Improved method for scoring probability of psychological test of admission rope based on Bayesian theory

Abstract

The invention relates to the technical field of psychology, in particular to an improved standard rope psychological test probability scoring method based on the Bayesian theory. The method comprises the following steps: S1, aiming at a standard rope test method of a psychological test, comparing physiological reaction intensities of a tested person on related questions and standard rope questions, and scoring each related question according to a difference degree of a comparison result to obtain experimental data; s2, analyzing experimental data to obtain binormal distribution parameters of an experimental result; s3, calculating a likelihood probability according to a normal distribution result; s4, setting a prior probability according to different permissible rope test methods; s5, calculating false negative and false positive condition probabilities; s6, calculating the lying posterior probability of the tested person; and S7, setting a score line for judging whether a lie lies or not. And through a Bayesian updating mechanism, the posterior probability is continuously adjusted according to the new evidence, so that the evaluation result is closer to reality.

Description

Technical Field

[0001] The invention relates to the technical field of psychometrics, and in particular to an improved probability scoring method for criterion psychological tests based on Bayesian theory. Background Art

[0002] The goal of psychological testing is to infer whether an individual is hiding something by detecting different physiological reactions when they are lying and telling the truth. If the person being tested shows signs of lying during a psychological test (lie detector), negative emotions such as tension, fear, and terror will trigger physiological reactions. This abnormal physiological reaction can be captured through a multi-channel physiological acquisition device (usually including skin electricity, pulse, and breathing), ultimately identifying the possibility that the person being tested is lying.

[0003] In the existing improved criterion psychological test probability scoring method based on Bayesian theory, the likelihood probability of the normal distribution obtained by polynomial fitting is inaccurate; the existing method calculates the likelihood probability of the normal distribution of the experimental scoring results by polynomial fitting. Obviously, the accuracy of the fitting function's description of the true cumulative probability is closely related to the sample sampling method, sample distribution and sample size, which can easily lead to overfitting and function distortion problems; for the posterior probability of lying or being honest in the monocular standard rope test method, the joint probability calculation method is used, which leads to the deviation of the result; the prior probability setting of lying or being honest in the multi-eye standard rope test method is unreasonable; the assumptions about false positives and false negatives are unreasonable. Therefore, an improved criterion psychological test probability scoring method based on Bayesian theory is provided. Summary of the invention

[0004] The purpose of the present invention is to provide an improved probability scoring method for standard psychological tests based on Bayesian theory, so as to solve the problems proposed in the above background technology that the likelihood probability of the normal distribution obtained by polynomial fitting in the existing improved probability scoring method for standard psychological tests based on Bayesian theory is inaccurate; the existing method calculates the likelihood probability for the normal distribution of the experimental scoring results by polynomial fitting, and it is obvious that the accuracy of the fitting function in describing the true cumulative probability is closely related to the sample sampling method, sample distribution and sample size, which can easily lead to overfitting and function distortion problems; for the posterior probability of lying or honesty of the monocular standard rope test method, a joint probability calculation method is used, which leads to deviation in the results; the setting of the prior probability of lying or honesty of the multi-eye standard rope test method is unreasonable; and the assumptions about false positives and false negatives are unreasonable.

[0005] To achieve the above object, the present invention aims to provide an improved probability scoring method for standard psychological tests based on Bayesian theory, comprising the following steps:

[0006] S1. The criterion test method for psychological testing compares the physiological response intensity of the subjects on relevant questions and criterion questions, and scores each relevant question according to the degree of difference in the comparison results to obtain experimental data;

[0007] S2. Obtain binormal distribution parameters of the experimental results by analyzing the experimental data;

[0008] S3. Calculate the likelihood probability based on the normal distribution results;

[0009] S4. Set the prior probability according to different criteria testing methods;

[0010] S5. Calculate the false negative and false positive conditional probabilities;

[0011] S6. Calculate the posterior probability of the person being tested lying based on the false negative and false positive conditional probability results;

[0012] S7. Set a score line to determine whether someone is lying.

[0013] As a further improvement of the technical solution, in S1, each relevant question is scored according to the degree of difference in the comparison results, and the specific scoring rules for the experimental data are obtained as follows:

[0014] Using a 7-point system, i.e. -3 to +3, the scoring rules are as follows:

[0015] There is no significant difference in the physiological response between R and C. R / C = 1: 0 points;

[0016] The physiological responses of R and C are generally different (1<(1R / C1)≦1.5), and they are scored ±1 points (strong R is scored “-”, strong C is scored “+”);

[0017] The physiological responses of R and C were significantly different (1.5 < (1R / C1) ≦ 3), and were scored ±2 points (strong R was scored “-”, and strong C was scored “+”);

[0018] If the physiological responses of R and C are significantly different (R / C>3), ±3 points will be awarded (strong R will be awarded “-”, strong C will be awarded “+”);

[0019] Among them, R represents relevant issues and C represents standard issues.

