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But you will never know the truth. So it seems more practical to assume that the parameter follows some distribution and that the hand is fixed. Just a more log

But you will never know the truth. So it seems more practical to assume that the parameter follows some distribution and that the hand is fixed. Just a more logical approach to gauging uncertainty in my opinion. But, this is not a "Frequentist versus Bayesian" post. I think the key is to use what is most fitting for the analysis at hand.

quacker 12y ago
You'll never know all of the data either. You don't need confidence/credible intervals if you can sample the entire population. Maybe one is more intuitive than the other, but I'm unswayed by the "one is fixed in real life" argument.
- kblarsen4 12y ago
  I noticed that I had a typo. I meant "data is fixed" not "hand is fixed," but I guess it was clear anyway. I see your point. Thanks for the input. I do think that P(hypothesis | Data) - the Bayesian way - is more intuitive than P(Data | hypothesis). I also think that the confidence interval is often misinterpreted as a credible interval. But that does not mean that the credible interval is the right choice for every analysis. From a purely practical sense, the data is fixed when you have your sample or have collected your time series data. This is the data you have and you can observe it. I do agree that the data may change when you collect more samples or get more history. But the Bayesian framework is set up well to handle that, as today's result can be tomorrow's prior. Having said all this, I don't think this debate takes away from the use cases outlined in this post. This is not meant to read as "Bayesian versus frequentist" but rather to highlight some important benefits of Bayesian analysis. For example, if I am building a pricing model that will be used to make actual decisions and my classical model is spewing out strange coefficients that do not seem to be consistent with external data and common sense. I want to infuse that model with outside information before I use the model to make real life decisions, or just shrink it. Bayesian regression gives up a structured and transparent way to handle these types of situations.
- pdonis 12y ago
  > You'll never know all of the data either. "The data is fixed" refers only to the data we know. (Otherwise, as you point out, there would be no issue since we would simply calculate the population statistics directly.) In the frequentist model, we have to pretend that this fixed data is actually a random distribution in order to calculate the probability we're interested in. In the Bayesian model, we just combine the known data with the prior to get the posterior probability; we don't have to pretend anything.
  - quacker 12y ago
    > "The data is fixed" refers only to the data we know. Okay, yeah. The sample is fixed. The entire population is random. I'll use this terminology. > In the frequentist model, we have to pretend that this fixed data is actually a random distribution With confidence intervals, we're modelling the entire population as a random distribution, using the fixed sample's mean and variance to compute estimates of the population's mean and variance. I think this is different than "pretending the sample is random". If you constructed a normal model of the sample, you would just use the sample's mean and standard deviation. But to model the population, you typically use the sample's standard error as an estimate of the population's standard deviation. This is critical. You have to account for the fact that the population is much larger than your sample.

quacker 12y ago

You'll never know all of the data either. You don't need confidence/credible intervals if you can sample the entire population. Maybe one is more intuitive than the other, but I'm unswayed by the "one is fixed in real life" argument.

kblarsen4 12y ago
I noticed that I had a typo. I meant "data is fixed" not "hand is fixed," but I guess it was clear anyway. I see your point. Thanks for the input. I do think that P(hypothesis | Data) - the Bayesian way - is more intuitive than P(Data | hypothesis). I also think that the confidence interval is often misinterpreted as a credible interval. But that does not mean that the credible interval is the right choice for every analysis. From a purely practical sense, the data is fixed when you have your sample or have collected your time series data. This is the data you have and you can observe it. I do agree that the data may change when you collect more samples or get more history. But the Bayesian framework is set up well to handle that, as today's result can be tomorrow's prior. Having said all this, I don't think this debate takes away from the use cases outlined in this post. This is not meant to read as "Bayesian versus frequentist" but rather to highlight some important benefits of Bayesian analysis. For example, if I am building a pricing model that will be used to make actual decisions and my classical model is spewing out strange coefficients that do not seem to be consistent with external data and common sense. I want to infuse that model with outside information before I use the model to make real life decisions, or just shrink it. Bayesian regression gives up a structured and transparent way to handle these types of situations.
pdonis 12y ago
> You'll never know all of the data either. "The data is fixed" refers only to the data we know. (Otherwise, as you point out, there would be no issue since we would simply calculate the population statistics directly.) In the frequentist model, we have to pretend that this fixed data is actually a random distribution in order to calculate the probability we're interested in. In the Bayesian model, we just combine the known data with the prior to get the posterior probability; we don't have to pretend anything.
- quacker 12y ago
  > "The data is fixed" refers only to the data we know. Okay, yeah. The sample is fixed. The entire population is random. I'll use this terminology. > In the frequentist model, we have to pretend that this fixed data is actually a random distribution With confidence intervals, we're modelling the entire population as a random distribution, using the fixed sample's mean and variance to compute estimates of the population's mean and variance. I think this is different than "pretending the sample is random". If you constructed a normal model of the sample, you would just use the sample's mean and standard deviation. But to model the population, you typically use the sample's standard error as an estimate of the population's standard deviation. This is critical. You have to account for the fact that the population is much larger than your sample.