CN111861033A - College entrance probability prediction method with white noise - Google Patents

College entrance probability prediction method with white noise Download PDF

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CN111861033A
CN111861033A CN202010749315.1A CN202010749315A CN111861033A CN 111861033 A CN111861033 A CN 111861033A CN 202010749315 A CN202010749315 A CN 202010749315A CN 111861033 A CN111861033 A CN 111861033A
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佘彦
赵龙霄
任庆伟
李峥
潘生林
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Zhejiang Cuiwen Technology Co Ltd
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Abstract

The invention discloses a college entrance probability prediction method with white noise, which comprises the following steps: constructing a prediction database and determining an equivalent fraction sample sequence; determining a fraction probability distribution function according to the equivalent fraction sample sequence, wherein the probability density function corresponding to the fraction probability distribution function is the superposition of a normal distribution probability density function and white noise; calculating an admission probability by using Bayesian estimation and a prediction database; and carrying out unbiased detection on the consensus optimal potential of the admission probability, wherein if the detection is established, the admission probability is the final predicted college probability of the college entrance examination. The method considers the variation of the admission fraction of colleges and universities caused by multiple uncertain factors, adds white noise into the model function, solves the influence of the uncertain factors on the admission probability, obtains the admission probability through Bayesian estimation, and further checks the reasonability of the obtained admission probability through the unbiased check of the consistent optimal potential, thereby increasing the accuracy of prediction and reducing the risk of admission failure.

