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"ABSTRAKPresenting seismic data in probability form is common practice in order to assess the uncertainty in hydrocarbon prospecting. It gives interpreters the ability to measure how sure they are about prospect they dealing with by looking at most probable value. In another side pre-stack data is now commonly available; it changes the paradigm about seismic inversion from just post-stack inversion turn into pre-stack inversion. The reason is obvious, by inverting pre-stack data will allow interpreter to obtain not only lithology information but fluid as well.The Bayes’ Rule is extension of conditional probability, it has been utilizes in many disciplines such us remote sensing, broadcasting, marketing and medical science to support in decision making. Bayes’ Rule is used to revise a probability value based on additional information that is later obtained. The same concept can also be applied to help decision making in hydrocarbon prospect evaluation where the output of pre-stack inversion can be transformed to probability volume supervised by well log data.This study uses P-Impedance and VP/VS as inputs because their combination is good indicator of lithology and hydrocarbon. Using Menampilkan data seismic dalam bentuk probabilitas merupakan cara yang umum dilakukan untuk mengikutsertakan informasi ketidak-pastian dari pekerjaan pemetaan prospek hidrokarbon. Hal tersebut memberikan interpreter peluang untuk mengukur seberapa yakin mereka terhadap prospek yang sudah dibuat dengan memanfaatkan informasi nilai “most-probable”. Pada sisi lain, ketersediaan pre-stack data sudah sangat umum dijumpai sehingga hal ini merubah cara pandang terhadap inversi seismic yang semula hanya dilakukan terhadap data post-stack menjadi inversi pre-stack. Hal tersebut memang beralasan karena dengan inversi pre-stack, interpreter tidak hanya dimungkinkan mendapatkan informasi litologi namun juga informasi tentang fluida.Aturan Bayes adalah merupakan bentuk lain dari probabilitas terkondisi, aturan ini telah banyak dimanfaatkan oleh berbagai disiplin ilmu seperti penginderaan jauh, peramalan cuaca, pemasaran dan ilmu medis untuk membantu dalam meminimalkan resiko saat pengambilan keputusan. Hal yang sama juga bias kita terapkan pada bidang ilmu bumi dimana keluaran dari proses inversi pre-stack dapat ditransformasi menjadi bentuk volum probabilitas dengan supervisi data sumuran.Penelitian ini menggunakan P-impedance dan VP/VS sebagai input karena kombinasi keduanya merupakan indikator yang baik untuk memisahkan litologi maupun hidrokarbon. Dengan menggunakan supervisi dari data sumuran kedua volume tersebut kemudian di transformasi menjadi bentuk kelas most-probable: (1) shale, (2) wet sand, (3) compacted sand, dan (4) hydrocarbon sand.

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ABSTRACTPresenting seismic data in probability form is common practice in order to assess the uncertainty in hydrocarbon prospecting. It gives interpreters the ability to measure how sure they are about prospect they dealing with by looking at most probable value. In another side pre-stack data is now commonly available; it changes the paradigm about seismic inversion from just post-stack inversion turn into pre-stack inversion. The reason is obvious, by inverting pre-stack data will allow interpreter to obtain not only lithology information but fluid as well.The Bayes’ Rule is extension of conditional probability, it has been utilizes in many disciplines such us remote sensing, broadcasting, marketing and medical science to support in decision making. Bayes’ Rule is used to revise a probability value based on additional information that is later obtained. The same concept can also be applied to help decision making in hydrocarbon prospect evaluation where the output of pre-stack inversion can be transformed to probability volume supervised by well log data.This study uses P-Impedance and VP/VS as inputs because their combination is good indicator of lithology and hydrocarbon. Using training set from well log the volumes then transformed into four most probable classes: (1) shale, (2) wet sand, (3) compacted sand, and (4) hydrocarbon sand."