[0020] As a further improvement of the technical solution, in S2, the specific steps of obtaining the binormal distribution parameters of the experimental results by analyzing the experimental data are as follows:

[0021] S2.1. Collect and organize physiological response data for honest and lying answers;

[0022] S2.2. Let the dataset of honest answers be X true={x1,x2,…,x n}, the data set of lying answers is X lie ={y1,y2,…,y m};

[0023] S2.3. Calculate the dataset X of honest answers true and the lying answer dataset X lie The mean and standard deviation of

[0024] S2.4. Use the mean and standard deviation calculated in step S2.3 to fit two normal distributions, one representing the distribution of physiological response intensity for honest answers and the other representing the distribution of physiological response intensity for lying answers.

[0025] As a further improvement of this technical solution, in S2.3, the data set X of honest answers is calculated true and the lying answer dataset X lie The specific expressions of the mean and standard deviation are:

[0026] For the honest answer dataset X true :

[0027] Mean

[0028] Standard Deviation

[0029] Where n represents the data set X true The number of elements in; μ1 represents the honest answer dataset X tru The average value of e; σ1 represents the honest answer data set X true The standard deviation of x i Represents X true The i-th data point in the data set; i represents the index variable;

[0030] For the lying answer data set X lie :

[0031] Mean

[0032] Standard Deviation

[0033] Where m represents the dataset X lie The number of elements in; μ2 represents lying answers to the dataset X lie The average value of σ2 indicates that the lying answer data set X lie The standard deviation of y j Represents the jth data point in the data set; j represents the index variable.

[0034] As a further improvement of the technical solution, in S2.4, the specific expression for fitting two normal distributions is:

[0035] Distribution of physiological response intensity for honest answers f true (z):

[0036]

[0037] Among them, f true (z) represents the probability density function of the physiological response intensity z in the case of honest answer;

[0038] Distribution of physiological response intensity to lying answers lie (z):

[0039]

[0040] Among them, f lie (z) represents the probability density function of the intensity z of the physiological reaction in the case of lying.

[0041] As a further improvement of the technical solution, in S3, the likelihood probability is calculated according to the normal distribution result:

[0042] The cumulative probability function according to the normal distribution is:

[0043]

[0044] Among them, F(x) represents the cumulative probability function of the normal distribution; P(X≤x) represents the probability that the value of the random variable X falls within the interval from negative infinity to x; t represents the integration variable, which represents the different values ​​considered in the integration process; e represents the base of the natural logarithm; μ represents the mean of the normal distribution; σ represents the standard deviation of the normal distribution; dt represents the definition of the integration variable;

[0045] When a person's score is x, according to the cumulative probability distribution formula of the normal distribution of the experimental results, the probability that he is lying is:

[0046]

[0047] Among them, P(-|L) represents the probability that the person being tested is lying when the score is x or higher;

[0048] The probability of being honest is:

[0049]

[0050] Among them, P(+|T) represents the probability that the person being tested is honest when the score is x or lower;

[0051] Since the above two formulas cannot be solved directly, the cumulative probability function in the Matlab function library can be used to calculate the likelihood function as follows:

[0052] P(-|L)=1-normcdf(x,μ1,σ1);

[0053] P(+|T)=normcdf(x,μ2,σ2);

[0054] Where normcdf represents the probability that the random variable X is less than or equal to a specific value x in a normal distribution with a given mean μ and standard deviation σ.

[0055] As a further improvement of the technical solution, in S4, the specific steps of setting the prior probability according to different criterion test methods are as follows:

[0056] For the monocular standard rope test method, the physiological response intensity of the relevant questions is always compared with the physiological response intensity of the standard rope questions on its left. The prior probabilities P(L) and P(T) can be understood as when the subject has not participated in the psychological test, that is, the subject has not received the score, the standard rope questions and the relevant questions are fair and have no difference to the subject. Therefore, it can be assumed that the prior probability of the subject lying or being honest is:

[0057] P(L)=P(T)=0.5;

[0058] For the multi-eye standard rope test method, the physiological response intensity of the relevant questions is always compared with the physiological response intensity of the criterion questions on the left and right sides. The prior probabilities P(L) and P(T) can be understood as when the subject has not participated in the psychological test, that is, the subject has not received a score, and all criterion questions and relevant questions are fair and have no difference to the subject, then when the subject compares two criteria and one relevant question, the probability distribution of lying or being honest is set as:

[0059]

[0060] P(T)=2 / 3=0.667;

[0061] Among them, P(L) represents the probability that the person being tested is lying; P(T) represents the probability that the person being tested is honest.

