Implementation of Bayesian Model Averaging Method to Calibrate Monthly Rainfall Ensemble Prediction over Java Island

Bayesian Model Averaging (BMA) is a statistical post-processing method for producing probabilistic forecasts from an ensemble prediction in the form of predictive Probability Density Function (PDF). BMA is commonly used to calibrate Ensemble Prediction System (EPS) in a shorter-range forecast. Here, we applied the BMA for a longer forecast at a seasonal interval. This study aimed to develop the implementation of the BMA method to calibrate the seasonal forecast (long range) of monthly rainfall from the RAW output of the EPS European Center for Medium-Range Weather Forecasts (ECMWF) system 4 model (ECS4). This model was calibrated with observational data from 26 stations over Java Island in 1981-2018. BMA predictive PDF was generated with a gamma distribution, which was obtained based on two training schemes, namely sequential (BMA-JTS) and conditional (BMA-JTC) training windows. Generally, both of BMA-JTS and BMA-JTC were able to produce better distribution characteristics of ensemble prediction than that of RAW model ECS4. Both BMA methods showed a good performance as indicated by a high accuracy, small bias, and small uncertainty to the observed rainfall. Our findings revealed that BMA-JTC was able to improve the quality of probabilistic forecasts of below and above normal events. The improvement was shown in most stations over Java Island, in which the model was a good skill forecast based on Brier Skill Score (BSS)

Stochastic and Deterministic Dynamic Model of Dengue Transmission Based on Dengue Incidence Data and Climate Factors in Bandung City

Indonesia, a country in the tropics, is an area of distribution and an endemic area of dengue. The death rate caused by dengue is relatively high In Indonesia. Therefore, the health authority must prioritize preventing and controlling dengue disease for a long-term policy. This study proposes a method based on dynamic climate variables in estimating the proportion of infected human and infected mosquito. We focus on the dengue case in Bandung city, one of the big cities in Indonesia, which is classified as endemic dengue. We applied the Poisson regression method involving dynamic climate variables to estimate the average number of infected human population. We then use these estimation results as the basis for approximating the proportion of infected human and mosquito populations using a deterministic and stochastic model approach. Effective reproduction number is also obtained here. The simulation results show that the stochastic model looks better in capturing dengue incidence data than the deterministic model. Therefore, dengue transmission can be reduced by controlling the abundance of mosquito populations, considering climate conditions and the historical number of infected human

Quantitative Measure to Differentiate Wicket Spike from Interictal Epileptiform Discharges

A number of benign EEG patterns are often misinterpreted as interictal epileptiform discharges (IEDs) because of their epileptiform appearances, one of them is wicket spike. Differentiating wicket spike from IEDs may help in preventing epilepsy misdiagnosis. The temporal location of IEDs and wicket spike were chosen from 143 EEG recordings. Amplitude, duration and angles were measured from the wave triangles and were used as the variables. In this study, linear discriminant analysis is used to create the formula to differentiate wicket spike from IEDs consisting spike and sharp waves. We obtained a formula with excellent accuracy. This study emphasizes the need for objective criteria to distinguish wicket spike from IEDs to avoid misreading of the EEG and misdiagnosis of epilepsy

Numerical methods for solving linear ill-posed problems

Doctor of PhilosophyDepartment of MathematicsAlexander G. RammA new method, the Dynamical Systems Method (DSM), justified recently, is applied to solving ill-conditioned linear algebraic system (ICLAS). The DSM gives a new approach to solving a wide class of ill-posed problems. In Chapter 1 a new iterative scheme for solving ICLAS is proposed. This iterative scheme is based on the DSM solution. An a posteriori stopping rules for the proposed method is justified. We also gives an a posteriori stopping rule for a modified iterative scheme developed in A.G.Ramm, JMAA,330 (2007),1338-1346, and proves convergence of the solution obtained by the iterative scheme. In Chapter 2 we give a convergence analysis of the following iterative scheme: u[subscript]n[superscript]delta=q u[subscript](n-1)[superscript]delta+(1-q)T[subscript](a[subscript]n)[superscript](-1) K[superscript]*f[subscript]delta, u[subscript]0[superscript]delta=0, where T:=K[superscript]* K, T[subscript]a :=T+aI, q in the interval (0,1),\quad a[subscript]n := alpha[subscript]0 q[superscript]n, alpha_0>0, with finite-dimensional approximations of T and K[superscript]* for solving stably Fredholm integral equations of the first kind with noisy data. In Chapter 3 a new method for inverting the Laplace transform from the real axis is formulated. This method is based on a quadrature formula. We assume that the unknown function f(t) is continuous with (known) compact support. An adaptive iterative method and an adaptive stopping rule, which yield the convergence of the approximate solution to f(t), are proposed in this chapter

