The current study illustrates the utilization of artificial neural network in statistical methodology. More specifically in survival analysis and time series analysis, where both holds an important and wide use in many applications in our real life. We start our discussion by utilizing artificial neural network in survival analysis. In literature there exist two important methodology of utilizing artificial neural network in survival analysis based on discrete survival time method. We illustrate the idea of discrete survival time method and show how one can estimate the discrete model using artificial neural network. We present a comparison between the two methodology and update one of them to estimate survival time of competing risks. To fit a model using artificial neural network, you need to take care of two parts; first one is the neural network architecture and second part is the learning algorithm. Usually neural networks are trained using a non-linear optimization algorithm such as quasi Newton Raphson algorithm. Other learning algorithms are base on Bayesian inference. In this study we present a new learning technique by using a mixture of the two available methodologies for using Bayesian inference in training of neural networks. We have performed our analysis using real world data. We have used patients diagnosed with skin cancer in the United states from SEER database, under the supervision of the National Cancer Institute. The second part of this dissertation presents the utilization of artificial neural to time series analysis. We present a new method of training recurrent artificial neural network with Hybrid Monte Carlo Sampling and compare our findings with the popular auto-regressive integrated moving average (ARIMA) model. We used the carbon dioxide monthly average emission to apply our comparison, data collected from NOAA.