From d515c66f7fc41767d30f3a040259b95c9a7fe42f Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?J=C3=A4kel=2C=20Frank?= <jaekel@psychologie.tu-darmstadt.de> Date: Fri, 4 Sep 2020 08:12:38 +0200 Subject: [PATCH] Made tasks a little more precise after experience with corrections --- signal_detection_homework.ipynb | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/signal_detection_homework.ipynb b/signal_detection_homework.ipynb index b1803be..a04c933 100644 --- a/signal_detection_homework.ipynb +++ b/signal_detection_homework.ipynb @@ -248,7 +248,7 @@ "source": [ "## Exercise 5\n", "\n", - "How biased should you have been in each of the other conditions, where $p\\neq0.5$? Given your estimate for your sensitivity $d'$, what should your criterion $\\lambda$ have been? In order to derive and compute the optimal $\\lambda$ for a given $d'$ and $p$ you will have to use Bayes' theorem. Let $X$ be the random variable based on which you decide and $S$ is the stimulus in a trial. A useful variant of Bayes' theorem is this:\n", + "How biased should you have been in each of the other conditions, where $p\\neq0.5$? Given your estimate for your sensitivity $d'$, what should your criterion $\\lambda$ have been? You will answer these questions in the next exercise. In order to derive and compute the optimal $\\lambda$ for a given $d'$ and $p$ you will have to use Bayes' theorem. Let $X$ be the random variable based on which you decide and $S$ is the stimulus in a trial. A useful variant of Bayes' theorem is this:\n", "\n", "$$\n", "\\frac{p(S=\\text{signal}\\mid X=x)}{p(S=\\text{noise}\\mid X=x)} = \\frac{p(X=x\\mid S=\\text{signal})}{p(X=x\\mid S=\\text{noise})}\\cdot\\frac{p(S=\\text{signal})}{p(S=\\text{noise})}\n", -- GitLab