A Stochastic Hypothesis Testing Model for Multi-term Series Problems, Based on Eye Fixations

2021 ◽  
pp. 257-274
Author(s):  
Rudolf Groner ◽  
Marina Groner
2012 ◽  
Vol 102 (6) ◽  
pp. 2410-2436 ◽  
Author(s):  
Pietro Ortoleva

Bayes' rule has two well-known limitations: 1) it does not model the reaction to zero-probability events; 2) a sizable empirical evidence documents systematic violations of it. We characterize axiomatically an alternative updating rule, the Hypothesis Testing model. According to it, the agent follows Bayes' rule if she receives information to which she assigned a probability above a threshold. Otherwise, she looks at a prior over priors, updates it using Bayes' rule for second-order priors, and chooses the prior to which the updated prior over priors assigns the highest likelihood. We also present an application to equilibrium refinement in game theory. (JEL D11, D81, D83)


2009 ◽  
Vol 51 (11) ◽  
pp. 1573-1585 ◽  
Author(s):  
Zhenyu Zhang ◽  
W.K. Chan ◽  
T.H. Tse ◽  
Peifeng Hu ◽  
Xinming Wang

2010 ◽  
Vol 224 ◽  
pp. 012056 ◽  
Author(s):  
Andy Adler ◽  
Pascal Gaggero ◽  
Yasheng Maimaitijiang

2019 ◽  
Author(s):  
Paul Smaldino

Science involves both theory building and fact finding. This chapter focuses on the fact- finding aspect. In this sense, science can be viewed as a process of signal detection for facts. We wish to discover true associations between variables. However, our methods for measurement are imprecise. We sometimes mistake noise for signal, and vice versa. How we conceptualize the scientific enterprise shapes how we go about the business of conducting research as well as how we strive to improve scientific practices. In this chapter, I’ll present several models of science. I’ll begin by showing ways in which the classic “hypothesis testing” model of science is misleading, and leads to flawed inferences. As a remedy, I’ll discuss models that treat science as a population process, with important dynamics at the group level that trickle down to the individual practitioners. Science that is robust and reproducible depends on understanding these dynamics so that institutional programs for improvement can specifically target them.


Perception ◽  
1981 ◽  
Vol 10 (1) ◽  
pp. 107-115 ◽  
Author(s):  
Robert I Reynolds

The temporal development of illusory contour figures was investigated with the use of backward masking to control the duration of processing. The integration of an illusory triangle is elicited after 100 ms of processing time. When a pattern yielding the impression of a brick background is added to the display the triangle is elicited after 100 ms, held as a viable construct for the next 200 ms, and then is no longer perceived. When the brick pattern is drawn so as to appear transparent, a sequence of four qualitatively different percepts arise, culminating in the perception of a triangle located behind the transparent pattern. These findings are consistent with a hypothesis-testing model in which the construct ‘triangle’ interacts with an increasing number of features of the stimulus array; at each interaction it may or may not be found to be consistent with the sensory evidence newly taken into account.


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