# How is 'updating priors' in Bayesian stats different from adding more measurements to the distribution in frequentist stats?

I'm an experimental physicist so please pardon me if my thinking about this is too concrete. Let's say I am taking a measurement over and over and trying to determine the "real" value of something, but my measurement has some inherent noise in it. Let's say I have taken 100 measurements so far.

From what I understand, in Bayesian statistics I would determine the probability that my thing has value X based on the 'priors' - in this case the distribution I have of my measurements so far, and I would update my prediction based on any further measurements I would make with some math.

In frequentist statistics, I would just update my experimentally measured distribution with each new measurement by adding it in to the set of measurements.

How are these two things different? The Bayesian version seems like an unnecessarily cumbersome way to just add a new measurement to my distribution. What am I missing here?

• With sufficient data, the prior becomes unimportant (at least in reasonable cases). But one thing to keep in mind is that it's not always possible/feasible to collect a lot of data. There are fields in which studies are published with 10-20 noisy data points. Having a well-defined prior is valuable there because you're less likely to be misled by small amounts of random variation in the study. – mkt Feb 24 at 16:13
• I see, thank you. it seems like having a prior which is influenced by one's personal biases may be more dangerous than staying agnostic... – SabrinaChoice Feb 24 at 23:49
• No, it isn't, because (1) the prior makes you define and defend your subjective beliefs, and (2) one's biases can come through in many ways other in a frequentist study. It may be different in many areas of physics, where hypotheses are constrained by well-defined, mathematical theory and systems can be isolated into smaller and smaller units for experimentation. In many sciences, this is not true, and hypotheses can seem arbitrary or developed ad hoc while studies are full of noisy confounders (see the replication crisis in social psychology for examples of how this can go wrong). – mkt Feb 25 at 7:38
• @mkt thanks for your comment. Can you expand on how the prior leads one to defend the subjective belief? On another note, I agree very much with your point (2)! – SabrinaChoice Mar 3 at 1:04
• @ mkt Thank you, that helps clear up some small misunderstandings I had. – SabrinaChoice Mar 16 at 3:20