Bayesian Analysis of Poverty Rates in the South-Western Part of Nigeria

Poverty is global serious issue which differs in various cultures across the world and over time, varies according to the understanding of the society. Poverty is the level wherein an individual or people do not have the fundamental money-related assets and basics for the least expectation for everyday comforts. Therefore, this study applies a bayesian approach to poverty rates using the wealth index data in the south-western part of Nigeria to examine their poverty levels. The likelihood was Bernoulli and the conjugate Beta distribuitions at five different parameter values [Beta (1, 1), Beta (2, 2), Beta (4, 4), Beta (8, 8) and Beta (10, 10)] were elicited for the prior. Thus, the Beta-Bernoulli posteriors were derived, fitted and their parameters estimated for both the poor data set and the non-poor data set. The result for the poor data showed that as values of the prior parameters increases the posterior mean increases and the posterior variance decreases. So, at Beta (10, 10), the posterior standard variance is the lowest which indicates that about 36% of South-Western Nigeria population are extremely poor. Also, the result for the non poor data shows that as the values of the posterior parameters increases with increase in the prior parameters values, the posterior variance for prior, Beta (1, 1) has the least value 10.78%. This means that about 11% of South-Western Nigeria population are extremely non poor (rich).

Sinkhole Scanner: A New Method to Detect Sinkhole-Related Spatio-Temporal Patterns in InSAR Deformation Time Series

Sinkholes are sudden disasters that are usually small in size and occur at unexpected locations. They may cause serious damage to life and property. Sinkhole-prone areas can be monitored using Interferometric Synthetic Aperture Radar (InSAR) time series. Defining a pattern using InSAR-derived spatio-temporal deformations, this study presents a sinkhole pattern detector, called the Sinkhole Scanner. The Sinkhole Scanner includes a spatio-temporal mathematical model such as a 2-dimensional time evolving Gaussian function as a kernel, which moves over the study area using a sliding window approach. The scanner attempts to fit the model over deformation time series of Constantly Coherent Scatterers (CCS) intersected by the window and returns the posterior variance as a measure of goodness of fit. In this way, the scanner searches for subsiding regions resembling sinkhole shapes over a sinkhole prone area. It is designed to detect large sinkholes with a high efficiency, and small sinkholes with a lower efficiency. It is tested at four different spatial scales, and on a simulated and real set of deformation data. Real data were obtained from Sentinel-1A SLC data in IW mode, over Ireland where a large sinkhole occurred on 24 September 2018. The Sinkhole Scanner was able to identify a pattern of low posterior variance zones consistent with the simulated set. In case of the real data, it is able to identify significantly low posterior variance zones near the sinkhole area with the lowest value being 51.1% of the maximum value. The results from Sinkhole Scanner over the real sinkhole site were compared with Multiple Hypothesis Testing (MHT), which identifies Breakpoint and Heaviside temporal anomalies in the deformation time series of CCS. MHT was able to identify high likelihood for Heaviside anomalies in deformation time series of CCS near the sinkhole site about 10 epochs before the sinkhole occurrence. We show that the Sinkhole Scanner is efficient in monitoring a large area and search for sinkholes and that MHT can be used successively to identify temporal anomalies in the vicinity of areas detected by the Sinkhole Scanner. Future research may address other Sinkhole shapes whereas the underlying stochastic model may be adjusted. We conclude that the Sinkhole Scanner is important to be applied at different levels of scale to converge on potential sinkhole centers.

Application of the method of robust estimation by posterior variance in detecting the raw error of geodetic control network

If the raw error appears in set of measuring data, it affects significantly on adjustment results and displacement values of monitoring points, thus conclusion about displacement of works is incorrect. The method of robust estimation by posterior variance for detecting the raw error bases on principle of choosing weight of robust estimation, this is the other type that belong to the least square statistical estimation, which is used to process the measuring data with raw error when they were given into random model of the adjustment problem. Through processing data of Son La hydroelectricity construction network, the obtained result proved that the method good efficiency, it not only finds the measuring value that contains the raw error, but also determines the value of the raw error nearly accurately, moreover, it is able to detect many raw error in the set of data.

