Judul: Geoinformatika pada Kasus Area Kecil dan Penerapannya untuk Mendeteksi Kantong-kantong Kemiskinan di Jember
Abstrak: Scan statistic is a method in Geinformatics considering spatial unsure to detect high or low potential area geographically and examine an area proportion parameter compare with others proportion statistically. This method detects extreme area (maximum or minimum) called hotspot. Hotspot means something unusual, anomalies, or critical condition area. Scan statistic is used to detect and evaluate area called Most Likely Cluster (MLC). It needs complete information about detected area with large sample size, while survey usually uses small sample size. One solution to overcome small sample size is by increasing sample size, but it is cost, time, and energy consuming. On the other side, there is a developing method in statistics to use survey data with small sample size, i.e. Small Area Estimation (SAE). Although this method is not used to compare among area, the biggest benefit from SAE is that it can be used to estimate area parameter complete, both surveyed and un-surveyed area. With complete estimation data, scan statistic can be used to detect hotspot or Most Likely Cluster (MLC). Based on the need of complete estimator value, SAE application is necessary in scan statistic. Quality of SAE application result in scan statistic depends on (i) sample size of hotspot, (ii) SAE estimation quality of model with some auxiliary variables and estimation methods, so SAE estimation methods need to be examined. SAE quality in handling small sample size case and scan statistic have been studied separately. This dissertation studies scan statistic in small sample size case, as an application of SAE on scan statistic. Estimation result gained through survey is called as Direct Estimate (DE), but usually with low accuracy and precision. There is a direct estimation proportion in MLC problem in Geoinformatics that can be replaced by estimation through SAE. This study’s purposes are to replace DE role with SAE estimation in Geoinformatics problem (in search for hotspot), to do cluster detection through scan statistic using small sample size by using SAE model into scan statistic, and use small area based Geoinformatics to detect poverty area pockets based on surveyed data and estimation of all village in Jember, East Java. This study is an application of SAE based scan statistic that is examined theoretically, by simulation, and by application on real data. SAE application on scan statistic can handle problems in detecting highly potential and statistically significant by using only small sample size. Simulation and application examination on real data are evaluated using statistic properties. Analysis continues with evaluation of correct classification on result gained. 100% correct classification through simulation examination on surveyed area is gained using Bayes and non-Bayes SAE. Bayes methods used in this study are spatial Hierarchical Bayes (HB) and non-spatial method, while non-Bayes methods used are EBLUP and SEBLUP. In un-surveyed area (large area), MLC will be bigger. HB1 (spatial correlation weighted) with hotspot proportion 0.95 is capable to estimate 80.97% correctly, while HB2 (nearest neighbor) is 75.62%. On the other side, EBLUP is only capable to estimate 65.99% of correct classification. From estimator property side, both methods (HB and EBLUP) have stable on result
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Judul: Metode Scan Statistic Model Binomial dengan Pendekatan Statistik Area Kecil
Abstrak: Metode scan statistic membutuhkan data populasi untuk mengidentifikasi area yang signifikan secara statistik dengan resiko tinggi terhadap suatu kasus tertentu. Namun demikian, dalam aplikasinya data populasi jarang tersedia dan hanya data contoh yang tersedia, sehingga muncul pertanyaan apakah metode scan statistic memiliki akurasi yang tinggi jika menggunakan data contoh. Penggabungan metode pendugaan area kecil (small area estimation, SAE) pada scan statistic diharapkan mampu meningkatkan akurasi pendugaan proporsi dan akurasi hotspot berdasarkan data contoh. Penerapan metode pendugaan area kecil pada scan statistic tersebut, terkait dengan pendugaan proporsi pada statistik uji kemungkinan maksimum dalam metode scan statistic. SAE dilakukan melalui teknik empirical Bayes (EB) terhadap model Beta-Binomial. Dalam karya ilmiah ini dilakukan simulasi dengan menetapkan proporsi ekstrim pada area tertentu sebesar 0.5, 0.7 dan 0.9. Hasil menunjukkan bahwa ketika proporsi ekstrim ditetapkan di suatu area sebesar 0.5, ternyata akurasi yang diperoleh belum memuaskan sebesar (42.7%). Jika proporsi ekstrim di suatu area ditingkatkan menjadi 0.7 dan 0.9, akurasi yang diperoleh dalam mendeteksi hotspot sudah cukup memuaskan walaupun ukuran contohnya kecil. Penerapan penduga langsung pada scan statistic memiliki akurasi yang sama dengan penduga tidak langsung untuk mendeteksi hotspot. Namun demikian, penduga tidak langsung dapat dikatakan lebih baik dibandingkan penduga langsung dalam hal pendugaan proporsi, karena telah mampu mengurangi galat dan bias penduga proporsi.
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Judul: Korpus Luteum Persisten pada Sapi serta Beberapa Aspek Penanggulangannya
Abstrak: Korpus luteum pada ovarium terbentuk pada hari ke lima atau ke enam setelah ovulasi terjadi. Bila pada uteru tidak terjadi kebuntingan, korpus luteun dinonaktifkan oleh hormon luteolitik yaitu prostaglandin yang dihasilkan dinding uterus. Jika pada uterus terjadi kebuntingan, korpus luteum tetap bertahan pada ovarium dan berfungsi secara normal, disebut korpus luteum graviditatum. Korpus luteum graviditatum aktif pada sapi betina (erti) selama total waktu 320 hari dalan satu tahun.
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