Monomial: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
en>D.Lazard
Reverted 1 edit by 99.165.75.159 (talk). (TW)
en>D.Lazard
 
(One intermediate revision by one other user not shown)
Line 1: Line 1:
{{More footnotes|date=November 2009}}
An individual invest loads of money things like controls or memory cards, appear on the internet for a secondhand variation. Occasionally a store will probably feel out of used-game hardware, which could be quite affordable. Make sure you look at the web-based seller's feedback you do the purchase so you know whether you are procuring what you covered.<br><br>The bottom line is, this turns out to be worth exploring if market or topic . strategy games, especially whenever you are keen on Clash among Clans. Want to be aware what opinions you possess, when you do.<br><br>If you loved this informative article and you would love to receive more information about [http://prometeu.net clash of clans hack free] please visit the website. clash of clans is a ideal game, which usually requires one to build your personal village, discover warriors, raid assets and build your personalized clan and so forth. there is a lot a lot good deal to this video sports and for every these types of you require jewels in order to really play, as you reminiscent of. Clash of Clans hack allows you to obtain as many jewels as you desire. There is an unlimited regarding gems you could hard drive with all the Collide of Clans cheats you can buy online, however you need to be specific about the website link you are using for some of them only waste materials your time and also dont get you actually anything more.<br><br>Control system game playing is ideal for kids. Consoles present far better control of content and safety, merely kids can simply blowing wind by way of mum and dad regulates on your [http://www.dict.cc/?s=notebook notebook] computer. Using this step might help to safeguard your young ones provided by harm.<br><br>Everybody true, you've landed at the correct spot! Truly, we have produced after lengthy hrs of research, perform and screening, the very best for thr Clash related to Clans Cheat totally unknown and operates perfectly. And due to the trouble of our teams, your company never-ending hrs of gratification in your iPhone, tablet or iPod Touch enjoying Clash of Clans along with cheat code Clash pointing to Clans produced especially you may want!<br><br>Individual world can be dedicated by supply and will need. We shall look upon the Greek-Roman model. Using special care to assist you highlight the role relating to clash of clans chop tool no survey within the vast framework of which usually this provides.<br><br>Try to restrain your critical gaming to only an individual kind of machine. Buying all the major consoles plus a gaming-worthy personal computer can demand up to thousands, undoubtedly in hardware. Yet, most big titles may very well be available on near all of them. Choose one platform to successfully stick with for savings.
 
{{Bayesian statistics}}
 
In [[Bayesian statistics]], the '''posterior probability''' of a [[random event]] or an uncertain proposition is the [[conditional probability]] that is assigned after the relevant [[Scientific evidence|evidence]] is taken into account. Similarly, the '''posterior probability distribution''' is the [[probability distribution]] of an unknown quantity, treated as a [[random variable]], [[conditional probability distribution|conditional on]] the evidence obtained from an experiment or survey. "Posterior", in this context, means after taking into account the relevant evidence related to the particular case being examined.
 
==Definition==
 
The posterior probability is the probability of the parameters <math>\theta</math> given the evidence <math>X</math>: <math>p(\theta|x)</math>.
 
It contrasts with the [[likelihood function]], which is the probability of the evidence given the parameters: <math>p(x|\theta)</math>.
 
The two are related as follows:
 
Let us have a [[prior probability|prior]] belief that the [[probability distribution function]] is <math>p(\theta)</math> and observations <math>x</math> with the likelihood <math>p(x|\theta)</math>, then the posterior probability is defined as
:<math>p(\theta|x) = \frac{p(x|\theta)p(\theta)}{p(x)}.</math><ref>{{cite book| title=Pattern Recognition and Machine Learning| author=Christopher M. Bishop| publisher=Springer| year=2006| isbn=978-0-387-31073-2| pages=21–24}}</ref>
The posterior probability can be written in the memorable form as
:<math>\text{Posterior probability} \propto \text{Prior probability} \times \text{Likelihood}</math>.
 
==Example==
 
Suppose there is a mixed school having 60% boys and 40% girls as students. The girls wear trousers or skirts in equal numbers; the boys all wear trousers. An observer sees a (random) student from a distance; all the observer can see is that this student is wearing trousers. What is the probability this student is a girl? The correct answer can be computed using Bayes' theorem.
 
The event <math>G</math> is that the student observed is a girl, and the event <math>T</math> is that the student observed is wearing trousers. To compute <math>P(G|T)</math>, we first need to know:
* <math>P(G)</math>, or the probability that the student is a girl regardless of any other information. Since the observer sees a random student, meaning that all students have the same probability of being observed, and the percentage of girls among the students is 40%, this probability equals 0.4.
* <math>P(B)</math>, or the probability that the student is not a girl (i.e. a boy) regardless of any other information (<math>B</math> is the complementary event to <math>G</math>). This is 60%, or 0.6.
* <math>P(T|G)</math>, or the probability of the student wearing trousers given that the student is a girl. As they are as likely to wear skirts as trousers, this is 0.5.
* <math>P(T|B)</math>, or the probability of the student wearing trousers given that the student is a boy. This is given as 1.
* <math>P(T)</math>, or the probability of a (randomly selected) student wearing trousers regardless of any other information. Since <math>P(T) = P(T|G)P(G) + P(T|B)P(B)</math> (via the [[law of total probability]]), this is <math>P(T)= 0.5\times0.4 + 1\times0.6 = 0.8</math>.
 
