Machine Learning Chapter comparison test

Confidence level (confidence) refers to the overall parameter probability statistics fall within a sample region, generally indicated by 1-α, α represents a significant degree; refers to the confidence interval at a certain confidence level, the sample statistics the overall error between parameter values and ranges. The larger the confidence interval, the higher the confidence level. For example, in the case of the same number of samples, do a hundred times experiment, there are 95 overall confidence interval contains the true value, confidence level of 95%.

 

FIG reaction conclusions 1-α confidence, Intuitively, corresponding to the non-hatched region in FIG.

 

 The right hand side represents the probability exceeds the number of errors in each of the reference samples together misclassification (hatched portion) should be less than a significance level α

 

t distribution called student-t distribution, often according to original sample was estimated mean and variance of the normal distribution of the sample is known. (If known population variance, then you should use the normal distribution to estimate the population mean.) (So a premise is: the total sample t distribution must comply with the normal distribution)

Subject to the standard normal distribution is assumed i.e. X X ~ N (0,1), Y n are subject to a degree of freedom chi-squared distribution i.e. Y ~ χ2 (n), and X and Y are independent, called

 

N is a distribution of degrees of freedom of the t-distribution, referred to as a Z ~ t (n);

T-distribution properties: the smaller the degree of freedom n, t and flat the profile; the greater the degree of freedom n, t closer to the standard normal distribution curve (u distribution) curve, a degree of freedom when infinity, t distribution to become a normal distribution.

 

 Chi-square distribution: If n mutually independent random variables ξ₁, ξ₂, ..., ξn, are subject to the standard normal distribution (also known as independent and identically distributed standard normal distribution ), then the n obey the standard normal distribution square configuration and a new random variable of the random variable, which is called a chi-square distribution

Suppose the following distribution t

 

 In fact, t is the abscissa, assuming a mean sample from a normal distribution is known, now known as 120, the degree of freedom for the n = 5,

100 normal distribution is desired, the variance 125, can be calculated at this time is t = 4. t = area under the fact profile after. 4 P value , if the calculated P = 0.01, P less than or equal 0.05 if we claim 5% significance level (according to needs and specific issues man may be) found may be denied "New distribution and known sample taken the same normal "hypothesis, i.e. the distribution of the new sample differs from the original known normal distribution. P to less significant level, the more significant the wrong assumption.