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:: Abstract List ::
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Probability and Stochastic Analysis |
ABS-121 |
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The Minimum Number of Observations in Space Time Autoregressive Modeling
Utriweni Mukhaiyar
Statistics Research Division, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia
Abstract
In accordance with the Weak Law of Large Number that the larger the size of observations, the closer the value of the parameter estimator its true value. But taking a large sample size is not an effective and efficient solution in modeling. This also applies to time series and space time modeling, A minimum reference value for the number of observations time is required, in order to obtain the appropriate model which is closer to the real model. In this research, the minimum number of observations is determined through the Monte-Carlo simulation for the Generalized Space Time Autoregressive (GSTAR) model. The criteria used are that the difference between the estimator and the true parameter for all observed locations are smaller than a small real value. It is complying with the principle of convergence in probability, that is the greater sample size then the smaller the errors. It is obtained that the smaller the time order of GSTAR model, the smaller the number of observations time is required. The closer the process to be a nonstationary, the longer the amount of observations time.
Keywords: minimum number of time, GSTAR model, stationary, error, convergence
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| Corresponding Author (Utriweni Mukhaiyar)
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| 122 |
Probability and Stochastic Analysis |
ABS-127 |
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Probabilistic Support Vector Regression for Histogram-Valued Data: A Case Study on Peatland Data
Fathimah Al-Ma^shumah, Kurnia Novita Sari
Institut Teknologi Bandung, Institut Teknologi Bandung,
Abstract
In geostatistics, spatial distribution data of environmental variables are often represented through histograms, which depict the relative frequencies of values within specified bins. This study investigates regression methods for histogram-valued data by extending the probabilistic approach of Support Vector Machine (SVM) regression. The primary focus is on applying this methodology to carbon distribution data in peatlands, where histograms illustrate variations in carbon content across different soil depths.
The study addresses both linear and nonlinear regression problems within the context of histogram data and conducts a simulation study to assess the performance of the proposed methodology. Subsequently, the methodology is applied to two real datasets: first, carbon distribution data from tropical peatlands, demonstrating changes in carbon content at various soil depths- and second, monthly precipitation histogram data from multiple meteorological stations to evaluate the impact of rainfall on soil variability.
The results indicate that the histogram-based SVM regression model provides accurate estimates for carbon distribution in peatlands and varying precipitation patterns. These findings contribute to improved peatland management strategies and offer insights into rainfall patterns affecting carbon distribution, which are crucial for climate change studies and environmental conservation.
Keywords: Probabilistic Support Vector Machine, Regression, Histogram-valued Data, Peatland
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| Corresponding Author (Fathimah Al-Mashumah)
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| 123 |
Probability and Stochastic Analysis |
ABS-130 |
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The Linear Combination of ARIMA Models in Constructing The Areal Rainfall Using Thiessen Polygon Weighted Method
Utriweni Mukhaiyar1, Muhammmad Rozzaq Hamidi2 , Elizabet Sri Rezeki3 , Naila Ratu Dianti4, Abdan Maulana Rohat5
1 Statistics Research Division, Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology, Bandung, Indonesia
2,5 Master Program in Actuarial Science, Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology, Bandung, Indonesia
3,4 Master Program in Mathematics Science, Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology, Bandung, Indonesia
Abstract
The construction of areal rainfall is crucial aspects in water resource management and disaster risk mitigation. The areal rainfall can be constructed as the linear combination of the actual rainfall in each stasion in the respected area. Thus, the rainfall modeling also be crucial. This research explores the integration of ARIMA models for temporal rainfall analysis and Thiessen polygon method for spatial analysis in constructing the areal rainfall. The ARIMA was used to model the monthly cumulative rainfall of eight rain gauge stations in Tasikmalaya area. The areal rainfall was subsequently constructed using the Thiessen polygon method based on actual rainfall, taking into account the spatial heterogeneity of the observation stations. It is obtained that the AR(1) is the appropriate model for the actual rainfall in each rain gauge station. Further analysis showed that a linear combination of AR(1) model from the rain gauge stations resulted in a consistent AR(1) model for areal rainfall. This research successfully provided practical and analytical evidence that a linear combinations of multiple AR(1) models result in a consistent AR(1) model.
Keywords: Rainfall Modeling, Areal Rainfall, ARIMA, Thiessen Polygon, Temporal and Spatial Analysis.
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| Corresponding Author (Muhammad Rozzaq Hamidi)
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