The Gamma distribution function Γ(x|α,β),α>0,β>0 is always used as a prior distribution density function of bayes expontional reliability growth model.

Results Experiments on 200 ultrasonic images, randomly divided into training set 100 and prediction set 100, showed that the Accuracy of SVM, Bayes, BP and Fisher was 0.960, 0.940, 0.932±0.013, 0.930 respectively.

We present a new scheme for uncertain reasoning based on Bayes' formula in likelihood ratio form in this paper.

The asymptotically optimal empirical bayes estimation in multiple linear regression model

Empirical Bayes estimation of the parameter vector θ=(β',σ2)' in a multiple linear regression modelY=Xβ+ε is considered, where β is the vector of regression coefficient, ε∽N(0,σI with σ2 unknown.

In this article, Bayes estimation of location parameters under restriction is brought forth.

Thus the results under Type- II right censoring can be used directly to get more accurate estimators by Bayes method.

In this papér, it is discussed from the statistical points of view the two main topics related to classifying the grades of thickness irregularity of cotton yarn, namely: (1) the method for setting the grades intervals, and (2) the method for classifying the sampled population into one of the grades previously defined. Concept on the critical values for setting grade intervals is introduced and discussed, the errors in classifying the sampled population due to thsee values are also intesvigated. An example for...

In this papér, it is discussed from the statistical points of view the two main topics related to classifying the grades of thickness irregularity of cotton yarn, namely: (1) the method for setting the grades intervals, and (2) the method for classifying the sampled population into one of the grades previously defined. Concept on the critical values for setting grade intervals is introduced and discussed, the errors in classifying the sampled population due to thsee values are also intesvigated. An example for determining these values is given. The problem on sampling by variable or by attributer is discussed. In the problem of sampling by variables, the Neyman and Pearson's theory on two types of errors, as well as the concepts of indifferent intervals are employed in determining the sample size for the purpose of classification. The functional relation n～kσ~2 is suggested showing that the required sample size is proportional to the population variance of the irregularity index, while the constant is changed with respect to the size of indifferent intervals and values of α and β In the problem of sampling by attributes, the Bayes' theorem is employed to verify the reliability of information by the sample size of nine used in factories. It is shown that this sample size is statistically insufficient on some account. Some further problem have been pointed for the further investigation.

The author first discussed the evaluation of the conditional probability and the general probability, and then discussed the evaluation of the compound probability. The first part of this paper deals with the conditional probabilities of fog for the different wind directions and shows that it is better calculated by the equation:P(F\W_i)=P(W_iF)/P(W_i) (1) where F represents the fog frequency and W_i represents the frequency of the wind from the direction i(i=1, 2,…16). By practical calculations it shows that...

The author first discussed the evaluation of the conditional probability and the general probability, and then discussed the evaluation of the compound probability. The first part of this paper deals with the conditional probabilities of fog for the different wind directions and shows that it is better calculated by the equation:P(F\W_i)=P(W_iF)/P(W_i) (1) where F represents the fog frequency and W_i represents the frequency of the wind from the direction i(i=1, 2,…16). By practical calculations it shows that the method adopted by M. Wurtele (1944) was unnecessary.The conditional probabilities of rainfall for the different wind directions have been calculated also by the same method as stated above. Furthermore, the attempts have been made to calculate the general probability of rainfall by applying the theorem of total probability and to calculate the conditional probability of wind direction after the rainfall has been observed by applying Bayes' theorem.In the second part it has been shown that P(B)=P(B_0)+P(B_1)+…+P(B_n), (2) where B denotes the event of having rain days at the station B; B_0 denotes the event of having rain days only at the station B; B_1 denotes the event that two stations including station B have rain days; B_2 denotes the event that three stations including the station B have rain days; and so on. Besides, by the theorem of compound probability the following formulas can be established: where i=1, 2,…n; i, j are taken for all combinations in the numbers 1, 2,…n; k=1, 2,…n except the numbers i and j; A_0=1.By formula (3) the probabilities of simultaneous occurrence of rain days at Hankow, Siangyang, Changsha and Chungking have been calculated for the different months. For the purpose of check the following three formulas have been derived in addition to the formula (2):P(B)=P(B_0)+2/3 P(B_1)+1/3 P(B_2)+1/3 [P(BA_1)+P(BA_2)+P(BA_3)], (4)P(BA_1)+P(BA_2)+P(BA_3)=P(B_1)+3/2 P(B_2)+3/2 P(B_3)+1/2 [P(BA_1A_2)++P(BA_2A_3)+P(BA_1A_3)] (5)andP(BA_1A_2)+P(BA_2A_3)+P(BA_1A_2)=P(B_2)+3P(B_3). (6)At last the author has demonstrated that the computation of the compound probability by formula (3) is more significant than that by direct computation from the definition of probability.

Based on our ten years' experience in diagnosis and differential diagnosis of primary liver cancer (PLC), positivities of 18 parameters including history, symptoms, signs, alpha fetoprotein (AFP) level, laboratory findings, ultrasound, liversoan, etc. have been selected for differential diagnosis of the following diseases; namely subclini-cal PLC, clinical PLC, AFP negative PLC or secondary liver cancer, liver cirrhosis in active stage, liver cirrhosis with atrophy, chronic hepatitis in active stage, liver hemangioma,...

Based on our ten years' experience in diagnosis and differential diagnosis of primary liver cancer (PLC), positivities of 18 parameters including history, symptoms, signs, alpha fetoprotein (AFP) level, laboratory findings, ultrasound, liversoan, etc. have been selected for differential diagnosis of the following diseases; namely subclini-cal PLC, clinical PLC, AFP negative PLC or secondary liver cancer, liver cirrhosis in active stage, liver cirrhosis with atrophy, chronic hepatitis in active stage, liver hemangioma, hepatic cyst and liver abscess. The probability of the diagnosis was calculated using Bayes Theory and employing APPLESOFT BASIC as programming language.237 pathologically verified oases covering all of the diseases mentioned above had been testified by a 48K APPLE TYPE II microcomputer. The total accuracy of computer-aided diagnosis of 237 oases of 9 types of disorders was 91.6% as compared with pathological diagnosis. Among them 155 cases of AFP positive PLC gained the highest accuracy 99.4%, while AFP negative PLC 89.2%. The overall accuracy rata in different disorders was: liver cancer 97.4% (187/192), hepatic cyst 85.7% (12/ 14), liver hemangioma 75.0% (9/12) and liver abscess 60% (3/5). It was rather difficult to differentiate cirrhosis and chronic hepatitis from liver cancer that the accuracy was reduced to 43% (6/14) only, according to the false negative (2.6%) and false positive (4.6%) were insignificant. The overall accuracy of computer-aided diagnosis might be comparable with clinical diagnostic accuracy by high level specialists of liver caneer (90.7%). It seems that computer-aided certainly has the definite advanges in differential diagnosis, confirming the diagnosis and suggesting the proper treatment during the early stage of liver cancer.