Description

College entrance probability prediction method with white noise
Technical Field
The invention relates to the technical field of data statistics, in particular to a college entrance probability prediction method with white noise.
Background
College entrance examination is an important turning point of life, and the filling of volunteers is an important link for determining the future direction of practice. Especially, when college entrance examination receives more and more attention, how to reasonably and efficiently fill in volunteers according to the college entrance examination score is even more important than the college entrance examination. As is known, the reporting of volunteers needs to be carried out by integrating a plurality of parameters, and the reporting of examinations assisted by so-called specialists or famous doctors in the society is judged only by the past experiences of the specialists or the famous doctors, is influenced by personal subjective factors and lacks of scientific basis. In such a big data age today, artificial intelligence is growing up, and college entrance examination reporting modes relying on data and algorithms are more and more accepted by examinees and parents.
The existing college entrance examination application method is only recommended simply according to score lines of the years and satisfaction degrees of colleges, namely, the method refers to a plurality of self ideal colleges selected by a test taker in advance, and screens out specific colleges fluctuating up and down in scores according to the college entrance examination scores of the test taker. The method does not consider the specific change situation and trend of the lowest admission score of a professional year over time, and does not consider other uncertain factors such as regional factors, policy factors, economic development factors and the like. Therefore, the method has great probability error of enrollment, and the examinee is easy to lose profits in the process of filling and submitting volunteers.
Disclosure of Invention
Therefore, it is necessary to provide a more scientific method for predicting college entrance probability for solving the problem of large registration prediction error existing in the prior college entrance examination aspiration filling method.
In order to solve the problems, the invention adopts the following technical scheme:
a college entrance probability prediction method with white noise comprises the following steps:
the method comprises the following steps: constructing a prediction database and determining an equivalent fraction sample sequence;
step two: determining a fraction probability distribution function according to the equivalent fraction sample sequence, wherein the probability density function corresponding to the fraction probability distribution function is the superposition of a normal distribution probability density function and white noise;
step three: calculating an admission probability using bayesian estimates and the prediction database;
step four: and carrying out unbiased detection on the consensus optimal potential of the admission probability, wherein if the detection is established, the admission probability is the final predicted high-entrance-to-average admission probability.
Compared with the prior art, the invention has the following beneficial effects:
the college entrance probability prediction method provided by the invention considers the variation of college entrance scores caused by multiple uncertain factors, adds white noise into a model function, represents the uncertain items in an entrance probability distribution function by introducing the white noise, solves the influence of the uncertain factors on the entrance probability, obtains the entrance probability by Bayes (Bayes) estimation, and further verifies the rationality of the obtained entrance probability by uniform optimal potential unbiased test, thereby increasing the accuracy of prediction and reducing the risk of entrance failure.
Drawings
FIG. 1 is a flow chart of a method for predicting probability of college entrance examination with white noise according to the present invention;
FIG. 2 is a graph of the fractional probability distribution function with white noise in the present invention.
Detailed Description
The following description is given of specific embodiments of the present invention in order to facilitate understanding of the objects, features and advantages of the present invention by those skilled in the art. It should be noted that the described embodiments are only some of the embodiments of the present invention, and not all of them. The present invention is not limited in scope by the specific embodiments, and all inventions utilizing the inventive concept are intended to be protected as long as the various changes are within the spirit and scope of the invention as defined and defined in the appended claims.
In order to better explain the scheme of the invention, the following description is combined with the accompanying drawings of the specification.
FIG. 1 is a flow chart of the prediction method of probability of college entrance with white noise according to the present invention. As shown in fig. 1, in an embodiment, the present invention provides a method for predicting probability of college entrance with white noise, which comprises the following steps:
step one (S100): and constructing a prediction database and determining an equivalent fractional sample sequence.
In this step, when the prediction database is constructed, it is necessary to count data such as the number of examinees in a preset year of a target province, the score ranking of a score to be measured in the preset year of the target province, the minimum admission score of a preset year of a target specialty of a target college and a batch line of the target province, and construct the prediction database based on these data, where the number of examinees in the preset year of the target province and the batch line of the target province can be queried on the enrollment web pages of the target province, the minimum admission score of the preset year of the target specialty of the target college located in the target province can be queried on the web pages of various college websites, and the score ranking of a score to be measured in the preset year of the target province can be queried on a segment table of the target province.
The equivalent fraction sample sequence is a set of scores of the next year in a preset year, which are found by utilizing a segment table and have the same order as the score to be detected. For example, in jilin province as an example, the score to be measured in 2019 is selected as x, the score of the next year in the preset year with the same rank is found in a segment table, and similar to discount processing in financial mathematics, the corresponding equivalent score sample sequence of the target specialty to be predicted is further found:
Figure BDA0002609496090000031
wherein
Figure BDA0002609496090000032
Representing that the fraction x to be measured is equivalent to the equivalent fraction of the last nth year, i is more than or equal to 1 and less than or equal to n, and n is the number of samples in the equivalent fraction sample sequence.
Optionally, the preset year is the last 3-5 years of the current year corresponding to the score to be measured, that is, the prediction database includes the number of examinees in the last 3-5 years of the target province, the score ranking of the score to be measured in the last 3-5 years of the target province, the lowest admission score of the target specialty in the last 3-5 years of the target university and the batch line of the target province.
Step two (S200): and determining a fraction probability distribution function according to the equivalent fraction sample sequence, wherein the probability density function corresponding to the fraction probability distribution function is the superposition of the normal distribution probability density function and white noise.
According to the method, the scores of the examinees are normally distributed, and a new score probability distribution function is obtained by adding white noise, namely an interference item, on the basis of the normal distribution probability density function.