Cyber Insurance Ratemaking: A Graph Mining Approach

Cyber insurance ratemaking (CIRM) is a procedure used to set rates (or prices) for cyber insurance products provided by insurance companies. Rate estimation is a critical issue for cyber insurance products. This problem arises because of the unavailability of actuarial data and the uncertainty of normative standards of cyber risk. Most cyber risk analyses do not consider the connection between Information Communication and Technology (ICT) sources. Recently, a cyber risk model was developed that considered the network structure. However, the analysis of this model remains limited to an unweighted network. To address this issue, we propose using a graph mining approach (GMA) to CIRM, which can be applied to obtain fair and competitive prices based on weighted network characteristics. This study differs from previous studies in that it adds the GMA to CIRM and uses communication models to explain the frequency of communications as weights in the network. We used the heterogeneous generalized susceptible-infectious-susceptible model to accommodate different infection rates. Our approach adds up to the existing method because it considers the communication frequency and GMA in CIRM. This approach results in heterogeneous premiums. Additionally, GMA can choose more active communications to reflect high communications contribution in the premiums or rates. This contribution is not found when the infection rates are the same. Based on our experimental results, it is apparent that this method can produce more reasonable and competitive prices than other methods. The prices obtained with GMA and communication factors are lower than those obtained without GMA and communication factors

Adjusting cyber insurance premiums based on frequency in a communication network

This study aims to compare cyber insurance premiums with and without the frequency in a communication network effect. As a cybersecurity factor, the frequency in a communication network is influencing the speed of cyberattack transmission. It means that a network or a high activity node is more vulnerable than a network with low activity. Traditionally, cyber insurance pricing considers historical data to set premiums or rates. Conversely, the network security level can evaluate using the Monte Carlo simulation based on the epidemic model. This simulation requires spreading parameters, such as infection rate, recovery rate, and self-infection rate. Our idea is to modify the infection rate as a function of the frequency in a communication network. To generate the data, the node-based model uses probability distributions for the communication mechanism. It adopts the co-purchase network formation in market basket analysis for build weighted edges and nodes Simulations are used to compare the initial infection rate and the modified infection rate. In this paper, we considered prism and Petersen graph topology as case studies. The relative difference is a metric to compare the significance of premium adjustment. The results show that the premium for a node with a low level in a communication network can reach 28.28% lower than the initial premium. For a network, the premium can reach 20.99% lower than the initial network premium. Based on these results, insurance companies can adjust cyber insurance premiums based on computer usage to offer a more appropriate price

Optimization in Item Delivery as Risk Management: Multinomial Case Using the New Method of Statistical Inference for Online Decision

Online activity increasing spreads with the power of technological development. Many studies reported the impact of online activities on decision making. From the statistical perspective, decision making is related to statistical inference. In this regard, it is interesting to propose a new method of statistical inference for online decisions. This method is built by the logarithm distribution of the likelihood function, which allows us to determine statistics using the normal statistical test approach iteratively. It means that the inference can be made in an online way every time new data arrive. Compared to classical methods (commonly, chi-squared), the advantage of this method is that it allows us to make decisions without storing large data. In particular, the novelty of this research is expressed in the algorithm, theorem, and corollary for the statistical inference procedure. In detail, this paper’s simulation discusses online statistical tests for multinomial cases and applies them to transportation data for item delivery, namely traffic density. Changes in traffic density resulted in changes to the strategy of item delivery. The goal is to obtain a minimum delivery time for the risk of losses