Streaming stochastic variational Bayes: An improved approach for inference with concept drifting data streams

Online learning is an essential tool for predictive analysis based on continuous, endless data streams. Adopting Bayesian inference for online settings allows hierarchical modeling while representing the uncertainty of model parameters. Existing online inference techniques are motivated by either the traditional Bayesian updating or the stochastic optimizations. However, traditional Bayesian updating suffers from overconfident posteriors, where posterior variance becomes too inadequate to adapt to new changes to the posterior with concept drifting data streams. On the other hand, stochastic optimization of variational objective demands exhausting additional analysis to optimize a hyperparameter that controls the posterior variance. In this paper, we present "Streaming Stochastic Variational Bayes" (SSVB) — a novel online approximation inference framework for data streaming to address the aforementioned shortcomings of the current state-of-the-art. SSVB adjusts its posterior variance duly without any user-specified hyperparameters to control the posterior variance while efficiently accommodating the drifting patterns to the posteriors. Moreover, SSVB can be easily adopted by practitioners for a wide range of models (i.e. simple regression models to complex hierarchical models) with little additional analysis. We demonstrate the superior performance of SSVB against Population Variational Inference (PVI), Stochastic Variational Inference (SVI) and Black-box Streaming Variational Bayes (BB-SVB) using two non-conjugate probabilistic models: multinomial logistic regression and linear mixed effect model. Furthermore, we also emphasize the significant accuracy gain with SSVB based inference against conventional online learning models for each task.

Streaming stochastic variational Bayes: An improved approach for inference with concept drifting data streams

Online learning is an essential tool for predictive analysis based on continuous, endless data streams. Adopting Bayesian inference for online settings allows hierarchical modeling while representing the uncertainty of model parameters. Existing online inference techniques are motivated by either the traditional Bayesian updating or the stochastic optimizations. However, traditional Bayesian updating suffers from overconfident posteriors, where posterior variance becomes too inadequate to adapt to new changes to the posterior with concept drifting data streams. On the other hand, stochastic optimization of variational objective demands exhausting additional analysis to optimize a hyperparameter that controls the posterior variance. In this paper, we present "Streaming Stochastic Variational Bayes" (SSVB) — a novel online approximation inference framework for data streaming to address the aforementioned shortcomings of the current state-of-the-art. SSVB adjusts its posterior variance duly without any user-specified hyperparameters to control the posterior variance while efficiently accommodating the drifting patterns to the posteriors. Moreover, SSVB can be easily adopted by practitioners for a wide range of models (i.e. simple regression models to complex hierarchical models) with little additional analysis. We demonstrate the superior performance of SSVB against Population Variational Inference (PVI), Stochastic Variational Inference (SVI) and Black-box Streaming Variational Bayes (BB-SVB) using two non-conjugate probabilistic models: multinomial logistic regression and linear mixed effect model. Furthermore, we also emphasize the significant accuracy gain with SSVB based inference against conventional online learning models for each task.

Gaussian Mean Field Regularizes by Limiting Learned Information

Variational inference with a factorized Gaussian posterior estimate is a widely-used approach for learning parameters and hidden variables. Empirically, a regularizing effect can be observed that is poorly understood. In this work, we show how mean field inference improves generalization by limiting mutual information between learned parameters and the data through noise. We quantify a maximum capacity when the posterior variance is either fixed or learned and connect it to generalization error, even when the KL-divergence in the objective is scaled by a constant. Our experiments suggest that bounding information between parameters and data effectively regularizes neural networks on both supervised and unsupervised tasks.

Streaming stochastic variational Bayes; An improved approach for Bayesian inference with data streams

Online learning is an essential tool for predictive analysis based on continuous, endless data streams. Adopting Bayesian inference for online settings allows hierarchical modeling while representing the uncertainty of model parameters. Existing online inference techniques are motivated by either the traditional Bayesian updating or the stochastic optimizations. However, traditional Bayesian updating suffers from overconfidence posteriors, where posterior variance becomes too inadequate to adapt to new changes to the posterior. On the other hand, stochastic optimization of variational objective demands exhausting additional analysis to optimize a hyperparameter that controls the posterior variance. In this paper, we present ''Streaming Stochastic Variational Bayes" (SSVB)—a novel online approximation inference framework for data streaming to address the aforementioned shortcomings of the current state-of-the-art. SSVB adjusts its posterior variance duly without any user-specified hyperparameters while efficiently accommodating the drifting patterns to the posteriors. Moreover, SSVB can be easily adopted by practitioners for a wide range of models (i.e. simple regression models to complex hierarchical models) with little additional analysis. We appraised the performance of SSVB against Population Variational Inference (PVI), Stochastic Variational Inference (SVI) and Black-box Streaming Variational Bayes (BB-SVB) using two non-conjugate probabilistic models; multinomial logistic regression and linear mixed effect model. Furthermore, we also discuss the significant accuracy gain with SSVB based inference against conventional online learning models for each task.