In the limit,Īll weight is given to the information coming from the sample and no weight is As a consequence, when theīecomes large, more and more weight is given to the sample mean. While the weight given to the prior mean does not. The weight given to the sample mean increases with That has higher precision (smaller variance). The signals are combined (linearly), but more weight is given to the signal Both the prior and the sample mean convey Of probability density functions (see also the Is the density of a normal distribution with mean Given the prior and the likelihood, specified above, the posteriorĬan put together the results obtained so far andĪ probability density function if considered as a function of This prior is used to express the statistician's belief that the unknownĪre quite unlikely (how unlikely depends on the variance To highlight the fact that the density depends on the unknown parameter Of the distribution is unknown, while its In this section, we are going to assume that the mean The observed sample used to carry out inferences is a vector The posterior distribution of the variance The prior predictive distribution conditional on the variance The posterior distribution of the mean conditional on the variance
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