566 research outputs found
Multiple perspectives on the concept of conditional probability
Conditional probability is a key to the subjectivist theory of probability; however, it plays a subsidiary role in the usual conception of probability where its counterpart, namely independence is of basic importance. The paper investigates these concepts from various perspectives in order to shed light on their multi-faceted character. We will include the mathematical, philosophical, and educational perspectives. Furthermore, we will inspect conditional probability from the corners of competing ideas and solving strategies. For the comprehension of conditional probability, a wider approach is urgently needed to overcome the well-known problems in learning the concepts, which seem nearly unaffected by teaching
The Three Doors Problem...-s
I argue that we must distinguish between:
(0) the Three-Doors-Problem Problem [sic], which is to make sense of some
real world question of a real person.
(1) a large number of solutions to this meta-problem, i.e., many specific
Three-Doors-Problem problems, which are competing mathematizations of the
meta-problem (0).
Each of the solutions at level (1) can well have a number of different
solutions: nice ones and ugly ones; correct ones and incorrect ones. I discuss
three level (1) solutions, i.e., three different Monty Hall problems; and try
to give three short correct and attractive solutions. These are: an
unconditional probability question; a conditional probability question; and a
game-theory question.
The meta-message of the article is that applied statisticians should beware
of solution-driven science.Comment: Submitted to Springer Lexicon of Statistics. Version 2: some minor
improvement
Dominance in the Monty Hall Problem
Elementary decision-theoretic analysis of the Monty Hall dilemma shows that
the problem has dominance. This makes possible to discard nonswitching
strategies, without making any assumptions on the prior distribution of factors
out of control of the decision maker. A path to the Bayesian and the minimax
decision-making environments is then straightforward.Comment: http://www.springerlink.com/content/8402812734520774/fulltext.pd
Three doors anomaly, “should I stay, or should I go”: an artefactual field experiment
This work aims to identify and quantify the biases behind the anomalous behavior of
people when they deal with the Three Doors dilemma, which is a really simple but
counterintuitive game. Carrying out an artefactual field experiment and proposing
eight different treatments to isolate the anomalies, we provide new interesting
experimental evidence on the reasons why subjects fail to take the optimal decision.
According to the experimental results, we are able to quantify the size and the
impact of three main biases that explain the anomalous behavior of participants:
Bayesian updating, illusion of control and status quo bias
Three doors anomaly, ‘‘should I stay, or should I go’’: an artefactual field experiment
This work aims to identify and quantify the biases behind the anomalous behavior of people when they deal with the Three Doors dilemma, which is a really simple but counterintuitive game. Carrying out an artefactual field experiment and proposing eight different treatments to isolate the anomalies, we provide new interesting experimental evidence on the reasons why subjects fail to take the optimal decision. According to the experimental results, we are able to quantify the size and the impact of three main biases that explain the anomalous behavior of participants: Bayesian updating, illusion of control and status quo bias
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