In the Bayesian framework، robust Bayesian methods concern on estimation of unknown parameters، or prediction of future observation، by specifying a class of priors instead of a single prior. Robust Bayesian methods have been used extensively in actuarial sciences for estimation of premium and prediction of future claim size. In this paper we consider robust Bayes estimation of premium and prediction of future claim size under two classes of prior distribution and under the scale invariant squared error loss function. Finally، by a simulation study and using prequential analysis، we compare the obtained robust Bayes estimators of future claim size.

In this study, various sources of uncertainty in demand and capacity and their direct and indirect dependencies according to their significant function in performance based earthquake engineering (PBEE), were incorporated proposing a practically new simple procedure. This procedure distinguishes and evaluates collapse probability of elementary mechanisms as well as computes their dependencies utilizing commonly used deterministic computer software through a full probabilistic methodology using β-unzipping and Bayesian methods. This procedure has been benchmarked for a typical 2D reinforced concrete moment frame and reliability index of the structure for the most probable collapse mechanism was obtained within a reliability-based framework. Moreover, the coefficients of dead, live and earthquake loads for a ACI load combination were reevaluated utilizing β-unzipping and Bayesian methods through the proposed procedure and were compared with the code''s coefficients. Good compatibility between obtained coefficients and code''s ones has been perceived and the probability of collapse, implicitly considered in the code, was revealed. It has been concluded that the coefficients extracted from Bayesian method are closer to the code''s ones comparing to those from β-unzipping method; however, requiring less primary computational effort and slight differences between the results, β-unzipping is usually more preferred by evaluators.

Appropriate credit scoring assessment assists financial institutions on loan pricing, determining amount of loan, loan risk management, reduction of default risk and increase in debt repayment. The purpose of this study is to estimate a credit scoring model for the agricultural loans in Kohgiloye & Bovair Ahmad Province. The logistic regression with the two estimation methods (classic and Bayesian) are used to construct the credit scoring models as well as to predict the borrower’s creditworthiness and default risk. Furthermore, Bayesian method was compared with the classical estimation methods. The Limdep and MLwiN softwares are used to estimate models by Classic and Bayesian approaches, respectively. Data were collected from 110 farmers in Kohgiloye & Bovair Ahmad Province in 2007. Results of the Bayesian method indicated that variables such as education, value of assets and age of farmers have positive effects, whereas borrowing from others; loan type, total debet to assets ratio and the duration of bank-borrower relationship have negative effect as important factors in determining the creditworthiness of the borrowers. The results also show that a higher value of assets implies a higher creditworthiness and a higher probability of a good loan. However, the negative sign found on the duration of bankborrower relationship, which contradict with the hypothesized sign, suggest that the borrower who has a longer relationship with the bank has a higher probability to default on debt repaymen. The overall prediction accuracy of the Bayesian credit scoring models is 90.91% and 89.91% in-sample and out-of-sample forecast, respectively, and is higher than the classic model on out-of-sample forecast. Thus, when the expected loss of misclassification are computed and compared, the results indicate that the misclassification cost of the Bayesian method is the best credit scoring model with the lowest misclassification costs. In summary, the empirical results in this study support the use of the Bayesian method in classifying and screening agricultural loan applications.

Nowadays, we have some data in different sciences which number of zeros is more than expected, such data are called zero-inflated which can be modeled by regressions for count data. Many researches have been conducted in the field of classical method on count data. Most of Bayesian analysis which is conducted for these data used zero-inflated Poisson regression. Therefore, the main purpose of this research is comparison of Bayesian and classic approaches in regression of zero-inflated negative binomial (NB) on data for determining the size estimation of people who have used alcohol more than once in last year.
Methods & Materials: This research had been in two provinces of Fars and Kerman in 2011, a sample size of each province was formed proportional to people of that province, and totally the calculated sample size was 700. Zero-inflated NB regression was fitted to the data in two Bayesian and classical methods, and then two methods have been compared. Results of Bayesian method were extracted in OpenBUGS software and through related codes in R and results of classical method were extracted in R software too.
After fitting classical method, variables of province, gender, age groups, and education had been effective on identifying number of alcoholics, but in Bayesian method, three variables of gender, age groups, and education have become significant. In this research, it was specified that obtained probability intervals from Bayesian method are much Widder than classical method.
Results of this research indicate that Bayesian method has better function than the classic

