# Find ξ Value with Maximum Likelihood

• ryusukekenji
In summary, the problem is that the author is trying to find the decay rate ζ for a parameter of \xi, but does not seem to understand how to do it.
ryusukekenji
http://bbs.mathchina.com/usr1PvjRWKew/4/22/graph_1261406609.jpg

I can't understand the equation, may I know is there any good idea to get the value of ξ?

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It is a little hard to read, but based on the curve and the Fig 1 label underneath , it looks like the values of $$\xi$$are plotted on the horizontal axis.

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http://cos.name/bbs/attachment/Mon_0912/15_88059_ae128f170c6c431.jpg

φ=non-increase function
tk=Time of observation k
I have built up may basic model, while just leaving decay speed ζ which I have no idea...

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Sorry. I didn't know you wanted to derive a value for a parameter of $$\xi$$. I took $$\xi$$ as given and thought we were asking about Maximum Likelihood Estimation.

I didnt stated whole model at first, that's why...
hmmm... It must apply Maximum Likelihood in order to get ζ ... but I am not really understand α and β which are probabilities of occurrence.

You still haven't told us what the problem really is! If it is to find the maximum likliehood estimator of $\zeta$ from the graph, then it looks to me like the maximum value on the graph occurs around $\zeta= 0.006$.

Example：

T1 T2 X Y Date
A B 1 0 01Jan
A C 2 2 03Jan
B D 3 1 03Jan
A D 1 1 08Jan
B C 0 0 08Jan
C B 2 1 09Jan
D A 1 0 14Jan
D B 2 3 15Jan
C A 2 1 15Jan
B A 1 1 18Jan

I have a dataset of observations on robot soccer competition. Right here I try to stated example above if let say I would like to count team scoring ability through individual double poisson with time series. Previous matches result will less effect through decay function.
The picture above is one of my reference, I would like to follow this paper's weighting function but I am not really know how to get the maximum likelihood of decay rate ζ.

## 1. What is the maximum likelihood method for finding ξ value?

The maximum likelihood method is a statistical approach used to estimate the parameters of a probability distribution, such as the ξ value, by finding the value that maximizes the likelihood of the observed data. This method assumes that the observed data is a random sample from a population with a known probability distribution.

## 2. How does the maximum likelihood method work?

The maximum likelihood method works by first defining a likelihood function, which is a measure of how likely it is for the observed data to occur at different values of the parameter ξ. The method then finds the value of ξ that maximizes this likelihood function, using mathematical techniques such as optimization algorithms.

## 3. What is the difference between maximum likelihood and least squares methods?

The maximum likelihood method is used to estimate the parameters of a probability distribution, while the least squares method is used to fit a line or curve to a set of data points. The maximum likelihood method is based on the likelihood function, while the least squares method is based on minimizing the sum of squared errors between the data points and the fitted line or curve.

## 4. Can the maximum likelihood method be used for any type of data?

Yes, the maximum likelihood method can be used for any type of data that can be described by a probability distribution. This includes continuous and discrete data, and data from various types of experiments and studies.

## 5. Are there any limitations to the maximum likelihood method?

One limitation of the maximum likelihood method is that it relies on the assumption that the observed data is a random sample from a population with a known probability distribution. If this assumption is not met, the estimated ξ value may not be accurate. Additionally, the method can be computationally intensive for complex models with many parameters.

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