Conservatism (Bayesian)

Definition:

Conservatism statistics refers to the tendency of Bayesian updating to be more cautious or slow in incorporating new data. It is the result of Bayesian belief updating being influenced by both prior beliefs and observed data, leading to a more cautious approach to updating probabilities.

Examples:

1. In A/B testing, Bayesian conservatism may result in a more cautious approach when updating the conversion rate estimates. If a website has a belief that the conversion rate is 5%, and after conducting an A/B test, it observes 10%, Bayesian conservatism would temper the update. Resulting in a belief that is closer to the prior belief of 5%, rather than fully embracing the 10%.
2. In financial forecasting, Bayesian conservatism may be evident when updating probabilities for investment decisions. If an investor believes that a stock has 50% chance of going up, Bayesian conservatism may result in a cautious update. Resulting in a belief that is not fully influenced by the positive news, but still retains some of the prior belief.

Evidence:

Research studies have shown that Bayesian updating tends to exhibit conservative behaviour in various domains. Including decision-making under uncertainty, risk assessment, and predictive modelling. Studies have shown that Bayesian conservatism can be observed in tasks involving estimation of probabilities, where updates tend to be biased towards the prior beliefs even after observing new data. Additionally, simulations and experiments have demonstrated how it can impact decision-making outcomes and the accuracy of probability estimates.

Summary:

Bayesian conservatism refers to the cautious or slow updating of probabilities in statistics. Prior beliefs are retained to a certain extent even after observing new data. It can also impact decision-making outcomes and the accuracy of probability estimates, leading to a more conservative approach.

Useful Resources:

1. “Bayesian Modeling in Bioinformatics” by Dipak K. Dey, Samiran Ghosh, Bani K. Mallick.
2. “Bayesian Data Analysis” by Andrew Gelman, John B. Carlin, Hal S. Stern, David B. Dunson, Aki Vehtari, Donald B. Rubin.
3. “Bayesian Reasoning and Machine Learning” by David Barber.
4. “Statistical Rethinking: A Bayesian Course with Examples in R and Stan” by Richard McElreath.
5. “Doing Bayesian Data Analysis: A Tutorial with R, JAGS, and Stan” by John Kruschke.

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