[0062] As a further improvement of the technical solution, in S5, the specific steps of calculating the false negative and false positive conditional probabilities are:

[0063] Suppose the test subject's score is x. When x>0, the test subject is identified as an honest person. At this time, the probability of misidentification is the ratio of the probability that the test subject is lying to the probability that the test subject is honest when the score is x, as shown below:

[0064]

[0065] When x < 0, the person being tested is identified as a liar. At this time, the probability of misidentification (i.e., false positive: the person being tested is actually honest) is the ratio of the probability that the person being tested is honest to the probability of lying when the score is x, as follows:

[0066]

[0067] When x = 0:

[0068] P(+|L) = P(-|T) = 0.5;

[0069] Among them, P(+|L) represents the false negative probability, and P(-|T) represents the false positive probability.

[0070] As a further improvement of this technical solution, in S6, according to the false negative and false positive conditional probability results, the specific probability of calculating the posterior probability of lying of the person being tested is:

[0071] When the person being tested is actually tested and the score after scoring is x, substituting P(-|L), P(+|T), P(L), P(T), P(+|L), P(-|T) obtained by the above steps into the following formula, the posterior probability of lying of the person being tested can be obtained:

[0072]

[0073] Among them, P(L|-) represents the posterior probability that the person being tested lies when observing a score value x or higher; P(-) represents the marginal probability of observing a score value x or higher.

[0074] As a further improvement of this technical solution, in S7, the specific rules for setting the cut-off score are:

[0075] When P(L|-) ≥ P1, the person being tested lies;

[0076] When P(L|-) ≤ P2, the person being tested is honest;

[0077] When P2 < P(L|-) < P1, there is no conclusion;

[0078] Among them, P1 represents the upper limit of the score of the lying probability; P2 represents the lower limit of the score of the lying probability.

[0079] Compared with the prior art, the beneficial effects of the present invention:

[0080] 1. In the improved Bayesian-based probability scoring method for standard psychological tests, the physiological response intensity is used for scoring, which reduces the influence of subjective judgment and increases the objectivity and consistency of the test. The distribution of physiological response intensity between honest and lying answers is determined through a large amount of experimental data, which improves the accuracy of the model. By calculating the likelihood probability, the probability of the observed physiological response intensity under honest or lying conditions can be quantified, providing the necessary input for subsequent Bayesian updates.

[0081] 2. In the improved Bayesian-based probability scoring method for criterion psychological tests, the prior probability reflects the basic assumptions about the behavior of the person being tested before the test, and can integrate background information and personal experience, making the final posterior probability closer to the actual situation. By calculating the false negative and false positive conditional probabilities, the performance of the test system can be fully understood, providing direction for further improvement. Through the Bayesian update mechanism, the posterior probability can be continuously adjusted according to new evidence, making the evaluation results closer to reality. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] Figure 1 is a flow chart of the overall method of the present invention;

[0083] Figure 2 Normal distribution curve for scoring experimental results. DETAILED DESCRIPTION

[0084] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0085] Embodiment 1:

[0086] See also Figure 1 As shown, this embodiment provides an improved probability scoring method for standard psychological tests based on Bayesian theory, comprising the following steps:

[0087] S1. The criterion test method for psychological testing compares the physiological response intensity of the subjects on relevant questions and criterion questions, and scores each relevant question according to the difference in the comparison results to obtain experimental data;

[0088] In this example, each relevant question is scored according to the degree of difference in the comparison results, and the specific scoring rules for the experimental data are as follows:

[0089] Using a 7-point system, i.e. -3 to +3, the scoring rules are as follows:

[0090] There is no significant difference in the physiological response between R and C. R / C = 1: 0 points;

[0091] The physiological responses of R and C are generally different (1<(1R / C1)≦1.5), and they are scored ±1 points (strong R is scored “-”, strong C is scored “+”);

[0092] The physiological responses of R and C were significantly different (1.5 < (1R / C1) ≦ 3), and were scored ±2 points (strong R was scored “-”, and strong C was scored “+”);

[0093] If the physiological responses of R and C are significantly different (R / C>3), ±3 points will be awarded (strong R will be awarded “-”, strong C will be awarded “+”);

[0094] Among them, R represents relevant issues and C represents standard issues.

