From 10f71d5661696996564d9300da0f8a2a8c9b9761 Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Sat, 9 Jan 2021 19:55:54 +0100 Subject: [PATCH] [likelihood] updated exercise --- likelihood/exercises/likelihood-1.tex | 3 +++ likelihood/lecture/likelihood.tex | 22 +++++++++++----------- 2 files changed, 14 insertions(+), 11 deletions(-) diff --git a/likelihood/exercises/likelihood-1.tex b/likelihood/exercises/likelihood-1.tex index 28b3946..c0b7f3d 100644 --- a/likelihood/exercises/likelihood-1.tex +++ b/likelihood/exercises/likelihood-1.tex @@ -15,6 +15,9 @@ \begin{questions} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\question \qt{Read chapter 9 on ``Maximum likelihood estimation''!}\vspace{-3ex} + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \question \qt{Maximum likelihood of the standard deviation} Let's compute the likelihood and the log-likelihood for the estimation diff --git a/likelihood/lecture/likelihood.tex b/likelihood/lecture/likelihood.tex index ea0cfd4..255ddd5 100644 --- a/likelihood/lecture/likelihood.tex +++ b/likelihood/lecture/likelihood.tex @@ -411,17 +411,6 @@ analysis. Neural systems face the very same problem. They also need to estimate parameters of the internal and external environment based on the activity of neurons. -In sensory systems certain aspects of the environment are encoded in -the neuronal activity of populations of neurons. One example of such a -population code is the tuning of neurons in the primary visual cortex -(V1) to the orientation of a bar in the visual stimulus. Different -neurons respond best to different bar orientations. Traditionally, -such a tuning is measured by analyzing the neuronal response strength -(e.g. the firing rate) as a function of the orientation of a black bar -and is illustrated and summarized with the so called -\enterm{tuning-curve} (\determ{Abstimmkurve}, -figure~\ref{mlecodingfig}, top). - \begin{figure}[tp] \includegraphics[width=1\textwidth]{mlecoding} \titlecaption{\label{mlecodingfig} Maximum likelihood estimation of @@ -440,6 +429,17 @@ figure~\ref{mlecodingfig}, top). orientation.} \end{figure} +In sensory systems certain aspects of the environment are encoded in +the neuronal activity of populations of neurons. One example of such a +population code is the tuning of neurons in the primary visual cortex +(V1) to the orientation of a bar in the visual stimulus. Different +neurons respond best to different bar orientations. Traditionally, +such a tuning is measured by analyzing the neuronal response strength +(e.g. the firing rate) as a function of the orientation of a black bar +and is illustrated and summarized with the so called +\enterm{tuning-curve} (\determ{Abstimmkurve}, +figure~\ref{mlecodingfig}, top). + The brain, however, is confronted with the inverse problem: given a certain activity pattern in the neuronal population, what is the stimulus? In our example, what is the orientation of the bar? In the