Gaussianization of Variational Bayesian Approximations with Correlated Non-nested Non-negligible Posterior Mean Random Effects Employing Non-negativity Constraint Analogs and Analytical Depossinization for Iteratively Fitting Capture Point, Aedes aegypti Habitat Non-zero Autocorrelated Prognosticators: A Case Study in Evidential Probabilities for Non-frequentistic Forecast Epi-entomological Time Series Modeling of Arboviral Infections

Abstract

Unfortunately, currently there is no literature contribution describing the frequency and distribution of potential, seasonal, Aedes (Ae.) aegypti, superbreeder, capture point covariates and their effect on epidemics of emerging diseases in county abatements. Ae. aegypti is one of the most significant mosquito species as it is capable of transmitting dengue fever, chikungunya, Zika, and yellow fever viruses. Here we regress an empirical dataset of potential, superbreeder, multivariate, Ae. aegypti, habitat, estimators (e.g., container volume, temperature, and relative humidity) spatiotemporally associated with immature, abundance counts of geographically sampled (henceforth geosampled), county abatement, capture points, to simulate seasonal prolific habitats in a single eco-geographic foci in Hillsborough County Florida. We employ an inferential, hierarchical, Bayesian paradigm with a subjective, maximum, likelihood (ML) estimator to unbiasedly parameterize the epi-entomological, time series dataset of seasonal sampled, aquatic habitat, optimizable signature prognosticators. A probabilistic, framework for distinguishing chaotic, random, geometric uncertainties about covariance matrices is demonstrated in PROC MCMC. An inner-product for spaces of random matrices is motivated and constructed. The assumption was that the inner-product on this space could exploit second-order co-exchangeability and related specifications in order to optimally simulate potential, seasonal, superbreeder covariates from an eco-georeferenceable dataset of, county abatement, capture point, empirical, Ae. aegypti, aquatic, larval/pupal habitat regressors. We introduce the basic idea of the analytical depoissonization on an implicit solution to the epi-entomological, time series that is, the asymptotic analysis of a sequence of Cauchy integrals on the complex plane with saddle point-like estimates. We show that a Bayesian treatment to the constrained probabilistic matrix factorization outperform simple linear estimation for rendering non-normality (multicollinearity, leptokurotic distributions) from regressed geosampled, seasonal, inferential covariates associated to potential, superbreeder, eco-georeferenceable Ae. aegypti foci. We employ extensions to heteroskedastic precision introduced in the literature by Haight (Handbook of the Poisson distribution, Wiley, New York, 1967) for depoissonizing geosampled, potential, seasonal, ento-epidemiological, capture points in order to translate the results of the vector arthropod model into the original (i.e., Bernoulli) model. Herein a maximum a posteriori probability (MAP) estimate was equated to the mode of the posterior' distribution in the simulated, distribution, regression paradigm for unbiasedly deducing statistical significance in a dataset of heuristically optimizable parameterizble estimators spatiotemporally associated to an eco-georeferenceable, prolific, county abatement Ae . aegypti foci. The MAP obtained a real time, capture point, approximation analogous to maximum likelihood estimation, but with an alternative augmented optimization which incorporated a prior distribution. We simulated datasets thereafter from a generalization of the Tukey-Lambda distribution employing the Ae. aegypti, capture point covariates which allowed us to control the levels of independence, kurtosis and skewness of the potential, prolific, habitat, parameterized estimators while simultaneously comparing the prognosticators by their Type I and Type II error rates. The model output revealed that the explanative habitat regressors were not invariant under re-parameterization and displayed a significant effect on abundance with a 95% confidence interval, with the covariate Container Volume having the strongest impact on the abundance of Ae. aegypti immatures.