Background In Pakistan, dengue fever has become a major concerning factor, given that it is a relatively new disease compared to malaria. The number of people affected by dengue fever has increased at least 10-fold in the last 15 years in specific areas of Pakistan. Therefore, it is necessary to analyse this disease to reduce or prevent the effects of dengue fever in the region. Methods Geographical information system (GIS) maps are used to identify the intensity of the spread according to the count of affected people in our study area. Generalised linear modelling (GLM) is used to study the significance of factors associated with dengue fever. Results The dengue virus is present throughout the year in specific areas of Pakistan. Karachi and Lahore are most significantly affected with cases in these two most populous cities of Pakistan reported every year. In the study period (2006–2017), 2011 was the most devastating year for Pakistan. Lahore recorded more than 17,000 confirmed cases with 290 deaths in a single year. The GLM analysis shows rainfall, the average maximum temperature, and hospitals to be significant factors in the prevalence of dengue fever. Conclusion This study finds that Sindh and Khyber Pakhtunkhwa are two of the primarily vulnerable provinces for the spread of dengue fever. Punjab has observed sporadic increases in dengue fever cases. In Pakistan, dengue cases increase in the rainfall season, especially during monsoon season. Lack of proper hospitals and clinics are another major factor, and mobile hospitals are needed in remote hotspot regions often affected by dengue fever. Finally, improved sanitation systems in metropoles would facilitate reducing breeding grounds for Aedes Aegypti larvae.

We propose a novel Bayesian approach to the problem of variable selection in multiple linear regression models. In particular, we present a hierarchical setting which allows for direct specification of a-priori beliefs about the number of nonzero regression coefficients as well as a specification of beliefs that given coefficients are nonzero. To guarantee numerical stability, we adopt a g-prior with an additional ridge parameter for the unknown regression coefficients. In order to simulate from the joint posterior distribution an intelligent random walk Metropolis-Hastings algorithm which is able to switch between different models is proposed. Testing our algorithm on real and simulated data illustrates that it performs at least on par and often even better than other well-established methods. Finally, we prove that under some nominal assumptions, the presented approach is consistent in terms of model selection. 45However, the g-prior depends on the inverse of the empirical covariance matrix of the selected predictors. This matrix is singular if the number of selected covariates is greater than the number of observations n and, further, may be almost rank deficient given that the predictors are highly correlated. To overcome this problem Wang et al. (2015) replaced the classical inverse with the Moore-Penrose generalized inverse and thus ended up with the so-called gsg-prior (see West (2003)). In contrast to them, we adopt a g-prior 50 with an additional ridge parameter for the unknown regression coefficients to guarantee nonsingularity of the empirical covariance matrix. This modification of the classical g-prior was first proposed by Gupta and Ibrahim (2007) and further investigated by Baragatti and Pommeret (2012).Finally, in Section 2.2 we state that our approach is consistent in terms of model selection according to the consistency definition given by Fernández et al. (2001). The proof of this result is deferred to the 55 appendix. Moreover, in Section 3, we evaluate our approach on the basis of real and simulated data and compare the results with the already described shrinkage methods. We show that our approach performs at least on par and often better than the comparative methods.

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Abstract. The restrictions of the analysis of natural processes which are observed at any point in space or time to a purely spatial or purely temporal domain may cause loss of information and larger prediction errors. Moreover, the arbitrary combinations of purely spatial and purely temporal models may not yield valid models for the space-time domain. For such processes the variation can be characterized by sophisticated spatio-temporal modeling. In the present study the composite spatio-temporal Bayesian maximum entropy (BME) method and transformed hierarchical Bayesian space-time interpolation are used in order to predict precipitation in Pakistan during the monsoon period. Monthly average precipitation data whose time domain is the monsoon period for the years 1974–2000 and whose spatial domain are various regions in Pakistan are considered. The prediction of space-time precipitation is applicable in many sectors of industry and economy in Pakistan especially; the agricultural sector. Mean field maps and prediction error maps for both methods are estimated and compared. In this paper it is shown that the transformed hierarchical Bayesian model is providing more accuracy and lower prediction error compared to the spatio-temporal Bayesian maximum entropy method; additionally, the transformed hierarchical Bayesian model also provides predictive distributions.