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This study approaches the Bayesian identification of moving average processes using an approximate likelihood function and a normal gamma prior density. The marginal posterior probability mass function of the model order is developed in a convenient form. Then one may investigate the posterior probabilities over the grid of the order and choose the order with the highest probability to solve the identification problem. A comprehensive simulation study is carried out to demonstrate the performance of the proposed procedure and check its adequacy in handling the identification problem. In addition, the proposed Bayesian procedure is compared with some non Bayesian automatic techniques and another Bayesian technique. The numerical results support the adequacy of using the proposed procedure in solving the identification problem of moving average processes.

Identification is one of the most important stages of a time series analysis. This paper develops a direct Bayesian technique to identify the order of multivariate autoregressive processes. By employing the conditional likelihood function and a matrix normal-Wishart prior density, or Jeffreys' vague prior, the proposed identification technique is based on deriving the exact posterior probability mass function of the model order in a convenient form. Then one may easily evaluate the posterior probabilities of the model order and choose the order that maximizes the posterior mass function to be the suitable order of the time series data being analyzed. Assuming the bivariate autoregressive processes, a numerical study, with different prior mass functions, is carried out to assess the efficiency of the proposed technique. The analysis of the numerical results supports the adequacy of the proposed technique in identifying the orders of multivariate autoregressive processes.

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Background: Condyle fractures account for 17.5 percent to 50 percent of all mandibular fractures, although there are still many debates on whether to treat them close or open. There are several techniques of managing the mandibular condyle, each with its own set of benefits and drawbacks. Aim: compare the innovative preauricular transmasseteric anteroparotid approach (P-TMAP) to the usual retromandibular transparotid technique. Patients and methods: 20 cases, patients with an odd number (1,3,5,7,9,11,13,15,17,19) received a preauricular transmasseteric anteroparotid approach (study group), while patients with a double number (2,4,6,8,10,12,14,16,18,20) had a retromandibular transparotid approach (control group) (control group). Patients were closely monitored for six months. Results: Fractures were caused by a road traffic accident (RTA) in 6(60%) of the cases, interpersonal violence in 3(30%) of the cases and falling in 1(10%) of the cases in both groups. Immediate postoperative facial nerve affection was higher in the transparotid approach group (30%) than in the anteroparotid approach group (10%), but both groups exhibited no statistically significant difference three months after surgery. There were no parotid injuries in any of the cases in either group.