[0095] By adopting a 7-point scoring rule to compare and score the intensity of the subjects' physiological reactions to relevant questions (R) and criterion questions (C), it is possible to finely distinguish the differences in physiological reactions of different intensities, thereby improving the accuracy of the scoring and the reliability of the scoring results, and ensuring the objectivity and effectiveness of the psychological test.

[0096] S2. Obtain binormal distribution parameters of the experimental results by analyzing the experimental data;

[0097] In this example, by analyzing the experimental data, the specific steps to obtain the binormal distribution parameters of the experimental results are:

[0098] S2.1. Collect and organize physiological response data for honest and lying answers;

[0099] S2.2. Let the dataset of honest answers be X true ={x1,x2,…,x n}, the data set of lying answers is X lie ={y1,y2,…,y m};

[0100] S2.3. Calculate the dataset X of honest answers true and the lying answer dataset X lie The mean and standard deviation of

[0101] In this example, we calculate the dataset X of honest answers true and the lying answer dataset X lie The specific expressions of the mean and standard deviation are:

[0102] For the honest answer dataset X true :

[0103] Mean

[0104] Standard Deviation

[0105] Where n represents the data set X true The number of elements in; μ1 represents the honest answer dataset X true The average value of σ1 represents the honest answer dataset X true The standard deviation of x i Represents X true The i-th data point in the data set; i represents the index variable;

[0106] For the data set X of lying answers lie :

[0107] Mean

[0108] Standard Deviation

[0109] Where m represents the dataset X lie The number of elements in; μ2 represents lying answers to the dataset X lie The average value of σ2 indicates that the data set X lie The standard deviation of y j Represents the jth data point in the data set; j represents the index variable.

[0110] By calculating the mean and standard deviation, the central tendency and dispersion of different data sets are quantified, providing the necessary statistical parameters for fitting the normal distribution.

[0111] S2.4. Use the mean and standard deviation calculated in step S2.3 to fit two normal distributions, one representing the distribution of physiological response intensity for honest answers and the other representing the distribution of physiological response intensity for lying answers.

[0112] In this example, the specific expression for fitting two normal distributions is:

[0113] Distribution of physiological response intensity for honest answers f true (z):

[0114]

[0115] Among them, f true (z) represents the probability density function of the physiological response intensity z in the case of honest answer;

[0116] Distribution of physiological response intensity to lying answers lie (z):

[0117]

[0118] Among them, f lie (z) represents the probability density function of the intensity z of the physiological reaction in the case of lying.

[0119] The calculated mean and standard deviation were used to fit two normal distributions, which accurately described the distribution of physiological response intensity of honest and lying answers, and provided reliable model support for subsequent probability calculations.

[0120] S3. Calculate the likelihood probability based on the normal distribution results;

[0121] In this example, the likelihood probability is calculated based on the normal distribution results:

[0122] The cumulative probability function according to the normal distribution is:

[0123]

[0124] Among them, F(x) represents the cumulative probability function of the normal distribution; P(X≤x) represents the probability that the value of the random variable X falls within the interval from negative infinity to x; t represents the integration variable, which represents the different values ​​considered in the integration process; e represents the base of the natural logarithm; μ represents the mean of the normal distribution; σ represents the standard deviation of the normal distribution; dt represents the definition of the integration variable;

[0125] When a person's score is x, according to the cumulative probability distribution formula of the normal distribution of the experimental results, the probability that he is lying is:

[0126]

[0127] Among them, P(-|L) represents the probability that the person being tested is lying when the score is x or higher;

[0128] The probability of being honest is:

[0129]

[0130] Among them, P(+|T) represents the probability that the person being tested is honest when the score is x or lower;

[0131] Since the above two formulas cannot be solved directly, the cumulative probability function in the Matlab function library can be used to calculate the likelihood function as follows:

[0132] P(-|L)=1-normcdf(x,μ1,σ1);

[0133] P(+|T)=normcdf(x,μ2,σ2);

[0134] Where normcdf represents the probability that the random variable X is less than or equal to a specific value x in a normal distribution with a given mean μ and standard deviation σ.

[0135] By using the cumulative probability function of the normal distribution to calculate the likelihood probability, the probability of the person being tested lying or being honest at a specific score can be accurately quantified, thereby providing a reliable statistical basis for subsequent Bayesian updates and enhancing the accuracy and scientificity of the test results. This method uses mature statistical tools (such as Matlab's normcdf function) to simplify the calculation process of complex integrals and improve calculation efficiency and accuracy.

