Béda révisi "Informasi Fisher"

38 bita dipupus ,  15 tahun yang lalu
===Conto===
 
TheInformasi informationdipiboga contained indina ''n'' independent [[Bernoulli trial]]s bebas, eachnu withunggal probabilityprobabiliti of successsukses ''θ'' maybisa bediitung calculatedsiga asdi followshandap ieu. In the followingRunduyannana, ''a'' representsngagambarkeun thejumlah numbersukses of successes, ''b'' thejumlah number of failuresgagal, andsarta ''n=a+b'' is the totalngarupakeun numberjumlah ofsakabeh trialspercobaan.
 
:<math>
::<math>=\frac{n}{\theta(1-\theta)}</math>
 
Garis kahiji sakadar ngahartikeun informasi; kadua migunakeun kanyataan kandungan informasi dina kacukupan statistik saru jeung eta sampel sorangan; garis katilu ngan perluasan watesan [[logarithm|log]] (jeung ngaleungitkeun konstant), kaopat jeung kalima ngan proses diferensiasi wrt ''&theta;'', kagenep ngagantikeun ''a'' jeung ''b'' ku ekspektasina , sarta katujuh ngarupakaeun manipulasi aljabar.
The first line is just the definition of information; the second uses the fact that the information contained in a sufficient statistic is the same as that of the sample itself; the third line just expands the [[logarithm|log]] term (and drops a constant), the fourth and fifth just differentiation wrt ''&theta;'', the sixth replaces ''a'' and ''b'' with their expectations, and the seventh is algebraic manipulation.
 
Hasil kabehannana, nyaeta
The overall result, viz
:<math>
I(\theta)=\frac{n}{\theta(1-\theta)}</math>
may be seen to be in accord with what one would expect, since it is the reciprocal of the variance of the sum of the ''n'' Bernoulli random variables..
 
InDina casekasus the parameterparamete &theta; isngarupakeun vectornilai valuedvektor, theinformasi informationngarupakeun isharti-positip a positive-definitetina matrixmatriks, whichnu definesdihartikeun asameter metric on thedina parameter spaceruang; consequentlyakibatna [[differential geometry]] isdipake applieddina toieu this topictopik. See Tempo[[Fisher information metric]].
 
[[Category:Statistics]][[Category:Information theory]]
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