Bayesian Regression of Government Expenditure on Revenue in Nigeria

The relationship between government expenditure and its revenue is generating serious debate among researchers. Similarly, their has been a controversy between the classical and the bayesian modelling. Therfore, this study examined the relationship between the government expenditure and its revenue in Nigeria using the bayesian approach. The finance data extracted from the Central Bank of Nigeria statistical bulletin from 1989 to 2018 were considered for the study. Bayesian linear regression was used to fit the model. Normal distribution was fit for the likelihood. Thus, normal-gamma prior was elicited for the bayesian regression parameters. The result showed that the Bayesian estimates with elicited normal-gamma prior produced a better posterior mean of 0.536 for the Total Revenue with a smaller posterior standard deviation of 0.00001 when compared with the OLS standard deviation of 0.05256. Similarly, the total revenue explained 78% variations in the Total expenditure. The constructed model fit was: Total Expenditure = 98.57128 + 0.53630* Total Revenue. This showed that a naira unit of the total expenditure will always be increased by 0.54 of the total revenue. Forecast of 30 years for the total expenditure using both OLS and Bayesian (normal gamma prior) were increasing as the years were progressing. Government should look for a way to increase its revenue in order to sustain the future expenses of the government since expenditure increases yearly.

Sensitivity of the Posterior Mean on the Prior Assumptions: An Application of the Ellipsoid Bound Theorem

This study examines the sensitivity of the posterior mean to change in the prior assumptions. Three plausible choices of prior which include informative, relative-non informative and non-informative priors are considered. The paper considers information level for a prior to cause a notable change in the Bayesian posterior point estimate. The study develops a framework for evaluating a bound for a robust posterior point estimate. The Ellipsoid Bound theorem is employed to derive the Ellipsoid Bound for an independent normal gamma prior distribution. The proposed modification ellipsoid bound for the large prior was establised by varrying different variance co-variance sizes for the independent normal gamma prior. This bound represents the range for the posterior mean when is insensitive and when it’s sensitive in both location and spread. The result shows that; for a large prior parameter value (greater than the OLS estimate) with a positive definite prior variance covariance matrix, and prior parameter values interval which contains the OLS estimate then, the posterior estimate will be less than both the OLS and the prior estimates. Similarly, if the lower bound of the prior parameter values range is greater than the OLS estimate then: The posterior estimate will be greater than the OLS estimate but smaller than the prior estimate. Furthermore, it is observed that no matter the degrees of confidence in the prior values, data information is powerful enough to modify it.

Bayesian Estimate of Parameters for ARMA Model Forecasting

This paper presents a Bayesian approach to finding the Bayes estimator of parameters for ARMA model forecasting under normal-gamma prior assumption with a quadratic loss function in mathematical expression. Obtaining the conditional posterior predictive density is based on the normal-gamma prior and the conditional predictive density, whereas its marginal conditional posterior predictive density is obtained using the conditional posterior predictive density. Furthermore, the Bayes estimator of parameters is derived from the marginal conditional posterior predictive density.

A Bayesian approach to construct confidence intervals for comparing the rainfall dispersion in Thailand

Natural disasters such as drought and flooding are the consequence of severe rainfall fluctuation, and rainfall amount data often contain both zero and positive observations, thus making them fit a delta-lognormal distribution. By way of comparison, rainfall dispersion may not be similar in enclosed regions if the topography and the drainage basin are different, so it can be evaluated by the ratio of variances. To estimate this, credible intervals using the highest posterior density based on the normal-gamma prior (HPD-NG) and the method of variance estimates recovery (MOVER) for the ratio of delta-lognormal variances are proposed. Monte Carlo simulation was used to assess the performance of the proposed methods in terms of coverage probability and relative average length. The results of the study reveal that HPD-NG performed very well and was able to meet the requirements in various situations, even with a large difference between the proportions of zeros. However, MOVER is the recommended method for equal small sample sizes. Natural rainfall datasets for the northern and northeastern regions of Thailand are used to illustrate the practical use of the proposed credible intervals.

On Model Comparison: Application of Savage-Dickey Density Ratio to Bayes Factor

Bayes factor is a major Bayesian tool for model comparison especially when the model priors are the same. In this paper, the Savage-Dickey Density Ratio (SDDR) is used to derive the Bayes factor to select a model from two competing models under consideration in a normal linear regression with an independent normal-gamma prior. The Gibbs sampling technique for the joint posterior distribution with equal prior precision for both the unrestricted and restricted models is used to obtain the model estimates. The result shows that the Bayes factor gave more support to the unrestricted model against the restricted and was consistent irrespective of changes in sample size.

Predicting PM10 concentration using Bayesian regression with Non-Informative Prior and Conjugate Prior Model

The aim of this study is to predict the next day PM10 concentration using Bayesian Regression with noninformative prior and conjugate prior models. The descriptive analysis of PM10, temperature, relative humidity, nitrogen dioxide (NO2), sulphur dioxide (SO2), carbon monoxide (CO) and ozone (O3) are also included. A case study used two-years of air quality monitoring data at three (3) monitoring stations to predict the future PM10 concentration with seven parameters (PM10, temperature, relative humidity, NO2, SO2, CO, and O3). The descriptive analysis showed that the highest mean PM10 concentration occurred at Klang station in 2011 (71.30 µg/m3) followed by 2012 (68.82 µg/m3). The highest mean PM10 concentration was at Nilai in 2012 (68.86 µg/m3) followed by 2011 (66.29µg/m3) respectively. The results showed that the Bayesian regression model used a conjugate prior with a normal-gamma prior which was a good model to predict the PM10 concentration for most study stations with (R2 = 0.67 at Jerantut station), (R2 = 0.61 at Nilai station) and (R2 = 0.66 at Klang station) respectively compared to a non-informative prior.