Using data for World Bank Development Indicators (2015) database from 1995 to 2013, this paper explores the impact of public health expenditure on national health outcomes in Tanzania while GDP per capita and improved sanitation facilities as explanatory variables were controlled for. Two national health outcomes indicators namely, infant and under-five mortality were used as dependent variables. With separate modeling approach, Frequentist and Bayesian based on time series and Markov Chain Monte Carlo (MCMC) respectively, empirical evidence shows that income, represented by real GDP per capita lower infant and under-five mortality in Tanzania. Under both methodological approach regardless of the sample size, we failed to support evidence that, public health expenditure and improved sanitation facilities had an impact on child health outcomes. Our results imply that, public health spending in Tanzania is poorly targeted to bring good child health outcomes. The paper draws attention to policy makers in Tanzania to focus either within public health spending composition or beyond to other close determinants of infant and under-five mortality.