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In Bayesian prediction of a Gaussian space-time model, unknown parameters are considered as random variables with known prior distributions and, then the posterior and Bayesian predictive distributions are approximated with discritization method. Since prior distributions are often unknown, in this paper, parametric priors are considered. Then the empirical Bayes approach is used to estimate the prior distributions. Replacing these estimates in the Bayesian predictive distribution, an empirical Bayes space-time predictor and prediction variance are determined. Then an environmental example is used to illustrate the application of the proposed method. Finally the accuracy of the empirical Bayes space-time predictor is considered with cross validation criterion.

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This paper offers a method of the estimation of the transition probability for the behaviors of financial time series by Markov Switching Autoregressive model. Using this model, the behaviors of fluctuations of exchange rate form two regimes low and high changes rate are considered. Results of prediction show that the persistence probability of regimes will be decreased. Thus, the probability of transition to other regime will be increased if process were in a specific regime.

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Penalized estimators for estimating regression parameters have been considered by many authors for many decades. Penalized regression with rectangular norm is one of the mainly used since it does variable selection and estimating parameters, simultaneously. In this paper, we propose some new estimators by employing uncertain prior information on parameters. Superiority of the proposed shrinkage estimators over the least absoluate and shrinkage operator (LASSO) estimator is demonstrated via a Monte Carlo study. The prediction rate of the proposed estimators compared to the LASSO estimator is also studied in the US State Facts and Figures dataset.

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Prediction of spatial variability is one of the most important issues in the analysis of spatial data. So predictions are usually made by assuming that the data follow a spatial model. In General, the spatial models are the spatial autoregressive (SAR), the conditional autoregressive and the moving average models. In this paper, we estimated parameter of SAR(2,1) model by using maximum likelihood and obtained formulas for predicting in SAR models, including the prediction within the data (interpolation) and outside the data (extrapolation). Finally, we evaluate the prediction methods by using image processing data.

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‎Modeling and efficient estimation of the trend function is of great importance in the estimation of variogram and prediction of spatial data. In this article, the support vector regression method is used to model the trend function. Then the data is de-trended and the estimation of variogram and prediction is done. On a real data set, the prediction results obtained from the proposed method have been compared with Spline and kriging prediction methods through cross-validation.  The criterion for choosing the appropriate method for prediction is to minimize the root mean square of the error. The prediction results for several positions with known values were left out of the data set (for some reason) and were obtained for new positions. The results show the high accuracy of prediction (for all positions and elimination positions) with the proposed method compared to kriging and spline.

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In this paper, the prediction of the lifetime of k-component coherent systems is studied using classical and Bayesian approaches with type-II censored system lifetime data. The system structure and signature are assumed to be known, and the component lifetime distribution follows a half-logistic model. Various point predictors, including the maximum likelihood predictor, the best-unbiased predictor, the conditional median predictor, and the Bayesian point predictor under a squared error loss function, are calculated for the coherent system lifetime. Since the integrals required for Bayes prediction do not have closed forms, the Metropolis-Hastings algorithm and importance sampling methods are applied to approximate these integrals. For type-II censored lifetime data, prediction interval based on the pivotal quantity, prediction interval HCD, and Bayesian prediction interval are considered. A Monte Carlo simulation study and a numerical example are conducted to evaluate and compare the performances of the different prediction methods.