René's URL Explorer Experiment

{"@context":"https://schema.org","@type":"DiscussionForumPosting","headline":"P(X = x) for continuous data is problematic","articleBody":"https://github.com/GeostatsGuy/DataScienceInteractivePython/blob/adf0515484c587a900d6991d81c504e99171611f/Interactive_Model_Fitting.ipynb#L56\r\n\r\nThe notebook useses the P(X | ... ) notation, which I would interpret as the conditional probability of the data. However, linear models would typically be used for continuous response data where P(X_i = \u003cvalue\u003e | ... ) is zero. Instead, one would use the densities, i.e. small p or f. \r\n\r\nFurthermore, since a product is used, this implies that the observations are independent from each other. Hence, as written a little further down:\r\n\r\n*OLS: - assumes that the errors have a mean of zero, constant variance and are independent of eachother (no correlation in error).*\r\n\r\nIs incomplete, because the same was assumed for the ML approach.\r\n\r\nAltogether, I find that the post a little confusion. As far as I know: For a Gaussian response distribution with KNOWN $\\sigma$ the OLS and MLE should be identical. I fail to completely understand what the exact data generating mechanism is in the example due to a lot of code, but for a simple normal X_1,...,X_n \\iid N(\\mu, \\sigma^2) there are explicit solutions available? As a suggestion: Maybe write the data generating mechanism clearer in math notation.","author":{"url":"https://github.com/mhoehle","@type":"Person","name":"mhoehle"},"datePublished":"2024-09-18T11:15:47.000Z","interactionStatistic":{"@type":"InteractionCounter","interactionType":"https://schema.org/CommentAction","userInteractionCount":0},"url":"https://github.com/6/DataScienceInteractivePython/issues/6"}