Accurate estimation of variance components using pedigree and genomic data is important for prediction of breeding values. Availability of high density single nucleotide polymorphisms (SNP) arrays and genotyping many individuals resulted in the increase of accuracy of population-based estimates. Genomic selection potentially can explain all genetic variance by markers. The aim of this study was to determine the amount of genomic additive variation for birth weight and weaning weight of Merino sheep by different minor allele frequency (MAF) groups using two statistical approaches i.e. REML and Bayesian.
Material and In this study, data of 2189 Merino sheep, genotyped by 50k Illumina SNP chip were used. After the quality control of genotyping data, 47342 markers remained for subsequent analysis. For birth weight and weaning weight 1331 and 2136 records were available, respectively. To study the association between allele frequency spectrum and captured additive genetic variance, all SNPs were partitioned in five MAF bins with the equal numbers of SNPs (0-0.18, 0.18-0.28, 0.28-0.36, 0.36-0.43 and 0.43-0.499). The analysis was performed using REML and a Bayesian method implemented via Gibbs sampling and RKHS model.
Using all common SNPs in REML approach, estimates of genomic heritability were 0.58±0.07 and 0.46±0.05 for birth weight and weaning weight, respectively. This heritability values in Bayesian analysis and RKHS method for these traits were estimated to be 0.58±0.07 and 0.46 ± 0.05, respectively. The amount of genetic variation explained by five different MAF groups was different in separate and joint analysis. The estimates from separate analysis were higher than joint analysis for two traits and two (REML and Bayesian) methods. In separate analysis, the genomic heritability was similar for all MAF bins by two approaches. In the joint analysis there were large differences between REML and Bayesian estimates in terms of explaining genetic variation across MAF subsets. For birth weight, SNPs with MAF 0.18-0.28 marked the largest amount of genomic heritability using REML method. In this method, heritability of Weaning weight was zero using SNP with MAF 0.43-0.499. All MAF bins contributed to genetic variation in Bayesian method. In separate analysis, sum of genomic variances for five MAF bins was larger than estimated variance by all set of SNPs together, while sum of this variances in joint analysis was same as the value of variance obtained by all SNPs for both traits and both statistical methods.
Variance components obtained by Bayesian method are more realistic, because they have less prediction error variance. Bayesian methods considered common prior distribution for the variance, so results of this method were more reliable than other methods. Although the number of SNPs in different groups was similar, the amount of genetic variance explained by the different MAF groups was different.

Disease or mortality rate map، geographically is desired for public health officials and epidemiologists. Point Poisson Kriging and Empirical Bayesian methods are used in estimating the map parameters. The aim of this study was to compare the precision of the methods in mapping of gastrointestinal cancer incidence in Iran. This study was application/ecology. The methodology was illustrated using gastrointestinal cancer data recorded in the ministry of health and medical education (in the non-infectious diseases management center) of Iran in years 2003-2007 from 336 counties. Poisson Kriging model was used to estimate the parameters of the map. Spacestat، OpenBUGS and ArcGIS9. 3 softwares were used for analysing the data and drawing maps. Mean incidence rate according to Empirical Bayesian method was 12. 99 and based on Point Poisson Kriging method was estimated 12. 64. Mean incidence rate variance using the Empirical Bayesian method was 2. 83 and based on Point Poisson Kriging method was estimated 3. 85. Maximum incidence rate according to Empirical Bayesian method was 42. 23 with variance of 2. 16 related to Sari county and minimum incidence rate was 0. 48 with variance of 0. 08 related to Sarbaz County. Maximum incidence rate using the Point Poisson Kriging method was estimated 40. 35 with variance of 0. 79 related to Sari county and minimum incidence rate of 0. 30 with variance of 2. 54 related to Sarbaz County. Poisson Kriging estimation method yields smaller standard error compared to Empirical Bayesian model. The Poisson Kriging method was recommended for estimation of disease mapping parameters since it generates less smoothing and yields smaller standard error.

