class: center, middle, inverse, title-slide # Data Order Invariance ### Dr. Dogucu --- layout: true <div class="my-header"></div> <div class="my-footer"> From Bayes Rules! book Copyright &copy; Drs. Alicia Johnson, Miles Ott & Mine Dogucu. <a href="https://creativecommons.org/licenses/by-nc-sa/4.0/">CC BY-NC-SA 4.0</a></div> --- `$$f(\theta | x_1,x_2) = f(\theta|x_2,x_1)$$` -- `$$f(\theta|x_1) = \frac{\text{prior}\cdot \text{likelihood}}{\text{normalizing constant}} = \frac{f(\theta)L(\theta|x_1)}{f(x_1)}$$` -- `$$f(\theta|x_2) = \frac{\text{prior}\cdot \text{likelihood}}{\text{normalizing constant}} = \frac{\frac{f(\theta)L(\theta|x_1)}{f(x_1)}L(\theta|x_2)}{f(x_2)}$$` -- `$$f(\theta|x_1,x_2) = \frac{f(\theta)L(\theta|x_1)L(\theta|x_2)}{f(x_1)f(x_2)}$$` -- `$$f(\theta|x_2,x_1) = \frac{f(\theta)L(\theta|x_2)L(\theta|x_1)}{f(x_2)f(x_1)}$$` -- `$$f(\theta | x_1,x_2) = f(\theta|x_2,x_1)$$`