Animal models are used to model the observations of animal performance that are genetically dependent. These models are considered as generalized linear mixed models and the genetic correlation structure of data is considered through random effects of breeding values. One goal of the mentioned models is to estimate variance components. In this research, an approximate Bayesian approach presented to estimate variance components in animal model and compared with the conventional Bayesian approach. A generated data set for hypothetical animal population with 1084 records was used. The observations are the animal's birth weight and the data includes dam ID, sire ID, sex and birth year. The effect of gender was considered as fixed effect and the effects of dam, animal and year of birth were used as random effect. Four different models were fitted by the conventional Bayesian approach and the appropriate model was selected by deviance information criteria. The approximate Bayesian approach was applied on it. Time consuming with a PC with configuration (Intel Core i7, 4GB, 2. 7 GHz) was about 120 second for the conventional Bayesian approach and little than 10 second for the approximate Bayesian approach. Goodness of fit was computed by relative root mean squared error of prediction that was respectively 0. 1568 and 0. 1499 for conventional Bayesian and the approximate Bayesian approaches. T-test was used to illustrate lack of significant different to fit weight of animals between two approaches. The null hypothesis was accepted with p-value 0. 98 that it shows mean of fitted animal weights for two approaches are equal.

This paper investigates relationship of 16 variables on economic growth in Iran, using Bayesian Model Averaging (BMA) and annual time series data from 1961 to 2014. “Inclusion probability” indicates that investment ratio, population growth rate (with a negative sign), imported capital good growth, labor force growth, and imported intermediate good growth take the first to fifth rank regarding their effects on economic growth respectively. The relationship between energy consumption and growth in non-oil production due to the low probability of this variable in the model is insignificant. Thus saving energy policies are not a threat to economic growth in Iran.

This paper addresses the problem of Bayesian estimation of the parameters, reliability and hazard function in the context of record statistics values from the two-parameter Lomax distribution. The ML and the Bayes estimates based on records are derived for the two unknown parameters and the survival time parameters, reliability and hazard functions. The Bayes estimates are obtained based on conjugate prior for the scale parameter and discrete prior for the shape parameter of this model. This is done with respect to both symmetric loss function (squared error loss), and asymmetric loss function (linear-exponential (LINEX)) loss function. The maximum likelihood and the different Bayes estimates are compared via Monte Carlo simulation study. A practical example consisting of real record values including in the data from an accelerated test on insulating fluid reported by Nelson was used for illustration and comparison. Finally, Bayesian predictive density function, which is necessary to obtain bounds for predictive interval of future record is derived and discussed using a numerical example.

The structure of a Bayesian network represents a set of conditional independence relations that hold in the domain. Learning the structure of the Bayesian network model that represents a domain can reveal in sights into its underlying causal structure. Automatically learning the graph structure of a Bayesian network is a challenge pursued within artificial intelligence studies. In this paper, a new algorithm based on learning automata is proposed for learning the structure of the Bayesian networks. In this algorithm, automata is used as a tool for searching in structure’s space (DAG’s space) of the Bayesian networks. The mathematical behavior of the proposed algorithm is studied.