[0136] S4. Set the prior probability according to different criteria testing methods;

[0137] In this example, the specific steps for setting the prior probability according to different criteria testing methods are as follows:

[0138] For the monocular standard rope test method, the physiological response intensity of the relevant questions is always compared with the physiological response intensity of the standard rope questions on its left. The prior probabilities P(L) and P(T) can be understood as when the subject has not participated in the psychological test, that is, the subject has not received the score, the standard rope questions and the relevant questions are fair and have no difference to the subject. Therefore, it can be assumed that the prior probability of the subject lying or being honest is:

[0139] P(L)=P(T)=0.5;

[0140] For the multi-eye standard rope test method, the physiological response intensity of the relevant questions is always compared with the physiological response intensity of the criterion questions on the left and right sides. The prior probabilities P(L) and P(T) can be understood as when the subject has not participated in the psychological test, that is, the subject has not received a score, and all criterion questions and relevant questions are fair and have no difference to the subject, then when the subject compares two criteria and one relevant question, the probability distribution of lying or being honest is set as:

[0141]

[0142] P(T)=2 / 3=0.667;

[0143] Among them, P(L) represents the probability that the person being tested is lying; P(T) represents the probability that the person being tested is honest.

[0144] By setting reasonable prior probabilities according to different standard rope test methods, it is ensured that the probability assumptions of the test subject lying or being honest before the test begins are based on the fairness and rationality of the test design, thereby improving the scientificity and reliability of the test results. This method not only ensures the symmetry in the single-eye standard rope test method, but also more accurately reflects the probability distribution of the test subject lying and being honest in the multi-eye standard rope test method, thereby enhancing the overall effectiveness of the test.

[0145] S5. Calculate the false negative and false positive conditional probabilities;

[0146] In this example, the specific steps for calculating the conditional probabilities of false negatives and false positives are:

[0147] Suppose the test subject's score is x. When x>0, the test subject is identified as an honest person. At this time, the probability of misidentification is the ratio of the probability that the test subject is lying to the probability that the test subject is honest when the score is x, as shown below:

[0148]

[0149] When x<0, the person being tested is identified as a liar. At this time, the probability of misidentification (i.e., false positive: the person being tested is actually an honest person) is the ratio of the probability that the person being tested is honest to the probability that he is a liar when the score is x, as shown below:

[0150]

[0151] When x=0:

[0152] P(+|L)=P(-|T)=0.5;

[0153] Among them, P(+|L) represents the false negative probability, and P(-|T) represents the false positive probability.

[0154] By calculating the conditional probabilities of false negatives and false positives, the probability of identifying errors under different scoring scores x is clarified, thus providing a quantitative assessment of the reliability of the test system, helping to reduce the risk of misjudgment and enhancing the accuracy and credibility of the test results. This method ensures that the probability of identifying errors can be accurately measured under different scoring conditions, thereby improving the effectiveness of the overall test.

[0155] S6. Calculate the posterior probability of the person being tested lying based on the false negative and false positive conditional probability results;

[0156] In this example, based on the false negative and false positive conditional probability results, the posterior probability of the person being tested lying is calculated as:

[0157] When the score of the person being tested is x after scoring during the actual test, substituting P(-|L), P(+|T), P(L), P(T), P(+|L), and P(-|T) obtained through the above steps into the following formula, the posterior probability of the person being tested lying can be calculated:

[0158]

[0159] Among them, P(L|-) represents the posterior probability that the person being tested lies when observing a score value x or higher; P(-) represents the marginal probability of observing a score value x or higher.

[0160] By calculating the posterior probability of lying P(L|-) of the person being tested, it combines the prior probability and new physiological response data, provides a comprehensive assessment of whether the person being tested lies, makes the decision-making process more scientific and reasonable, and reduces the risk of misjudgment through dynamic update and quantitative measurement, enhancing the reliability and practicality of the test results.

[0161] S7. Set a cut-off score to determine whether lying occurs.

[0162] In this example, the specific rules for setting the cut-off score are as follows:

[0163] When P(L|-) ≥ P1, the person being tested lies;

[0164] When P(L|-) ≤ P2, the person being tested is honest;

[0165] When P2 < P(L|-) < P1, there is no conclusion;

[0166] Among them, P1 represents the upper limit of the score of the lying probability; P2 represents the lower limit of the score of the lying probability.

[0167] Example 2:

[0168] The present invention provides Example 2:

[0169] The present invention provides a method for suppressing electromagnetic interference of instrument cables. The following will further explain the present invention in combination with the reference appendix Figure 2 and the specific implementation manners.

