[Q] Concept of Maximum likelihood
KP Hwang
I am an engineer who is interested in Probability theory.
Recently I study much about ML..
But I think its too difficult to understand..
Can anybody explain the concept of ML...?
Thank you..
and.. Good luck everybody..
Tjen-Sien Lim
A trip to your local university library, book store, or even cyber space (say
Amazon.com) would solve your problem. Get any book on "introductory
mathematical statistics".
--
Tjen-Sien Lim
ts...@recursive-partitioning.com
www.Recursive-Partitioning.com
____________________________________________________________________
Get your free Web-based email! http://recursive-partitioning.zzn.com
Rich Ulrich
wrote:
...
> I am an engineer who is interested in Probability theory.
>
> Recently I study much about ML..
>
> But I think its too difficult to understand..
>
> Can anybody explain the concept of ML...?
One book that was quite readable even though it was somewhat
technical: "Likelihood", by A.W.F. Edwards, 1972.
From the flyleaf: "In this book, Dr Edwards advances the thesis that
all such approaches [ like Fisher's 'fiducial probability'] fail
simply because the appropriate axiomatic basis for inductive inference
is not that of probability, with its addition axiom, but that of
likelihood, < ...> relative support among different hypotheses."
Edwards wants to convince readers to accept likelihood as the main
principle of statistical inference.
If you want something other than that theoretical introduction, I
think you may look for discussions of ML and other approaches in
textbooks on statistical estimation or theory.
--
Rich Ulrich, wpi...@pitt.edu
http://www.pitt.edu/~wpilib/index.html
rob...@sonero.colorado.edu
> > Can anybody explain the concept of ML...?
>
> One book that was quite readable even though it was somewhat
> technical: "Likelihood", by A.W.F. Edwards, 1972.
> Edwards wants to convince readers to accept likelihood as the main
> principle of statistical inference.
I found on the web a short essay by Edwards, in which he outlines his
position on inference by likelihood:
http://www.cimat.mx/reportes/enlinea/D-99-10.html
Edwards mentions two concepts: (1) The "Law of Likelihood", which
states that the relative evidence for an hypothesis H1 over another H2
is to be assessed by the ratio of the likelihood functions, L(H1)/L(H2).
(2) The "Likelihood Principle", which states that the likelihood
function entirely summarizes the information brought into an inference
by the data -- aside from the likelihood, the data do not affect an
inference.
The two principles are related but not equivalent. In particular,
Bayesians accept the Likelihood Principle, but not the Law of
Likelihood -- Bayesians do accept the likelihood function as the
only way the data influence an inference, but do not accept the
likelihood ratio as the way to assess relative strength of evidence;
instead they would use the posterior odds or a similar function, which
takes the prior probability of hypotheses into account.
To clarify terms -- broadly speaking, a likelihood function is any
conditional probability considered as a function of a variable on
which one is conditioning. That is, p(X|Y) considered as a function
of Y (with X fixed) is a likelihood function for Y. Typically X are
observed data and Y are model parameters, but that is just one case.
The maximum likelihood approach is to find the value of Y which
has greater p(X|Y) than any other; in the case mentioned, the
parameter values which make the observed data most probable. This is
an application of the Law of Likelihood.
The web page mentioned above has citations that may be helpful.
Regards,
Robert Dodier
Sent via Deja.com http://www.deja.com/
Before you buy.
henk
The idea behind ML is quite simple. Suppose you have a dataset and you
assume it is generated by a statistical proces [distribution] with unknown
parameters. ML says the most logical choice of parameters is that which has
the largest probability to generate this particular set of data.