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Introduction: There are two main methods in probability statistics: Parameter Statistics and non-Parameter Statistics (or parameter estimation and non-parameter estimation ). Where,
Parameter
extremum point of the likelihood function is
The maximum likelihood estimate of the parameter p is
It can be seen that the probability p of each event in two distributions is equal to the probability of the event occurring in N independent repetitive random trials.
If we do 20 experiments, there are 12 positive, negative 8
Then the parameter value p is 12/20 = 0.6 according to the maximum likelihood
two distributions is equal to the probability of event occurrence in N independent repeated random tests.
If we do 20 experiments, there will be 12 front-end labs and 8 back-end labs
According to the maximum likelihood estimation, the parameter value p is 12/20 = 0.6.
2. Maximum Posterior Estimation Map
The maximum posterior
the two distributions is equal to the probability of event occurrence in N independent repeated random tests.
If we do 20 experiments, there will be 12 front-end labs and 8 back-end labs
According to the maximum likelihood estimation, the parameter value p is 12/20 = 0.6.
2. Maximum Posterior Estimation Map
The maximum posterior
Why do you use parameter estimation?
In Bayesian method, the prior probability and conditional density function are estimated beforehand, and then the classifier is designed. However, in most cases, the number of training samples is always too small, and when used to denote a high number of feature dimensions, the estimation of the conditional density fu
In mathematical statistics, the total x we have seen is generally unknown. Even if, according to previous experience and data, X obeys that type of distribution, its numerical characteristics (such as mathematical expectation, variance, moment) are unknown. These unknown numeric characteristics and the unknowns contained in the total x are called unknown parameters (parameters). In order to estimate the true value or the interval of the unknown functi
Seventh Chapter parameter estimation
Content Summary:
One, point estimate
1, set for the overall sample, the overall distribution function is known as the parameters to be evaluated for the corresponding sample observations. The problem of point estimation is to construct an appropriate statistic and estimate the value
the above figure, because we priori think P is about equal to 0.5, so that the hyper-parameters A and B are equal, we choose equal to 5).Now we can solve the extremum point of the map estimation function, and the maximum posteriori estimate of P is obtained by the same p derivative number.The following two items are the derivation of log (P (P|alpha,beta))And the results of the maximum likelihood estimation
Parameter estimation is based on sampling and sampling distribution, and the general parameters are inferred according to sample statistics. 1 principle of parameter estimation
1 estimate and Estimated valueEstimate: The name of the statistic used to estimate the overall
estimation, the most important point before using NLMINB () is to determine the initial value, the closer the initial value is to the real value, the more accurate the result of the calculation. We suspect that the distribution of the data is two normal mixed, the probability p directly with 0.5 to do the initial value. With the x-axis values (approximately 50 and 80>) corresponding to the two peaks in the
Estimated
Point estimation: for a given population and sample, if an unknown parameter of the population is estimated using the value of a statistic, this estimation method is called point estimation, which is called the point estimator. For example, sample mean is used to estimate the overall mean, and sample variance
We often encounter non-parameter estimation problems-K nearest neighbor, meanshift, and Kernel Density Estimation. Therefore, we plan to learn this part of the theoretical knowledge system over the past two days, feel it here.
1. Introduction: questions about height differences between men and women.
This is a question that the interviewer asked me when I int
6.3 Interval estimation of two normal populations(1) Two total variance knownThe function Twosample.ci () that calculates the confidence interval in R is as follows, with the input parameter being the standard deviation of sample x, Y, confidence α, and two samples.> twosample.ci=function (X,Y,ALPHA,SIGMA1,SIGMA2) {+ n1=length (x); N2=length (y) + xbar=mean (x)-mean (y) + Z =qnorm (1-ALPHA/2) *sqrt (SIG
Problem background:
We know the distribution of the population, but we do not know the parameters of the distribution, so we need to estimate the unknown parameters.
Two estimations of the types:
1. Point estimation
2. Interval estimation
1. Point estimation
Including momen
algorithm repeats the following two steps until convergence.Step 1: Estimate (E) Step: Use the current hypothesis H and the observed data x to estimate the probability distribution on y to calculate Q (h ' | h).Q (h ' | h) ←e[ ln P (y|h ') | h, X ]Step 2: Maximize (M) Step: Replace the assumption H with the assumption H ' that maximizes the Q function:H ←argmaxq (h ' | h)parameter
, then X1 and X2 only one of them, the greater the correlation between features the greater the absolute value of the correlation coefficient, the correlation coefficient matrix can be used to filter the characteristics.Estimating parameters with samples
Moment estimation
Moment estimation method, also known as "moment method Estimation", is to use
Note: The following is organized in the July algorithm April 2016 class training handout, see: http://www.julyedu.com/Content Introduction:A. Important statisticsB. Important theorems and inequalitiesC. Parameter estimationA. Important statisticsFirst, probability and statisticsProbability: The distribution of known population, the probability of calculating eventsStatistics: The overall
that the user is satisfy for the last click of the document, then the attractiveness variable and the satisfaction variable are observed. This is simplified DCM, which has:3) MLE for SDBN2. The EM algorithmConsider the random variable in the Bayesian network and its parent node. The probability is the parameterBernoulli distribution. An EM algorithm can be used to estimate the parameters of a variable in the parent node if it cannot be observe.1) Exp
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