[0170] 1. Calculate the score values of relevant problems

[0171] For the control question technique of psychological testing, usually by comparing the intensity of the physiological responses of the person being tested to relevant questions (R) and control questions (C), each relevant question is scored according to the degree of difference in the comparison results to obtain experimental data. Usually, a 7-point scale is adopted, that is, -3 to +3, and the scoring rules are as follows:

[0172] There is no obvious difference in the physiological responses of R and C, R / C = 1: get 0 points;

[0173] The physiological responses of R and C are generally different (1<(1R / C1)≦1.5), and they are scored ±1 points (strong R is scored “-”, strong C is scored “+”);

[0174] The physiological responses of R and C were significantly different (1.5 < (1R / C1) ≦ 3), and were scored ±2 points (strong R was scored “-”, and strong C was scored “+”);

[0175] There is a significant difference between the physiological responses of R and C (R / C>3), and a score of ±3 is awarded (strong R is scored as "-", strong C is scored as "+").

[0176] Among them, R represents relevant issues and C represents standard issues.

[0177] 2. Obtaining the binormal distribution parameters of experimental results

[0178] A total of 400 subjects were included, 200 of whom participated in the simulated innocent (honest) experiment and 200 participated in the simulated theft experiment. All subjects answered negatively to questions related to theft. Then, the subjects were subjected to psychological tests (lie detection) using the monocular standard rope test method to obtain the following results: Figure 2 The bimodal normal distribution curve is shown as follows:

[0179] Among them: the normal distribution parameters of the simulated guilty (mostly negative scores) scores are: μ1 (mean), σ1 (standard deviation); the normal distribution parameters of the simulated innocent (mostly positive scores) scores are: μ2 (mean), σ2 (standard deviation).

[0180] 3. Calculate likelihood probability

[0181] According to the definition of the cumulative probability function (CDF) of the normal distribution, the cumulative probability function of the normal distribution is:

[0182]

[0183] Among them, F(x) represents the cumulative probability function of the normal distribution; P(X≤x) represents the probability that the value of the random variable X falls within the interval from negative infinity to x; t represents the integration variable, which represents the different values ​​considered in the integration process; e represents the base of the natural logarithm; μ represents the mean of the normal distribution; σ represents the standard deviation of the normal distribution; dt represents the definition of the integration variable;

[0184] When a person's score is x, according to the cumulative probability distribution formula of the normal distribution of the experimental results, the probability of him getting a negative score (lying) is:

[0185]

[0186] Among them, P(-|L) represents the probability that the person being tested is lying when the score is x or higher;

[0187] The probability of a positive score (honesty) is:

[0188]

[0189] Among them, P(+|T) represents the probability that the person being tested is honest when the score is x or lower;

[0190] Since the above two formulas cannot be solved directly, the cumulative probability function in the Matlab function library can be used to calculate the likelihood function as follows:

[0191] P(-|L)=1-normcdf(x,μ1,σ1);

[0192] P(+|T)=normcdf(x,μ2,σ2);

[0193] Where normcdf represents the probability that the random variable X is less than or equal to a specific value x in a normal distribution with a given mean μ and standard deviation σ.

[0194] 4. Setting Prior Probability

[0195] For the monocular standard rope test method, the physiological response intensity of the relevant questions is always compared with the physiological response intensity of the standard rope questions on its left. The prior probabilities P(L) and P(T) can be understood as when the subject has not participated in the psychological test (lie detection), that is, the subject has not received the score, the standard rope questions and the relevant questions are fair to the subject and there is no difference. Therefore, it can be assumed that the prior probability of the subject lying or being honest is:

[0196] P(L)=P(T)=0.5;

[0197] For the multi-objective standard rope test method, the physiological response intensity of the relevant questions is always compared with the physiological response intensity of the criterion questions on the left and right sides. The prior probabilities P(L) and P(T) can be understood as when the subject has not yet participated in the psychological test (lie detection), that is, the subject has not yet received a score, and all criterion questions and relevant questions are fair and have no difference to the subject. When the subject compares two criteria and one relevant question, the probability distribution of lying or being honest is set as:

[0198]

[0199] P(T)=2 / 3=0.667;

[0200] Among them, P(L) represents the probability that the person being tested is lying; P(T) represents the probability that the person being tested is honest.

[0201] 5. Calculate the false negative / false positive conditional probability

[0202] The probability of a false negative (a liar gets a positive score) is denoted as P(+|L), and the probability of a false positive (an honest person gets a negative score) is denoted as P(-|T).

