scholarly journals A Bridge from Monty Hall to the Hot Hand: The Principle of Restricted Choice

2019 ◽  
Vol 33 (3) ◽  
pp. 144-162 ◽  
Author(s):  
Joshua B. Miller ◽  
Adam Sanjurjo
Keyword(s):  
Conditional Probability ◽  
Selection Bias ◽  
Experimental Subject ◽  
Card Game ◽  
Hot Hand ◽  
Monty Hall ◽  
Monty Hall Problem ◽  
Available Information ◽  
Inferential Rule

We show how classic conditional probability puzzles, such as the Monty Hall problem, are intimately related to the recently discovered hot hand selection bias. We explain the connection by way of the principle of restricted choice, an intuitive inferential rule from the card game bridge, which we show is naturally quantified as the updating factor in the odds form of Bayes’s rule. We illustrate how, just as the experimental subject fails to use available information to update correctly when choosing a door in the Monty Hall problem, researchers may neglect analogous information when designing experiments, analyzing data, and interpreting results.

scholarly journals A Bridge from Monty Hall to the Hot Hand: Restricted Choice, Selection Bias, and Empirical Practice

2018 ◽  
Author(s):  
Joshua Benjamin Miller ◽  
Adam Sanjurjo
Keyword(s):  
Conditional Probability ◽  
Selection Bias ◽  
Experimental Subject ◽  
Bayes Rule ◽  
Card Game ◽  
Hot Hand ◽  
Monty Hall ◽  
Monty Hall Problem ◽  
Available Information ◽  
Inferential Rule

We show how classic conditional probability puzzles, such as the Monty Hall problem, are intimately related to the hot hand selection bias. We explain the connection by way of the principle of restricted choice, an intuitive inferential rule from the card game bridge, which we show is naturally quantified as the updating factor in the odds form of Bayes Rule. We illustrate how, just as the experimental subject fails to use available information to update correctly when choosing a door in the Monty Hall problem, researchers may neglect analogous information when designing experiments, analyzing data, and interpreting results.

scholarly journals The Use of Official Statistics in Self-Selection Bias Modeling

2016 ◽  
Vol 32 (4) ◽  
pp. 887-905 ◽  
Author(s):  
Luciana Dalla Valle
Keyword(s):  
Selection Bias ◽  
Small Businesses ◽  
Real Data ◽  
Sources Of Information ◽  
Quality Of Data ◽  
Official Statistics ◽  
Step Method ◽  
Development Education ◽  
Self Selection ◽  
Available Information

Abstract Official statistics are a fundamental source of publicly available information that periodically provides a great amount of data on all major areas of citizens’ lives, such as economics, social development, education, and the environment. However, these extraordinary sources of information are often neglected, especially by business and industrial statisticians. In particular, data collected from small businesses, like small and medium-sized enterprizes (SMEs), are rarely integrated with official statistics data. In official statistics data integration, the quality of data is essential to guarantee reliable results. Considering the analysis of surveys on SMEs, one of the most common issues related to data quality is the high proportion of nonresponses that leads to self-selection bias. This work illustrates a flexible methodology to deal with self-selection bias, based on the generalization of Heckman’s two-step method with the introduction of copulas. This approach allows us to assume different distributions for the marginals and to express various dependence structures. The methodology is illustrated through a real data application, where the parameters are estimated according to the Bayesian approach and official statistics data are incorporated into the model via informative priors.

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