Specifically, the process of determining a fractional probability distribution function from the equivalent fractional sample sequence comprises the steps of:
step two, firstly: from equivalent fractional sample sequences
Figure BDA0002609496090000045
Calculating the sample mean value by the following calculation formula:
Figure BDA0002609496090000041
wherein n is the number of samples in the equivalent fractional sample sequence;
step two: from equivalent fractional sample sequences
Figure BDA0002609496090000046
Calculating the standard deviation of the sample by the following formula:
Figure BDA0002609496090000042
step two and step three: since the probability density function of the score is normally distributed, the probability density function is:
Figure BDA0002609496090000043
wherein the content of the first and second substances,
Figure BDA0002609496090000044
is white noise, is the derivative of brownian motion, which is also a gaussian process, satisfying a normal distribution. The invention adopts white noise to represent uncertain factors which can influence the final admission probability in the college entrance examination.
White noise or its derivative form, brownian motion, is commonly used in stock and option pricing to represent factors that interfere with stock price trends, and the same reasoning applies here, since the factors that affect admission are not constant and can vary with different policies in different years or different countries or even global fluctuations. White noise is added to depict the uncertain factors, so that the obtained probability is more scientific.
The fractional probability distribution function is:
Figure BDA0002609496090000051
substituting the probability density function into the fraction probability distribution function to obtain a new fraction probability distribution function as follows:
Figure BDA0002609496090000052
fig. 2 is a graph showing the fractional probability distribution function after white noise is added.
Step three (S300): the probability of enrollment is calculated using bayesian estimation and a prediction database.
In this step, the Bayesian formula is used, the number of examinees in the preset year of the target province in the prediction database, the score ranking of the score to be measured in the preset year of the target province, the lowest admission score of the preset year of the target specialty in the target colleges and universities, and the batch line of the target province are combined, the admission probability is calculated, and the formula for calculating the admission probability by using the Bayesian estimation and the prediction database is as follows:
Figure BDA0002609496090000053
wherein the content of the first and second substances,
Figure BDA0002609496090000054
the representatives consider the ranking, number of provinces and the fractional conditional probability of the batch line,
Figure BDA0002609496090000055
representing the probability of the score to be tested reaching the lowest admission score.
Step four (S400): and carrying out unbiased detection on the consensus optimal potential of the admission probability, wherein if the detection is established, the admission probability is the final predicted college probability of the college entrance examination.
In this step, a unified optimality unbiased test (UMPUT) needs to be performed on the enrollment probability obtained in step S300 to determine whether the obtained enrollment probability distribution function model is reasonable, so as to determine whether the computed enrollment probability is reasonable.
The unbiased test of consistent optimal potential for the probability of enrollment includes the following steps:
order to
Figure BDA0002609496090000061
Only the sample standard deviation need be considered
Figure BDA0002609496090000062
One parameter, which becomes a single parameter hypothesis testing problem;
consider the original hypothesis
Figure BDA0002609496090000063
And alternative assumptions
Figure BDA0002609496090000064
Our purpose is to demonstrate the original hypothesis H0Is correct, i.e. the alternative hypothesis H is eliminated1。
Phi (x) is a test at level alpha, the test function is:
Figure BDA0002609496090000065
wherein, c1And c2Two real numbers; optionally σ' < σ1Or σ' > σ2Consider:
Figure BDA0002609496090000066
for convenience of representation, let the probability density function be:
Figure BDA0002609496090000067
wherein the content of the first and second substances,
Figure BDA0002609496090000068
if k exists1And k2So that:
Figure BDA0002609496090000069
the test is established and the probability of enrollment is reasonable. k is a radical of1And k2The conditions should be satisfied:
Figure BDA00026094960900000610
Figure BDA00026094960900000611
so that when x is equal to c1And x ═ c2In time, there are:
Figure BDA0002609496090000071
there is thus the following system of equations:
Figure BDA0002609496090000072
wherein, c1And c2Known as k1And k2Unknown, solve the system of equations to obtain k1And k2：
Figure BDA0002609496090000073
Since σ' < σ1＜σ2And c1＜c2Therefore, it is
(σ1·c1+σ2·c2)-(σ1·c2+σ2·c1)＝(σ1-σ2)·(c1-c2)＞0
(σ′·c1+σ2·c2)-(σ′·c2+σ2·c1)＝(σ′-σ2)·(c1-c2)＞0
(σ1·c1+σ′·c2)-(σ1·c2+σ′·c1)＝(σ1-σ′)·(c1-c2)＜0
Thus k1＞0，k2Less than 0; order to
Figure BDA0002609496090000074
Wherein:
Figure BDA0002609496090000075
b1＝σ1-σ′＞0，b2＝σ2-σ′＞0
and b is1＜b2Where x is c1And x ═ c2In time, there are:
Figure BDA0002609496090000076
the curve being unimodal, according to which the curve is plotted
Figure BDA0002609496090000077
Figure BDA0002609496090000078
From this, k can be found1And k2I.e., assuming evidence, also indicates that the predicted probability of enrollment is within a reasonable range.
Finally, for example, the probability of enrollment according to the above steps is shown. First, the number of college entrance examination students in a certain province in 2015-charge 2018 is obtained as follows:
Figure BDA0002609496090000081
by querying a segment table, the lowest entry score and ranking of the province to a professional of a college are as follows:
year of year 2015 years 2016 (year) 2017 2018 years old
Lowest score 556 560 543 573
Average score 562 564 552 579
Ranking 9724 10578 10101 9828
The province 2015 and 2018 are divided into:
year of year 2015 years 2016 (year) 2017 2018 years old
Average score 510 514 491 516
The province 2015 and 2018 year primary and secondary lines are as follows:
year of year 2015 years 2016 (year) 2017 2018 years old
A book line 525 530 507 533
Two-line 405 402 379 405
According to the prediction method of the college entrance probability with white noise, the probability that the examinee with the score 563 to be tested in 2019 can be admitted by the professional college in colleges and universities is predicted to be 61.72%, and the admission probability is in a reasonable range through the uniform optimal potential unbiased test.
The college entrance probability prediction method provided by the invention considers the variation of college entrance scores caused by multiple uncertain factors, adds white noise into a model function, represents the uncertain items in an entrance probability distribution function by introducing the white noise, solves the influence of the uncertain factors on the entrance probability, obtains the entrance probability by Bayes (Bayes) estimation, and further verifies the rationality of the obtained entrance probability by uniform optimal potential unbiased test, thereby increasing the accuracy of prediction and reducing the risk of entrance failure.
The technical features of the embodiments described above may be arbitrarily combined, and for the sake of brevity, all possible combinations of the technical features in the embodiments described above are not described, but should be considered as being within the scope of the present specification as long as there is no contradiction between the combinations of the technical features.
The above-mentioned embodiments only express several embodiments of the present invention, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the inventive concept, which falls within the scope of the present invention. Therefore, the protection scope of the present patent shall be subject to the appended claims.