[0203] Suppose the test subject's score is x. When x>0, the test subject is identified as an honest person. At this time, the probability of identification error (i.e. false negative: the test subject is actually a liar) is the ratio of the probability of the test subject lying to the probability of being honest when the score is x, as shown below:

[0204]

[0205] When x<0, the person being tested is identified as a liar. At this time, the probability of misidentification (i.e., false positive: the person being tested is actually an honest person) is the ratio of the probability that the person being tested is honest to the probability that he is a liar when the score is x, as shown below:

[0206]

[0207] When x=0:

[0208] P(+|L)=P(-|T)=0.5;

[0209] Among them, P(+|L) represents the false negative probability, and P(-|T) represents the false positive probability.

[0210] 6. Calculate the posterior probability of the person being tested lying based on the false negative and false positive conditional probability results

[0211] When the subject is actually tested and his score is x after being graded, substitute P(-|L), P(+|T), P(L), P(T), P(+|L), and P(-|T) obtained through the above steps into the following formula to obtain the posterior probability that the subject is lying:

[0212]

[0213] Where P(L|-) represents the posterior probability that the subject is lying when a score x or higher is observed; P(-) represents the marginal probability of observing a score x or higher.

[0214] 7. Set the score line

[0215] Set the upper limit of the probability of lying to P1 (for example: 60%), and the lower limit of the score to P2 (for example: 40%), that is:

[0216] When P(L|-)≥P1, the person being tested is lying;

[0217] When P(L|-) ≤ P2, the person being tested is honest;

[0218] When P2 < P(L|-) < P1, there is no conclusion.

[0219] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited by the above embodiments. The above embodiments and the descriptions in the specification are only preferred examples of the present invention and are not used to limit the present invention. Without departing from the spirit and scope of the present invention, the present invention will have various changes and improvements, and these changes and improvements all fall within the scope of the present invention claimed.

Claims

1. An improved probability scoring method for standard psychological tests based on Bayesian theory, characterized by: The following steps are involved: S1. The criterion test method for psychological testing compares the physiological response intensity of the subjects on relevant questions and criterion questions, and scores each relevant question according to the degree of difference in the comparison results to obtain experimental data; S2. Obtain binormal distribution parameters of experimental results by analyzing experimental data; S3. Calculate the likelihood probability based on the normal distribution results; S4. Set the prior probability according to different criteria testing methods; S5. Calculate the false negative and false positive conditional probabilities; S6. Calculate the posterior probability of the person being tested lying based on the false negative and false positive conditional probability results; S7. Set a score line to determine whether someone is lying.

2. The improved Bayesian-based probability scoring method for psychological testing according to claim 1 is characterized in that: In S1, each relevant question is scored according to the degree of difference in the comparison results, and the specific scoring rules for the experimental data are obtained as follows: Using a 7-point system, i.e. -3 to +3, the scoring rules are as follows: There is no significant difference in the physiological response between R and C. R / C = 1: 0 points; There is a general difference between the physiological responses of R and C, and a score of ±1 is awarded; The physiological responses of R and C were significantly different, and were scored ±2 points; The physiological responses of R and C were significantly different, and ±3 points were awarded; Among them, R represents relevant issues and C represents standard issues.

3. The improved Bayesian-based probability scoring method for psychological testing according to claim 1 is characterized in that: In S2, the specific steps of obtaining the binormal distribution parameters of the experimental results by analyzing the experimental data are as follows: S2.

1. Collect and organize physiological response data for honest and lying answers; S2.

2. Let the dataset of honest answers be X true ={x1,x2,…,x n }, the data set of lying answers is X lie ={y1,y2,…,y m }; S2.

3. Calculate the dataset X of honest answers true and the lying answer dataset X lie The mean and standard deviation of S2.

4. Use the mean and standard deviation calculated in step S2.3 to fit two normal distributions, one representing the distribution of physiological response intensity for honest answers and the other representing the distribution of physiological response intensity for lying answers.

4. The improved Bayesian-based probability scoring method for psychological testing according to claim 3 is characterized in that: In S2.3, the dataset X of honest answers is calculated. true and the lying answer dataset X lie The specific expressions of the mean and standard deviation are: For the honest answer dataset X true : Mean Standard Deviation Where n represents the data set X true The number of elements in; μ1 represents the honest answer dataset X true The average value of σ1 represents the honest answer dataset X true The standard deviation of x i Represents X true The i-th data point in the data set; i represents the index variable; For the data set X of lying answers lie : Mean Standard Deviation Where m represents the dataset X lie The number of elements in; μ2 represents lying answers to the dataset X lie The average value of σ2 indicates that the lying answer data set X lie The standard deviation of y j Represents the jth data point in the data set; j represents the index variable.

