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[likelihood] updated exercise

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Jan Benda 2021-01-09 19:55:54 +01:00
parent 454c7178c7
commit 10f71d5661
2 changed files with 14 additions and 11 deletions
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likelihood/exercises/likelihood-1.tex
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@ -15,6 +15,9 @@
\begin{questions} \begin{questions}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\question \qt{Read chapter 9 on ``Maximum likelihood estimation''!}\vspace{-3ex}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\question \qt{Maximum likelihood of the standard deviation} \question \qt{Maximum likelihood of the standard deviation}
Let's compute the likelihood and the log-likelihood for the estimation Let's compute the likelihood and the log-likelihood for the estimation

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likelihood/lecture/likelihood.tex
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@ -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 estimate parameters of the internal and external environment based on
the activity of neurons. 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] \begin{figure}[tp]
\includegraphics[width=1\textwidth]{mlecoding} \includegraphics[width=1\textwidth]{mlecoding}
\titlecaption{\label{mlecodingfig} Maximum likelihood estimation of \titlecaption{\label{mlecodingfig} Maximum likelihood estimation of
@ -440,6 +429,17 @@ figure~\ref{mlecodingfig}, top).
orientation.} orientation.}
\end{figure} \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 The brain, however, is confronted with the inverse problem: given a
certain activity pattern in the neuronal population, what is the certain activity pattern in the neuronal population, what is the
stimulus? In our example, what is the orientation of the bar? In the stimulus? In our example, what is the orientation of the bar? In the