Find ξ Value with Maximum Likelihood

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Discussion Overview

The discussion revolves around finding the value of the parameter ξ using Maximum Likelihood Estimation (MLE) in the context of a decay function related to a dataset from a robot soccer competition. Participants explore the relationship between various parameters and the graphical representation of the data.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant expresses confusion about the equation and seeks guidance on determining the value of ξ.
  • Another participant notes that the values of ξ appear to be plotted on the horizontal axis of the provided graph.
  • A participant shares a model involving a non-increasing function φ and mentions uncertainty regarding the decay speed ζ.
  • One participant clarifies that they misunderstood the initial request, thinking the discussion was about MLE rather than deriving a value for ξ.
  • A participant acknowledges the need to apply MLE to find ζ but expresses confusion about the probabilities α and β.
  • Another participant suggests that if the goal is to find the maximum likelihood estimator of ζ from the graph, it seems to occur around ζ = 0.006.
  • A participant provides a dataset related to robot soccer competition and describes their intention to analyze team scoring ability through a double Poisson model, referencing a paper's weighting function but indicating uncertainty about obtaining the maximum likelihood of the decay rate ζ.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding the parameters involved and the application of MLE. There is no consensus on how to derive the value of ξ or the decay rate ζ, and multiple viewpoints and uncertainties remain present in the discussion.

Contextual Notes

Participants have not fully stated their models or assumptions, leading to potential gaps in understanding. The discussion includes unresolved mathematical steps and dependencies on definitions that are not clarified.

ryusukekenji
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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?
 
Last edited by a moderator:
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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 [tex]\xi[/tex]are plotted on the horizontal axis.
 
Last edited:
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...
 
Last edited by a moderator:
Sorry. I didn't know you wanted to derive a value for a parameter of [tex]\xi[/tex]. I took [tex]\xi[/tex] 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 [itex]\zeta[/itex] from the graph, then it looks to me like the maximum value on the graph occurs around [itex]\zeta= 0.006[/itex].
 
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.
 

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