The comparision between P-value and posterior probability has a long history. The re-
sult so far have an reconcilability in one-sided hypotheses and irreconcilability in two-sided
hypotheses. From the decision-theory point of viwe, there are a few articles about the compar-
ision between these two criterion. In this thesis, we considered the admissibility of these two
criterion for two important distributions Exponential distribution and Parato distributiob. It
was shown that in both distributions Exponential and Parato for one-sided hypotheses there
is the same results for P-value and posterior probability. both are admissible estimators for
null hypotheses. Also for two-sided hypotheses, it has been shown that there is a irreconcil-
ability between these to criterion, in Exponential distribution while posterior probability is an
admissible estimator for null hypotheses, P-value is a inadmissible estimator. In the case of
restricted parameter space, the P-value is not a admissible estimator in one-sided or two-sided
hypotheses. A modified P-value was given to lead a admissible estimator.

 In classical infrence, the most optimum property is uniformly most powerful (UMP) test. However, In many cases these tests are not available. Also, these tests are not available in two-sided hypothesis for the exponential family.Therfore, the ststisticans suggested more powerful tests which are weaker optimal tests with respect to UMP tests for two-side hypothesise, In exponential familya for one or two-sidehypothesis with a nusiance parameter the optimal tests leads to conditional tests which are UMP in the unbiased tests. In such situations, we search for more powerful tests than the classicl UMP unbiased tests. In this study a more powerful test then UMP unbiased test has been suggest.In this Thesis(research) We considered both one-sided and two-sided hypotheses for comparing two poisson means and also with considered one-sided hypotheses two binomial proportions. The performance of this method has been investigated by numerical stuy.

Discriminate and classification are two main problems in statistical multivariate analysis. Clustering of time series using Fourier analyses is one of these method and is important because of independent periodogram calculations at different frequencies. This leads to have more easy calculation in cluster analysis or comparison between two time series.
The problem often arises in practice is unequal length of the time series.
In this study an approach has been given that using the increasing or decreasing the length of time series we catch the same length of two series.
In ‎the‎s‎is several important distances clustering time series, including Kullback-Leibler, Chernoff and Mahalanobis, are studied with unequal observations in each series.
We also studied the performance these distances with simulation. We have shown that the Chernoff distance is more efficient than any other distance.
Finally using the Chernoff discrimination distance, we clustered the populations in 19 states of America.
The results showed that these 20 states can be classified in two cluster southern (large population) and north-east stats (small population).

This thesis is concerned with the comparison of P-value and Bayesian measure in two-sided and one-sided hypothesis for the variance of Normal distribution with known and unknown mean (nuisance parameter)‎. ‎For tow-sided hypotheses‎, ‎First‎, ‎using fixed prior distributions for test parameter‎, ‎the posterior probability is obtained and compared with the P-value when an appropriate prior is suggested for the nuisance parameter‎. ‎Second‎, ‎lower bounds of the posterior probability of H0‎, ‎under a reasonable class of prior‎ ‎distributions are compared with the P-value.Results revealed showed that without nuisance and in the presence of nuisance parameter for the‎ ‎model‎, ‎these two approaches can lead to different results in statistical inference‎. ‎Then‎, ‎sensitivity of posterior probability of null hypothesis is investigated by different prior distributions‎. ‎The results also showed that sensitivity was poor and different prior distributions for nuisance parameter were not affected by the comparison between two methods.‎ ‎But‎, ‎in contrast to two-sides hypotheses‎, ‎when we use a fixed prior‎, ‎there is reconcilability between two approaches in one-sided hypotheses

The problem of comparing the significance measures and the Bayesian measures in the one-sided and two-sided testing problems has been widely considered by statisticians‎. ‎The most of founds indicate that there is different results between Bayesian and classical point of views in two-sided testes‎. ‎However‎, ‎there is no the case for one-sided tests in which the results are similar‎. ‎Most of the previous works are focused in one dimension cases and without nuisance parameters‎. ‎In this thesis‎, ‎the comparision between Bayesian measures are considered in multivariate normal distribution‎. ‎Due to prior distribution selection in Bayes test‎, ‎the comparison is achieved in two methods‎. ‎In the first method‎, ‎a specific prior distribution is chosen and posterior probability of null hypothesis computed‎. ‎This posterior probability of null hypothesis is then compared with the P-value‎. ‎In the second method‎, ‎the lower bound of the posterior probability of null hypothesis‎, ‎over some reasonable classes of prior distribution are derived and compared with the P-value‎. ‎Also‎, ‎it shown that the sensivity with respect to prior distribution is weak when we used the posterior probability affected to comparison between two methods‎. ‎It is shown that‎, ‎the conflict between P-value and Bayesian evidence in addition to the prior distribution of other factors is highly dependent on the sample size and existance nuisance parameters in sample‎. ‎So that unlike the univariate agreement between the two styles is the the test in multidimensional differences between the two measures exist‎. ‎The two-sided test when nuisance parameter in the model is present as in univariate‎, ‎there is difference between the two test methods.

In time series analysis, it may be exist a sequential outlier points at an interval. This set of outliers called patch of outlier, recently has been paid attention by the statisticians. Detection of additive outlier patches may be difficult in the presence of severe masking and swamping effects. Recently, Bayesian approaches have been used in time series, to detect of outlier patch with Markov Chain Monte Carlo algo- rithm. Justel et al. (2001) propose a procedure to detect patches of additive outlier in an autoregressive process. Adaptive Gibbs sampling identifies the beginning and the end of possible outlier patches using the existing Gibbs sampling, then carries out an adaptive procedure with block interpolation to handle patches of outlier. We use adaptive Gibbs sampling to detection additive outlier patches and estimate their outlier magnitude in AR models. The simulation study shows that this procedure has relatively high effectiveness. As an application example the data of monthly golden Bahar Azadi coin prices are considered. This data collected from April 1985 to October 2014. The data anal- ysed to detect additive outliers patches and estimate their outlier magnitude. The results show that this series has not additive outliers patches but it has some additive outliers.