Aim: To estimate the change in years of life lost (YLL) due to gastric cancer mortality after correcting for misclassification in registering causes of death using the Bayesian method.
For evaluating the health status of a country and determining priority of risk factors, some epidemiologic indicators are needed. Due to premature death, YLL is one of the most widely used indicators. To have an exact estimate of YLL, an accurate death registry data is needed, but the Iranian death registry is subject to misclassification error.
Material and Gastric cancer mortality data from 2006 to 2010 for Iran were extracted from national death statistics. The rate of misclassification in registered causes of deaths was estimated, using Bayesian method for each year. Then YLL of gastric cancer is estimated for different age-sex categories before and after implementing Bayesian method.
Using Bayesian method, the estimated misclassification rate for gastric cancer in cancer without label group were 5%, 3%, 3%, 7% and 7% respectively from 2006 to 2010. Estimated Years of life lost due to gastric cancer before correcting misclassification were respectively 111684.93, 114957.31, 112391.93, 112250.53 and 113300.92 person-years for years 2006 to 2010. After correcting misclassification, the total YLL of gastric cancer increased to 1535.19, 921.11, 908.39, 2566.39 and 2507.00 person-years, respectively from 2006 to 2010.
If health policy makers ignore the existence of misclassification in registered causes of death, they may underestimate the burden of some causes of death and overestimate some others.

The purpose of this paper is to investigate the effect of stock market demand side shock on a selection of macroeconomic variables with the approach of stochastic dynamic equilibrium (DSGE) models. For this purpose, data from the period 1368-98 with seasonal frequency and Bayesian method have been used to estimate the model parameters, in which the initial values ​​for the parameters are determined as the previous distribution and these initial values ​​are combined with the results of maximum likelihood estimation based on real data. It becomes. If the initial information in the previous distribution is complete and accurate and the maximum likelihood estimate cannot help the model estimate, the Bayesian method becomes a calibration. But if the previous distribution information was completely incorrect and inaccurate, the Bayesian method becomes the maximum likelihood method. In the intermediate state, Bayesian method is a combination of two methods of calibration and maximum likelihood. In general, capital market shocks can affect macroeconomic variables in two ways. The first route is household consumption expenditures and the second route is corporate investment expenditures. Therefore, the direct effects of stock price fluctuations on total expenditures have made the stock market known as a leading indicator in the economy and therefore have been considered in experimental studies. In this study, the shock from the capital market area is considered based on the market demand segment, in which the tendency of households to keep their assets in the form of stocks increases. The results show that private investment, production, inflation and consumption expenditures increase and interest rates decrease with the shock of a measure deviation from the demand side of the stock market.

In the present research, stock returns were predicted using the Bayesian model approach in Tehran Securities Exchange. Therefore, the research hypothesis that based on Bayesian method has higher accuracy in predicting returns than autoregressive models was developed and tested. In order to examine the hypothesis, information related to the index of 30 selected industries in the Tehran Stock Exchange during the period from 2017/03/25 to 2020/08/24 was used. The index return was predicted based on two methods for 30 out-of-sample data. First autoregressive models were fitted on returns of each index and then the next 30 days of returns were predicted based on these models. Then after identifying the optimal model lags through the Bayesian Model Averaging method, autoregressive models were fitted with the optimal lags and the next 30 days predictions were obtained under this method.In order to compare the accuracy of the methods in predicting the return, RMSE and MAE criteria were used, and the values of these error criteria were compared using Wilcoxon Nonparametric Pairwise comparison tests.The results showed that Bayesian method leads to increase the accuracy of model prediction in out of sample data.

The concept of financial sustainability has been in the economic literature for nearly two decades. In the theoretical financial literature, firm financial sustainability can be described as a financial system consisting of financial intermediaries, markets, and market infrastructures that are capable of withstanding risk shocks and resolving financial imbalances. Therefore, according to the above argument, the purpose of the present study is to present a proposed model for measuring the financial sustainability of the company by using Econophysics and artificial neural network using a sample of 132 companies listed in Tehran Stock Exchange during 2015-2019. The results of the first hypothesis show that the prediction of financial sustainability based on the Econophysics method can provide better results. Also, based on the result of the second hypothesis, the Bayesian method can predict better financial sustainability. Finally, by comparing the Econophysics and Bayesian approaches to predicting financial sustainability of the firm, it can be concluded that the prediction of financial sustainability based on the economophysical method yields better results than the Bayesian method.