20240907 - law of total probability

10-Prediction.Rmd

@@ -251,6 +251,24 @@ $$
 (\#eq:conditionalProbabilityRevised)
 $$
 
+We can then estimate the marginal probability of the event, substititing in $P(R | \text{not } C)$, using the law of total probability.
+The [`petersenlab`](https://cran.r-project.org/web/packages/petersenlab/index.html) package [@R-petersenlab] contains the `pA()` function that estimates the marginal probability of one event, $A$.
+
+```{r, eval = FALSE, class.source = "fold-hide"}
+pA <- function(pAgivenB, pB, pAgivenNotB){
+  value <- (pAgivenB * pB) + pAgivenNotB * (1 - pB)
+
+  value
+}
+```
+
+```{r}
+pA(
+  pAgivenB = .95,
+  pB = .003,
+  pAgivenNotB = .007171515)
+```
+
 The [`petersenlab`](https://github.com/DevPsyLab/petersenlab) package [@R-petersenlab] contains the `pBgivenNotA()` function that estimates the probability of one event, $B$, given that another event, $A$, did not occur.\index{petersenlab package}\index{Bayesian!Bayes' theorem}
 
 ```{r, eval = FALSE, class.source = "fold-hide"}