Claims (7)

1. A college entrance probability prediction method with white noise is characterized by comprising the following steps:
the method comprises the following steps: constructing a prediction database and determining an equivalent fraction sample sequence;
step two: determining a fraction probability distribution function according to the equivalent fraction sample sequence, wherein the probability density function corresponding to the fraction probability distribution function is the superposition of a normal distribution probability density function and white noise;
step three: calculating an admission probability using bayesian estimates and the prediction database;
step four: and carrying out unbiased detection on the consensus optimal potential of the admission probability, wherein if the detection is established, the admission probability is the final predicted high-entrance-to-average admission probability.
2. The method of claim 1, wherein the step of determining the fractional probability distribution function based on the equivalent fractional sample sequence comprises the steps of:
step two, firstly: from equivalent fractional sample sequences
Figure FDA0002609496080000011
Calculating the sample mean value by the following calculation formula:
Figure FDA0002609496080000012
wherein n is the number of samples in the equivalent fractional sample sequence;
step two: from equivalent fractional sample sequences
Figure FDA0002609496080000013
Calculating the standard deviation of the sample by the following formula:
Figure FDA0002609496080000014
step two and step three: since the probability density function of the score is normally distributed, the probability density function is:
Figure FDA0002609496080000015
wherein the content of the first and second substances,
Figure FDA0002609496080000016
is white noise;
obtaining a fractional probability distribution function according to the probability density function as follows:
Figure FDA0002609496080000021
3. the method for predicting probability of college entrance with white noise according to claim 1 or 2, wherein the formula for calculating the probability of college entrance by using bayesian estimation and the prediction database is:
Figure FDA0002609496080000022
wherein the content of the first and second substances,
Figure FDA0002609496080000023
represents the fractional conditional probability that the probability of the score,
Figure FDA0002609496080000024
representing the probability of the score to be tested reaching the lowest admission score.
4. The method for predicting college entrance probability with white noise according to claim 1 or 2, wherein the unbiased test of the consistent optima for the entrance probability comprises the following steps:
order to
Figure FDA0002609496080000025
Only the sample standard deviation need be considered
Figure FDA0002609496080000026
One parameter, which becomes a single parameter hypothesis testing problem;
consider the original hypothesis
Figure FDA0002609496080000027
And alternative assumptions
Figure FDA0002609496080000028
Phi (x) is a test at level alpha, the test function is:
Figure FDA0002609496080000029
wherein, c1And c2Two real numbers; optionally σ' < σ1Or σ' > σ2Consider:
Figure FDA00026094960800000210
for convenience of representation, let the probability density function be:
Figure FDA00026094960800000211
wherein the content of the first and second substances,
Figure FDA00026094960800000212
if k exists1And k2So that:
Figure FDA0002609496080000031
then the test is established, the probability of admission is reasonable, k1And k2The conditions should be satisfied:
Figure FDA0002609496080000032
Figure FDA0002609496080000033
so that when x is equal to c1And x ═ c2In time, there are:
Figure FDA0002609496080000034
there is thus the following system of equations:
Figure FDA0002609496080000035
wherein, c1And c2Known as k1And k2Unknown, solve the system of equations to obtain k1And k2：
Figure FDA0002609496080000036
Since σ' < σ1＜σ2And c1＜c2Therefore, it is
(σ1·c1+σ2·c2)-(σ1·c2+σ2·c1)＝(σ1-σ2)·(c1-c2)＞0
(σ′·c1+σ2·c2)-(σ′·c2+σ2·c1)＝(σ′-σ2)·(c1-c2)＞0
(σ1·c1+σ′·c2)-(σ1·c2+σ′·c1)＝(σ1-σ′)·(c1-c2)＜0
Thus k1＞0，k2Less than 0; order to
Figure FDA0002609496080000037
Wherein:
Figure FDA0002609496080000041
b1＝σ1-σ′＞0，b2＝σ2-σ′＞0
and b is1＜b2Where x is c1And x ═ c2In time, there are:
Figure FDA0002609496080000042
the curve being unimodal, according to which the curve is plotted
Figure FDA0002609496080000043
Figure FDA0002609496080000044
From this, k can be found1And k2I.e., assuming evidence, also indicates that the predicted probability of enrollment is within a reasonable range.
5. The method of predicting probability of college entrance with white noise according to claim 1,
the prediction database comprises the number of examinees in a preset year of the target province, the score ranking of the score to be detected in the preset year of the target province, the lowest admission score of the preset year of the target major of the target colleges and universities and the batch line of the target province.
6. The method of predicting probability of college entrance with white noise according to claim 5,
the equivalent fraction sample sequence is a set of scores of the next year in a preset year, which are found by utilizing a segment table and have the same order as the score to be detected.
7. The method for predicting college entrance probability with white noise according to claim 5 or 6,
the preset year is the last 3-5 years of the current year corresponding to the fraction to be detected.
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112632470A (en) * 2020-12-23 2021-04-09 浙江萃文科技有限公司 Method for establishing college entrance probability based on UMPUT probability test

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112632470A (en) * 2020-12-23 2021-04-09 浙江萃文科技有限公司 Method for establishing college entrance probability based on UMPUT probability test

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