Introduction Studying crime data has become one of the essential topics in the world due to its connection with human security. Analyzing this type of data can effectively prevent future crimes and identify spatial patterns and factors that facilitate the commission of crimes to control crime-prone areas. Most of the time, crime data has a spatio-temporal structure that causes the formation of different spatio-temporal patterns. Therefore, spatio-temporal monitoring of crime data is essential in identifying factors that cause crime and preventing crime. An important issue in many cities is related to crime events, and the spatio-temporal Bayesian approach leads to identifying crime patterns and hotspots. In Bayesian analysis of spatio-temporal crime data, there is no closed form for posterior distribution because of its non-Gaussian distribution and the existence of latent variables. In this case, we face challenges such as high dimensional parameters, extensive simulation and time-consuming computation in applying MCMC methods. Material and Methods In this paper, we apply INLA to analyze crime data in Colombia. To describe the above concepts, a three-stage hierarchical model is considered. The advantages of this method can be the estimation of criminal events at a specific time and location and exploring unusual patterns in places. Results and Discussion The Bayesian analysis of crime data is usually performed as Bayesian infer ence of pure spatial or temporal patterns. However, such spatial or temporal Bayesian analyses are not suitable for crime data. In this article, in a case study, Bayesian hierarchical spatio-temporal analysis of crime data in Colombia was discussed using the INLA approach, which considers spatio-temporal dependence and makes the model more flexible in detecting unusual patterns. Exploratory data analysis is also discussed, detecting areas with unusual behaviour over time. Four different models were fitted to the data, and the best model that includes spatio-temporal interaction was selected using the DIC criterion. The research results identify the most important centre of crime in the Kennedy area of Bogotá, , as well as the highest crime rate in the time frame. Then, hierarchical spatio-temporal Bayesian analysis of these data was done with the INLA approach. Conclusion The advantage of using this Bayesian approach is that it includes the effects of spatio-temporal correlation in the model and makes the model flexible in detecting areas with abnormal behaviour over time and in different places. For this purpose, four different models, including side effects and spatio-temporal combination, were fitted to the crime data. The best model, including the spatio-temporal interaction effect, was proposed using the deviance information criterion. The comprehensive and scientific comparison of the two Bayesian methods INLA and the MCMC algorithm in terms of accuracy, speed and even accessibility and convenient use for researchers requires independent scientific and practical research because, for example, the various methods of sampling in the MCMC algorithms and sometimes its different methods in INLA make it difficult to compare accuracy. How to use parallel calculations in the application of these two methods is also effective in comparing the speed, and simply comparing the outputs cannot express the advantage of one method over the other.

Monitoring process mean and variance simultaneously in a single control chart simplifies the process monitoring. If in addition, a simultaneous control chart is capable of recognizing the source of contamination, this capability leads to additional simplicity. These are the reasons why simultaneous control charts have attracted many researchers and manufacturers. Recently, in the statistical process control literature some control charts have been introduced which are based on the idea of Bayesian predictive density. This type of control charts, not only brings into account the uncertainty concerning the estimation of unknown parameters, but also do not need extensive simulations for computation of control limits. These control charts have been introduced for mean and variance in both univariate and multivariate situations. Up to now, no simultaneous control chart has been introduced based on Bayesian predictive density. In this paper, using the idea of Bayesian predictive density, we introduce a new simultaneous control chart for monitoring univariate mean and variance. We illustrate the important capabilities of this new chart through simulated data. This new chart is applicable when parameters are unknown. In other words, it brings into account the uncertainty concerning the unknown parameters. This chart is able to recognize the source of contamination and is sensitive to small changes in the mean and variance. In this chart the control limits, needless of simulation, can simply be obtained from normal table.

Sometimes, in econometrics problems the observations are not independent, so that their dependence is due to the location of observations in the studied space. To analyze these data are used the spatial regression models. Due to the large number of parameters in these models are used the iteration algorithms to obtain the maximum likelihood estimations, so that it encounters problems such as the complexity of the calculation. In addition in economic studies, the number of observation is large and it seems useful to use the Bayesian approach. The main purpose is using the Bayesian and the Likelihood approaches to estimate the parameters of the three spatial econometric models. Then, comparing the performance of these two approaches, as well as comparing the performance of these three spatial regression models and finally the three models are implemented on two real data. It is observed that the results of the Bayesian approach are more credible than the likelihood approach in these type of econometric models.

The central banks typically respond to inflationary fluctuations and production gaps by using monetary policy tools. The financial crisis in 2007 indicated that the monetary policy of central banks and pricing tools used to stabilize the economy have not been effective. Thus central banks utilized unconventional monetary policy to achieve financial stability the index of financial conditions indicates the financial climate affecting firms and households. This paper aims to identify and analyze the channel of monetary policy transmission and estimate the effect of the index of financial conditions on Iran's economic activity during the 2005-2017 period. Then, using the forward and backward distribution in the Bayesian VAR model, the impulse variables and immediate response to the financial condition indicator in the period under review are estimated. The findings of the paper indicate that financial conditions have negatively affected GDP and private sector investment, and credit growth has played a significant role in the financial condition index.