BAYESIAN APPROACH || with Complete Solutions.

Bayesian Metaphor correct answers -Three approaches or metaphors for human cognition - Information processing metaphor - Connectionist Metaphor - Bayesian Metaphor Information processing metaphor correct answers -the mind as a serial computer,with memory stores, buffers, executive control, ... Connectionist Metaphor: correct answers -the mind as a brain,with parallel distributed processing Bayesian Metaphor correct answers -the mind as doing statistical inference Statistics correct answers -Data rarely tell us what we want to know - Typically very little of what could be observed actually is observed, so data are sparse - Typically measurements are not perfect, so data are noisy -Statistics is for understanding data, what hypotheses are supported by the data, and what can be inferred or predicted from the data Bayesian Models of Mind correct answers -Bayesian statistics describes one way (arguably the best way) to make inferences and predictions about hypotheses and models based on sparse and noisy data - That is a good description (at the computational level) of the goals and challenges faced by the mind - Making inferences, judgments, decisions about complicated mental representation or events from limited and imperfect information Led to recent development of Bayesian models of cognition (e.g., Chater et al 2006) including - categorization,induction,reasoning,learning,language development, vision, ... Bayesian Approach correct answers -Bayesian statistics is a framework for making inferences based on incomplete and uncertain information, based on structured models -Deals with "models" and "data" - Modelsaremadeupof - Parameters (variables) that are possible values for facts about the world - whether a berry is poisonous, how old a person is, how large an apple is, ... - Likelihoods (data‐generating functions) that are possible ways or processes by which the world generates information - smoking causes cancer, rain makes the grass wet, old people tend to wear glasses, ... - Data are observations made in the world - my stomach hurts, the grass is wet this morning, a group of smokers died of cancer Bayesian Inference correct answers -Bayes rule provides the "rational" way to update and test models of how the world works - update prior belief in a model to a posterior belief based on data - prior is how likely parameter values are or a data‐generating hypothesis is before you have seen the data