) melodies tend to remain within a narrow pitch range; (b) note‐to‐note intervals within a melody tend to be small; and (c) notes tend to conform to a distribution (or key profile) that depends on the key. The model is tested in three ways. First, it is tested on its ability to identify the keys of a set of folksong melodies. Second, it is tested on a melodic expectation task in which it must judge the probability of different notes occurring given a prior context; these judgments are compared with perception data from a melodic expectation experiment. Finally, the model is tested on its ability to detect incorrect notes in melodies by assigning them lower probabilities than the original versions. (shrink)

In everyday life, people typically observe fragments of causal networks. From this knowledge, people infer how novel combinations of causes they may never have observed together might behave. I report on 4 experiments that address the question of how people intuitively integrate multiple causes to predict a continuously varying effect. Most theories of causal induction in psychology and statistics assume a bias toward linearity and additivity. In contrast, these experiments show that people are sensitive to cues biasing various integration rules. (...) Causes that refer to intensive quantities (e.g., taste) or to preferences (e.g., liking) bias people toward averaging the causal influences, whereas extensive quantities (e.g., strength of a drug) lead to a tendency to add. However, the knowledge underlying these processes is fallible and unstable. Therefore, people are easily influenced by additional task‐related context factors. These additional factors include the way data are presented, the difficulty of the inference task, and transfer from previous tasks. The results of the experiments provide evidence for causal model and related theories, which postulate that domain‐general representations of causal knowledge are influenced by abstract domain knowledge, data‐driven task factors, and processing difficulty. (shrink)

My research program proposes that children have representations and learning mechanisms that can be characterized as causal models of the world Bayesian Fundamentalism.”.

How do human infants learn the causal dependencies between events? Evidence suggests that this remarkable feat can be achieved by observation of only a handful of examples. Many computational models have been produced to explain how infants perform causal inference without explicit teaching about statistics or the scientific method. Here, we propose a spiking neuronal network implementation that can be entrained to form a dynamical model of the temporal and causal relationships between events that it observes. The network uses spike-time (...) dependent plasticity, long-term depression, and heterosynaptic competition rules to implement Rescorla–Wagner-like learning. Transmission delays between neurons allow the network to learn a forward model of the temporal relationships between events. Within this framework, biologically realistic synaptic plasticity rules account for well-known behavioral data regarding cognitive causal assumptions such as backwards blocking and screening-off. These models can then be run as emulators for state inference. Furthermore, this mechanism is capable of copying synaptic connectivity patterns between neuronal networks by observing the spontaneous spike activity from the neuronal circuit that is to be copied, and it thereby provides a powerful method for transmission of circuit functionality between brain regions. (shrink)

Severity of Test (SoT) is an alternative to Popper's logical falsification that solves a number of problems of the logical view. It was presented by Popper himself in 1963. SoT is a less sophisticated probabilistic model of hypothesis testing than Oaksford & Chater's (O&C's) information gain model, but it has a number of striking similarities. Moreover, it captures the intuition of everyday hypothesis testing.

Oaksford & Chater (O&C) focus on patterns of typical adult reasoning from a probabilistic perspective. We discuss implications of extending the probabilistic approach to lifespan development, considering the role of working memory, strategy use, and expertise. Explaining variations in human reasoning poses a challenge to Bayesian rational analysis, as it requires integrating knowledge about cognitive processes.

Human cognition requires coping with a complex and uncertain world. This suggests that dealing with uncertainty may be the central challenge for human reasoning. In Bayesian Rationality we argue that probability theory, the calculus of uncertainty, is the right framework in which to understand everyday reasoning. We also argue that probability theory explains behavior, even on experimental tasks that have been designed to probe people's logical reasoning abilities. Most commentators agree on the centrality of uncertainty; some suggest that there is (...) a residual role for logic in understanding reasoning; and others put forward alternative formalisms for uncertain reasoning, or raise specific technical, methodological, or empirical challenges. In responding to these points, we aim to clarify the scope and limits of probability and logic in cognitive science; explore the meaning of the explanation of cognition; and re-evaluate the empirical case for Bayesian rationality. (shrink)

We use our knowledge of causal relationships to imagine possible events. We also use these relationships to look deep into the past and infer events that were not witnessed or to infer what can not be directly seen in the present. Knowledge of causal relationships allows us to go beyond the here and now. This chapter introduces a new theoretical framework for how this very basic concept might be mentally represented. It proposes an epistemological theory of causation — that is, (...) a theory that specifies the nature of people's knowledge of causation, the notion of causation used in everyday language and reasoning. (shrink)