Estimation of UAE population using Bayesian Theorem - Research Paper Example

A common use to which this theory has been put to is the development of time series forecasts for populations. In this case, this theory will be used to analyze the population data for United Arab Emirates. In most instances, the use of Bayesian theory is based on its mathematical framework ability that is able to provide inference on matters using probability (Hoff 116). In this project, the use of a Bayesian approach is adopted since through it the uncertainties that may exist in the model, data or even model parameters are integrated coherently in a consistent manner thus, allowing for easy inference (Gelman 75).

The framework for this analysis will entail the adoption of a methodology for a time series forecasting that shall include stochastic volatility and autoregressive models fitted into historical timeline data about the population of UAE. Most instances that entail forecasting of population data apply a frequentist/classical approach, in which case, the Bayesian model offers the best flexibility by its ability to specify uncertainties upon which forecasting can be performed (Ruggeri, Michael & Insua 80).

Principles of Bayes Law Bayes theorem otherwise known as the Bayes law tries to express how the degree at which one believes in a subjective matter should change to be in line with evidence; this is known as the Bayesian inference. This theory was further developed by Laplace and got it published later on in the 1800s. The aim of this theory is to measure the extent of belief. Using this theory, the belief is either confirmed or otherwise based on the evidence collected. Hence, there is the initial belief or the prior that can be denoted by P (A) and then there is the evidence collected or the posterior denoted as P (B) and there is the quotient denoted as P(B/A) or P(B) which it shows how B supports the belief A (Leonard & John 69).

The main assumptions made in the Bayes theorem are: Tests are not events, for example there is a difference between a malaria tests and actually having malaria, the test is different from the event. It is believed that tests are flawed and hence can be challenged; they can detect things that don’t exist which are called a false positive, and miss things that exist; referred to as a false negative. The false positives skew the results; there is a high likelihood that the positive results are incorrect.

Natural numbers are preferred over percentages. In summary, the Bayes theory gives the probability of an event given the test probabilities (Grover 120). A review of approaches to population projections The application of certain simple criteria can enable the obtaining of macro-level methods of population projection and its typologies. This may entail the use of simple extrapolations of the growth rates or size of the population, uncertainty approach and the methodology of the method. The estimation of the dimensionality of populations in the simplest forms always utilizes extrapolations while the uncertainty approach may be ignored or quantified by the use of probabilities.

The Bayesian model utilizes both the extrapolation and time series analysis in the determination of end results for stochastic projections (Koch 41). The UAE population According to the UAE Department of Statistics (uaestatistics.gov.ae), the following figures were obtained from the census that was done in the years between 1975 and 2005. Year Total no. of Expatriates Total no. of Citizens 1975 356,343 201,544 1980 751,555