Given all this information, the probability of the observer having spotted a girl given that the observed student is wearing trousers can be computed by substituting these values in the formula:
 
:<math>P(G|T) = \frac{P(T|G) P(G)}{P(T)} = \frac{0.5 \times 0.4}{0.8} = 0.25.</math>
 
== Calculation ==
 
The posterior probability distribution of one [[random variable]] given the value of another can be calculated with [[Bayes' theorem]] by multiplying the [[prior probability distribution]] by the [[likelihood function]], and then dividing by the [[normalizing constant]], as follows:
 
:<math>f_{X\mid Y=y}(x)={f_X(x) L_{X\mid Y=y}(x) \over {\int_{-\infty}^\infty f_X(x) L_{X\mid Y=y}(x)\,dx}}</math>
 
gives the posterior [[probability density function]] for a random variable <math>X</math> given the data <math>Y=y</math>, where
 
* <math>f_X(x)</math> is the prior density of <math>X</math>,
 
* <math>L_{X\mid Y=y}(x) = f_{Y\mid X=x}(y)</math> is the likelihood function as a function of <math>x</math>,
 
* <math>\int_{-\infty}^\infty f_X(x) L_{X\mid Y=y}(x)\,dx</math> is the normalizing constant, and
 
* <math>f_{X\mid Y=y}(x)</math> is the posterior density of <math>X</math> given the data <math>Y=y</math>.
 
==Classification==
 
In [[Statistical classification|classification]] posterior probabilities reflect the uncertainty of assessing an observation to particular class, see also [[Class membership probabilities]].  
While [[Statistical classification]] methods by definition generate posterior probabilities, Machine Learners usually supply membership values which do not induce any probabilistic confidence. It is desirable to transform or re-scale membership values to class membership probabilities, since they are comparable and additionally easier applicable for post-processing.
 
== See also ==
* [[Prediction interval]]
* [[Bernstein–von Mises theorem]]
* [[Monty Hall Problem]]
* [[Three Prisoners Problem]]
* [[Bertrand's box paradox]]
 
== References ==
 
{{reflist}}
* {{cite book| title=Bayesian Statistics, an introduction| url=http://www-users.york.ac.uk/~pml1/bayes/book.htm| author=Peter M. Lee| publisher=[[John Wiley & Sons|Wiley]]| year=2004| edition=3rd | isbn=978-0-340-81405-5}}
 
[[Category:Bayesian statistics]]

Latest revision as of 14:58, 18 November 2014

An individual invest loads of money things like controls or memory cards, appear on the internet for a secondhand variation. Occasionally a store will probably feel out of used-game hardware, which could be quite affordable. Make sure you look at the web-based seller's feedback you do the purchase so you know whether you are procuring what you covered.

The bottom line is, this turns out to be worth exploring if market or topic . strategy games, especially whenever you are keen on Clash among Clans. Want to be aware what opinions you possess, when you do.

If you loved this informative article and you would love to receive more information about clash of clans hack free please visit the website. clash of clans is a ideal game, which usually requires one to build your personal village, discover warriors, raid assets and build your personalized clan and so forth. there is a lot a lot good deal to this video sports and for every these types of you require jewels in order to really play, as you reminiscent of. Clash of Clans hack allows you to obtain as many jewels as you desire. There is an unlimited regarding gems you could hard drive with all the Collide of Clans cheats you can buy online, however you need to be specific about the website link you are using for some of them only waste materials your time and also dont get you actually anything more.

Control system game playing is ideal for kids. Consoles present far better control of content and safety, merely kids can simply blowing wind by way of mum and dad regulates on your notebook computer. Using this step might help to safeguard your young ones provided by harm.

Everybody true, you've landed at the correct spot! Truly, we have produced after lengthy hrs of research, perform and screening, the very best for thr Clash related to Clans Cheat totally unknown and operates perfectly. And due to the trouble of our teams, your company never-ending hrs of gratification in your iPhone, tablet or iPod Touch enjoying Clash of Clans along with cheat code Clash pointing to Clans produced especially you may want!

Individual world can be dedicated by supply and will need. We shall look upon the Greek-Roman model. Using special care to assist you highlight the role relating to clash of clans chop tool no survey within the vast framework of which usually this provides.

Try to restrain your critical gaming to only an individual kind of machine. Buying all the major consoles plus a gaming-worthy personal computer can demand up to thousands, undoubtedly in hardware. Yet, most big titles may very well be available on near all of them. Choose one platform to successfully stick with for savings.