Sorry slightly confused here, bias (although an F concept, since it relies on “true parameter value”) is sort of orthogonal to B vs F.
Estimates based on either B or F techniques could be biased or unbiased.
Quoth famous Bayesian Andrew Gelman:
“I can’t keep track of what all those Bayesians are doing nowadays—unfortunately,
all sorts of people are being seduced by the promises of automatic inference through
the “magic of MCMC”—but I wish they would all just stop already and get back to
doing statistics the way it should be done, back in the old days when a p-value stood
for something, when a confidence interval meant what it said, and statistical bias was
something to eliminate, not something to embrace.”
Heh. I’m not a strong advocate of Bayesianism, but when someone says their estimator is unbiased, that doesn’t fill me with trust. There are many problems where the unique unbiased estimator is ridiculous (e.g. negative with high probability when the true parameter is always positive, etc.)
Sorry slightly confused here, bias (although an F concept, since it relies on “true parameter value”) is sort of orthogonal to B vs F.
Estimates based on either B or F techniques could be biased or unbiased.
Quoth famous Bayesian Andrew Gelman:
“I can’t keep track of what all those Bayesians are doing nowadays—unfortunately, all sorts of people are being seduced by the promises of automatic inference through the “magic of MCMC”—but I wish they would all just stop already and get back to doing statistics the way it should be done, back in the old days when a p-value stood for something, when a confidence interval meant what it said, and statistical bias was something to eliminate, not something to embrace.”
(http://www.stat.columbia.edu/~gelman/research/published/badbayesmain.pdf)
Heh. I’m not a strong advocate of Bayesianism, but when someone says their estimator is unbiased, that doesn’t fill me with trust. There are many problems where the unique unbiased estimator is ridiculous (e.g. negative with high probability when the true parameter is always positive, etc.)
Sure, unbiasedness is a weak property:
If you throw a dart either one foot to the left or one foot to the right of the bullseye, you are unbiased wrt the bullseye, but this is stupid.
Consistency is a better property.