diff --git a/02-Discrete-Bayes.ipynb b/02-Discrete-Bayes.ipynb index d7e060c..b157953 100644 --- a/02-Discrete-Bayes.ipynb +++ b/02-Discrete-Bayes.ipynb @@ -5822,7 +5822,7 @@ "\n", "The literature often gives you these equations in the form of integrals. After all, an integral is just a sum over a continuous function. So, you might see Bayes' theorem written as\n", "\n", - "$$P(A \\mid B) = \\frac{P(B \\mid A)\\, P(A)}{\\int P(B \\mid A) P(B) \\mathtt{d}y}\\cdot$$\n", + "$$P(A \\mid B) = \\frac{P(B \\mid A)\\, P(A)}{\\int P(B \\mid A_j) P(A_j) \\mathtt{d}A_j}\\cdot$$\n", "\n", "In practice the denominator can be fiendishly difficult to solve analytically (a recent opinion piece for the Royal Statistical Society [called it](http://www.statslife.org.uk/opinion/2405-we-need-to-rethink-how-we-teach-statistics-from-the-ground-up) a \"dog's breakfast\" [8]. Filtering textbooks are filled with integral laden equations which you cannot be expected to solve. We will learn more techniques to handle this in the **Particle Filters** chapter. Until then, recognize that in practice it is just a normalization term over which we can sum. What I'm trying to say is that when you are faced with a page of integrals, just think of them of sums, and relate them back to this chapter, and often the difficulties will fade. Ask yourself \"why are we summing these values\", and \"why am I dividing by this term\". Surprisingly often the answer is readily apparent." ]