سائنس اور روحانیت کی تمثیل: ایک تحقیقی جائزہ

Spirituality is usually understood as a way of being that flows from a certain profound experience of reality, which is known as ‘mystical’, ‘religious’, or ‘spiritual’ experience. There are numerous descriptions of this experience in the literature of the world’s religions, which tend to agree that it is a direct, non-intellectual experience of reality with some fundamental characteristics that are independent of cultural and historical contexts. Spiritual and scientific quests are two complementary inquiries into reality. Any feeling of antagonism between them is a product of a narrow vision. Science deals with what is measurable; religion is the quest for discovering and understanding the immeasurable. A scientist is not intelligent if he denies the existence of the immeasurable. There is nothing that is anti-science but there is a lot that is beyond science. The two quests have to go hand in hand. We not only need to have an understanding of the laws that govern the phenomena occurring in the external world around us but also we need to discover order and harmony in our consciousness. Human understanding is incomplete unless it covers both aspects of reality: matter as well as consciousness. Indeed the division between the scientific and spiritual quests is itself the creation of the human mind. Reality is one undivided whole which includes both matter and consciousness. Our thoughts, being limited by our experience, divide the external world from the inner world of our consciousness, in much the same way as our mind divides time from space though they are both two aspects of a single continuum۔

Bayesian Analysis of Mixture Distributions

In this thesis, we consider type-I mixtures of the members of a subclass of one parameter exponential family. This subclass includes Exponential, Rayleigh, Pareto, a Burr type XII and Power function distributions. Except the Exponential, mixtures of distributions of this subclass get either no or least attention in literature so far. The elegant closed form expressions for the Bayes estimators of the parameters of each of these mixtures are presented along with their variances assuming uninformative and informative priors. The proposed informative Bayes estimators emerge advantageous in terms of their least standard errors. An extensive simulation study is conducted for each of these mixtures to highlight the properties and comparison of the proposed Bayes estimators in terms of sample sizes, censoring rates, mixing proportions and different combinations of the parameters of the component densities. A type-IV sample consisting of ordinary type-I, right censored observations is considered. Bayesian analysis of the real life mixture data sets is conducted as an application of each mixture and some interesting observations and comparisons have been observed. The systems of non-linear equations to evaluate the classical maximum likelihood estimates, the components of the information matrices, complete sample expressions, the posterior predictive distributions and the equations for the evaluation of the Bayesian predictive intervals are derived for each of these mixtures as relevant algebra. The predictive intervals are evaluated in case of the Rayleigh mixture only for a number of combinations of the hyperparameters to look for a trend among the hyperparameters that may lead towards an efficient estimation.