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Weighted regression is common in frequentist approaches to regression. Typically, the weights are known and can be interpreted as the amount each data point is allowed to influence the link between the variables in question. This can be written as \(\mathbf{y} = \sum _i w_i \beta _i x_i\) where \(w_i\) is the 'weighting'.
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Bayesian Statistics: A Beginner's Guide
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This is the story of what influenced me to become a Bayesian statistician after being trained as a classical frequentist statistician, and practicing only that mode of statistics for many years.
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