5. The improved Bayesian-based probability scoring method for psychological testing according to claim 3 is characterized in that: In S2.4, the specific expression for fitting two normal distributions is: Distribution of physiological response intensity for honest answers f true (z): Among them, f true (z) represents the probability density function of the physiological response intensity z in the case of honest answer; Distribution of physiological response intensity to lying answers lie (z): Among them, f lie (z) represents the probability density function of the intensity z of the physiological reaction in the case of lying.

6. The improved Bayesian-based probability scoring method for psychological testing according to claim 1, characterized in that: In S3, the likelihood probability is calculated according to the normal distribution result: The cumulative probability function according to the normal distribution is: Among them, F(x) represents the cumulative probability function of the normal distribution; P(X≤x) represents the probability that the value of the random variable X falls within the interval from negative infinity to x; t represents the integration variable, which represents the different values ​​considered in the integration process; e represents the base of the natural logarithm; μ represents the mean of the normal distribution; σ represents the standard deviation of the normal distribution; dt represents the definition of the integration variable; When a person's score is x, according to the cumulative probability distribution formula of the normal distribution of the experimental results, the probability that he is lying is: Among them, P(-|L) represents the probability that the person being tested is lying when the score is x or higher; The probability of being honest is: Among them, P(+|T) represents the probability that the person being tested is honest when the score is x or lower; The cumulative probability function in the Matlab function library is used to calculate the likelihood function as follows: P(-|L)=1-normcdf(x,μ1,σ1); P(+|T)=normcdf(x,μ2,σ2); Where normcdf represents the probability that the random variable X is less than or equal to a specific value x in a normal distribution with a given mean μ and standard deviation σ.

7. The improved Bayesian-based probability scoring method for psychological testing according to claim 1 is characterized in that: In S4, the specific steps of setting the prior probability according to different criteria testing methods are as follows: The prior probabilities P(L) and P(T) are the probabilities of the tested person lying or being honest before taking the psychological test, that is, before the tested person has obtained a score. Therefore, the prior probabilities of the tested person lying or being honest are as follows: P(L) = P(T) = 0.5; The prior probabilities P(L) and P(T) are the probabilities of the tested person lying or being honest when the tested person has not taken the psychological test, that is, before the tested person has obtained a score. When the tested person makes a comparison between two control questions and one relevant question, the probability distribution of lying or being honest is set as follows: P(T) = 2 / 3 = 0.667; Among them, P(L) represents the probability that the tested person lies; P(T) represents the probability that the tested person is honest.

8. The improved Bayesian-based probability scoring method for psychological testing according to claim 1 is characterized in that: In step S5, the specific steps for calculating the false negative and false positive conditional probabilities are as follows: The score of the tested person is x. When x > 0, the tested person is identified as an honest person. At this time, the probability of misidentification is the ratio of the probability of the tested person lying and the probability of being honest when the score is x, as follows: When x < 0, the tested person is identified as a liar. At this time, the probability of misidentification (i.e., false positive: the tested person is actually an honest person) is the ratio of the probability of the tested person being honest and the probability of lying when the score is x, as follows: When x = 0: P(+|L) = P(-|T) = 0.5; Among them, P(+|L) represents the false negative probability, and P(-|T) represents the false positive probability.

9. The improved Bayesian-based probability scoring method for psychological testing according to claim 1, characterized in that: In step S6, according to the results of the false negative and false positive conditional probabilities, the specific probability of calculating the posterior probability of the tested person lying is as follows: When the tested person takes the actual test and the score after scoring is x, substitute P(-|L), P(+|T), P(L), P(T), P(+|T), P(-|T) obtained by the above steps into the following formula to calculate the posterior probability of the tested person lying: Among them, P(L|-) represents the posterior probability that the tested person lies when observing a score value x or higher; P(-) represents the marginal probability of observing a score value x or higher.

10. The improved Bayesian-based probability scoring method for psychological testing according to claim 1, characterized in that: In step S7, the specific rules for setting the cut-off score are as follows: When P(L|-) ≥ P1, the tested person lies; When P(L|-) ≤ P2, the tested person is honest; When P2 < P(L|-) < P1, no conclusion can be drawn; Among them, P1 represents the upper limit of the score of the lying probability; P2 represents the lower limit of the score of the lying probability.

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