bayesian method

Air pollution in the metropolis of Tehran is a serious environmental issue. Assigning an optimal budget to deal with air pollution problems in the East (no.4) and West (no.22) regions of Tehran, determining the optimal proportion of green spaces and determining the ratio of applying optimal traffic constraints in these two regions, and addressing similar problems, are all necessary and require a statistical optimization scale for resolving them. Unfortunately, so far, no study has been done in this regard, and research on this issue is needed. The main purpose of this research is to investigate the difference between the air pollution in East and West of Tehran and provide a benchmark for responding to the above issues. A new statistical approach has been proposed in this study for comparing air pollution in the East and West of Tehran, which eliminates the problems associated with conventional methods such as the t-test and nonparametric tests. In this method, the air pollution index values of the two regions have been modelled using a suitable statistical distribution and, then, the probability that air pollution in the East of Tehran would be more than in the western part of it would be reached through a Bayesian method. The value of this probability, called R, has been used as an optimal scale for allocating air pollution-related assets between the two regions. Air pollution data was collected in the east and west of Tehran in the winter of 2016 in terms of air quality index (AQI) and was modelled using distributions with a power hazard function. The mean and standard deviations for air pollution data in the East of Tehran have been obtained as 76.70 and 37.074, respectively, and the corresponding statistics for the West of Tehran were 72.14 and 34.166, respectively. Although, the sample mean of AQI in the East of Tehran is a little greater than in the West, the nonparametric Mann-Whitney test shows that there is no significant difference between air quality of these two regions. The 95% Bayesian confidence interval of R has been obtained (0.594 and 0.436) and a Bayes estimate of R has been obtained at 0.519. According to the results, although there is no significant difference (at a confidence level of 95%) between the air pollution in the eastern and the western parts of the city, with a probability 0.519, the air in the East of Tehran was more polluted than the West. Also, this probability value is an optimal scale which can be applied to the appropriate allocation of facilities related to air pollution between the two regions. That is, 51.9% of facilities related to air pollution should be allocated to the East of Tehran and 48.1% should be allocated to its western part. It seems that the proper allocation of funds from different regions of Tehran to control Tehran's air pollution can be a step towards solving this problem. The statistical method presented in this study provides an optimal amount for allocating funds to the East and West of Tehran. Officials can use the optimal amount based on this method to create appropriate policies for the proper distribution of funds and facilities in East and West Tehran. For example, to maximize the effectiveness of tree-planting in air purification, with this proportion it is better to plant trees in the eastern part of the city more than in the western part. Also, it is suggested that traffic constraints in eastern Tehran should be greater than in the western part of it.

Determination of inter-seismic deformations such as fault slip-rate can usually be achieved by using geodetic observations, earthquake geology and paleo-seismology, as well as mechanical, empirical and numerical modeling. In these models, combination of the fault seismic parameters and the GPS data can help estimate the fault slip-rate, the elastic thickness of the lithosphere, the earthquakes recurrence time, the relaxation time of the asthenosphere, the elapsed time of earthquake and the locking depth of the fault. In this study, we utilize the geodetic data of the North Tabriz Fault (NTF) by using random Bootstrap sampling and conducting numerical modeling by code writing in the R and MATLAB softwares. In this concern, the fault slip-rate and elastic layer thickness are estimated to be ~4-6.5±1 mm/yr and ~5-25 km, respectively, for the NW segment of the NTF. Similarly, model results for the SE segment of the fault indicate a slip-rate of ~3.5-5.5±1 mm/yr and elastic layer thickness of ~8-16 km. For the NW segment of the NTF, the asthenosphere relaxation time, earthquake recurrence time and elapsed time are estimated to be ~160-185 years, ~650-950 years and ~200-1400 years, respectively. Model results for the SE segments of the NTF indicate an asthenosphere relaxation time of ~220-340 years, an earthquake recurrence time of ~750-1050 years and an elapsed time of ~200-1500 years, respectively. The results are well consistent with the other paleoseismological and geological results.

Due to subsurface heterogeneity and existing vagueness in geophysical interpretation, identifying and interpretation of facies in wellbores is always prone to uncertainty and risk. Nowadays several methods have developed for quantitative facies interpretation. These methods are generally divided into deterministic and stochastic categories. Deterministic methods, in spite of their simple modeling procedure, cannot expose the amount of error or accuracy of the model. On the other hand, stochastic methods, in addition to quantifying the error of the model, can provide the probability of the model’s accuracy in each point of the reservoir. The Bayesian approach is one of the stochastic methods that use conditional probabilities for modeling. This approach, as well as probabilistic modeling of hydrocarbon facies, quantitatively computes the effect of additional data in decreasing the error of the classification. Information entropy theory, by quantifying the intrinsic uncertainty in each model input parameter, can easily provide the selection of valuable parameters. The present study was carried out on one of the wells of Mansuri oil field, south of Iran. After generation of training data by using rock physics techniques and Gassmann’s relation, the value of each input parameter was identified by entropy analysis. Then, by use of Bayesian analysis and valuable parameters, oil facies classification and discrimination was implemented. The five optimum parameters were elastic impedance, compressional wave velocity, shear wave velocity, density and porosity. The amount of error in this method is approximated to be 11 percent. This investigation also showed that gamma ray parameter does not have a drastic positive effect on identification and discrimination procedure of oil facies, which has a good agreement with the results of entropy analysis.