Question

请问，如果利用最大似然法求模型参数（在MATLAB中）

请问大家，MATLAB中有没有基于最大似然法求模型参数的函数？
需要解决的问题是：现在有相关的数据和数据的模型，想根据数据来拟合模型中的的参数，在MATLAB中有，但只知道是基于最小二乘法，请问MATLAB中有没有基于最大似然方法的估计函数，麻烦大家了:)

Answer 1

有啊，看帮助文件吧。
>>help mle
MLE Maximum likelihood estimation.
PHAT = MLE(DATA) returns maximum likelihood estimates (MLEs) for the
parameters of a normal distribution, computed using the sample data in
the vector DATA.

[PHAT, PCI] = MLE(DATA) returns MLEs and 95% confidence intervals for
the parameters.

[...] = MLE(DATA,'distribution',DIST) computes parameter estimates for
the distribution specified by DIST. DIST is a character string
containing the name of one of the distributions supported by MLE.

[...] = MLE(DATA, ..., '冲历NAME1',VALUE1,'NAME2',VALUE2,...) specifies
optional argument name/value pairs chosen from the following list.
Argument names are case insensitive and partial matches are allowed.

Name Value
'censoring'慎塌 A boolean vector of the same size as DATA,
containing ones when the corresponding elements of
DATA are right-censored observations and zeros when
the corresponding elements are exact observations.
Default is all observations observed exactly.
Censoring is not supported for all distributions.
'frequency' A vector of the same size as DATA, containing
non-negative integer frequencies for the corresponding
elements in DATA. Default is one observation per
element of DATA.
'alpha' A value between 0 and 1 specifying a confidence level
of 100*(1-alpha)% for PCI. Default is alpha=0.05 for
95% confidence.
'散孝搜ntrials' A scalar, or a vector of the same size as DATA,
containing the total number of trials for the
corresponding element of DATA. Applies only to the
binomial distribution.
'options' A structure created by a call to STATSET, containing
numerical options for the fitting algorithm. Not
applicable to all distributions.

MLE can also fit a custom distribution that you define using
distribution functions, in one of three ways:

[...] = MLE(DATA,'pdf',PDF,'cdf',CDF,'start',START,...) returns MLEs
for the parameters of the distribution defined by the probability
density and cumulative distribution functions PDF and CDF. PDF and CDF
are function handles created using @. They accept as inputs a vector
of data and one or more individual distribution parameters, and return
vectors of probability density values and cumulative probability
values, respectively. If the 'censoring' name/value pair is not
present, you may omit the 'cdf' name/value pair. MLE computes the
estimates by numerically maximizing the distribution's log-likelihood,
and START is a vector containing initial values for the parameters.

[...] = MLE(DATA,'logpdf',LOGPDF,'logsf',LOGSF,'start',START,...)
returns MLEs for the parameters of the distribution defined by the log
probability density and log survival functions LOGPDF and LOGSF. LOGPDF
and LOGSF are function handles created using @. They accept as inputs
a vector of data and one or more individual distribution parameters,
and return vectors of logged probability density values and logged
survival function values, respectively. This form is sometimes more
robust to the choice of starting point than using PDF and CDF
functions. If the 'censoring' name/value pair is not present, you may
omit the 'logsf' name/value pair. START is a vector containing initial
values for the distribution's parameters.

[...] = MLE(DATA,'nloglf',NLOGLF,'start',START,...) returns MLEs for
the parameters of the distribution whose negative log-likelihood is
given by NLOGLF. NLOGLF is a function handle specified using @, that
accepts the four input arguments
PARAMS - a vector of distribution parameter values
DATA - a vector of data
CENS - a boolean vector of censoring values
FREQ - a vector of integer data frequencies
NLOGLF must accept all four arguments even if you do not supply the
'censoring' or 'frequency' name/value pairs (see above). However,
NLOGLF can safely ignore its CENS and FREQ arguments in that case.
NLOGLF returns a scalar negative log-likelihood value and, optionally,
a negative log-likelihood gradient vector (see the 'GradObj' STATSET
parameter below). START is a vector containing initial values
for the distribution's parameters.

PDF, CDF, LOGPDF, LOGSF, or NLOGLF can also be cell arrays whose first
element is a function handle as defined above, and whose remaining
elements are additional arguments to the function. MLE places these
arguments at the end of the argument list in the function call.

The following optional argument name/value pairs are valid only when
'pdf' and 'cdf', 'logpdf' and 'logcdf', or 'nloglf' are given.

'lowerbound' A vector the same size as START containing lower bounds
for the distribution parameters. Default is -Inf.
'upperbound' A vector the same size as START containing upper bounds
for the distribution parameters. Default is Inf.
'optimfun' A string, either 'fminsearch' or 'fmincon', naming the
optimization function to be used in maximizing the
likelihood. Default is 'fminsearch'. You may only
specify 'fmincon' if the Optimization Toolbox is
available.

When fitting a custom distribution, use the 'options' parameter to
control details of the maximum likelihood optimization. See
STATSET('mlecustom') for parameter names and default values. MLE
interprets the following STATSET parameters for custom distribution
fitting as follows:

'GradObj' 'on' or 'off', indicating whether or not FMINCON
can expect the function provided with the 'nloglf'
name/value pair to return the gradient vector of the
negative log-likelihood as a second output. Default
is 'off'. Ignored when using FMINSEARCH.
'DerivStep' The relative difference used in finite difference
derivative approximations when using FMINCON, and
'GradObj' is 'off'. May be a scalar, or the same
size as START. EPS^(1/3) by default. Ignored when
using FMINSEARCH.
'FunValCheck' 'on' or 'off', indicating whether or not MLE should
check the values returned by the custom distribution
functions for validity. Default is 'on'. A poor
choice of starting point can sometimes cause these
functions to return NaNs, infinite values, or out of
range values if they are written without suitable
error-checking.
'TolBnd' An offset for upper and lower bounds when using
FMINCON. MLE treats upper and lower bounds as
strict inequalities (i.e., open bounds). With
FMINCON, this is approximated by creating closed
bounds inset from the specified upper and lower
bounds by TolBnd. Default is 1e-6.

Answer 2

能不能告诉我一下呀 谢谢了