"[ABSTRAKMenampilkan data seismic dalam bentuk probabilitas merupakan cara yang umum dilakukan untuk mengikutsertakan informasi ketidak-pastian dari pekerjaan pemetaan prospek hidrokarbon. Hal tersebut memberikan interpreter peluang untuk mengukur seberapa yakin mereka terhadap prospek yang sudah dibuat dengan memanfaatkan informasi nilai ?most-probable?. Pada sisi lain, ketersediaan pre-stack data sudah sangat umum dijumpai sehingga hal ini merubah cara pandang terhadap inversi seismic yang semula hanya dilakukan terhadap data post-stack menjadi inversi pre-stack. Hal tersebut memang beralasan karena dengan inversi pre-stack, interpreter tidak hanya dimungkinkan mendapatkan informasi litologi namun juga informasi tentang fluida.Aturan Bayes adalah merupakan bentuk lain dari probabilitas terkondisi, aturan ini telah banyak dimanfaatkan oleh berbagai disiplin ilmu seperti penginderaan jauh, peramalan cuaca, pemasaran dan ilmu medis untuk membantu dalam meminimalkan resiko saat pengambilan keputusan. Hal yang sama juga bias kita terapkan pada bidang ilmu bumi dimana keluaran dari proses inversi pre-stack dapat ditransformasi menjadi bentuk volum probabilitas dengan supervisi data sumuran.Penelitian ini menggunakan P-impedance dan VP/VS sebagai input karena kombinasi keduanya merupakan indikator yang baik untuk memisahkan litologi maupun hidrokarbon. Dengan menggunakan supervisi dari data sumuran kedua volume tersebut kemudian di transformasi menjadi bentuk kelas most-probable: (1) shale, (2) wet sand, (3) compacted sand, dan (4) hydrocarbon sand.

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ABSTRACTPresenting seismic data in probability form is common practice in order to assess the uncertainty in hydrocarbon prospecting. It gives interpreters the ability to measure how sure they are about prospect they dealing with by looking at most probable value. In another side pre-stack data is now commonly available; it changes the paradigm about seismic inversion from just post-stack inversion turn into pre-stack inversion. The reason is obvious, by inverting pre-stack data will allow interpreter to obtain not only lithology information but fluid as well.The Bayes? Rule is extension of conditional probability, it has been utilizes in many disciplines such us remote sensing, broadcasting, marketing and medical science to support in decision making. Bayes? Rule is used to revise a probability value based on additional information that is later obtained. The same concept can also be applied to help decision making in hydrocarbon prospect evaluation where the output of pre-stack inversion can be transformed to probability volume supervised by well log data.This study uses P-Impedance and VP/VS as inputs because their combination is good indicator of lithology and hydrocarbon. Using training set from well log the volumes then transformed into four most probable classes: (1) shale, (2) wet sand, (3) compacted sand, and (4) hydrocarbon sand.;Presenting seismic data in probability form is common practice in order to assess the uncertainty in hydrocarbon prospecting. It gives interpreters the ability to measure how sure they are about prospect they dealing with by looking at most probable value. In another side pre-stack data is now commonly available; it changes the paradigm about seismic inversion from just post-stack inversion turn into pre-stack inversion. The reason is obvious, by inverting pre-stack data will allow interpreter to obtain not only lithology information but fluid as well.The Bayes? Rule is extension of conditional probability, it has been utilizes in many disciplines such us remote sensing, broadcasting, marketing and medical science to support in decision making. Bayes? Rule is used to revise a probability value based on additional information that is later obtained. The same concept can also be applied to help decision making in hydrocarbon prospect evaluation where the output of pre-stack inversion can be transformed to probability volume supervised by well log data.This study uses P-Impedance and VP/VS as inputs because their combination is good indicator of lithology and hydrocarbon. Using training set from well log the volumes then transformed into four most probable classes: (1) shale, (2) wet sand, (3) compacted sand, and (4) hydrocarbon sand.;Presenting seismic data in probability form is common practice in order to assess the uncertainty in hydrocarbon prospecting. It gives interpreters the ability to measure how sure they are about prospect they dealing with by looking at most probable value. In another side pre-stack data is now commonly available; it changes the paradigm about seismic inversion from just post-stack inversion turn into pre-stack inversion. The reason is obvious, by inverting pre-stack data will allow interpreter to obtain not only lithology information but fluid as well.The Bayes? Rule is extension of conditional probability, it has been utilizes in many disciplines such us remote sensing, broadcasting, marketing and medical science to support in decision making. Bayes? Rule is used to revise a probability value based on additional information that is later obtained. The same concept can also be applied to help decision making in hydrocarbon prospect evaluation where the output of pre-stack inversion can be transformed to probability volume supervised by well log data.This study uses P-Impedance and VP/VS as inputs because their combination is good indicator of lithology and hydrocarbon. Using training set from well log the volumes then transformed into four most probable classes: (1) shale, (2) wet sand, (3) compacted sand, and (4) hydrocarbon sand.;Presenting seismic data in probability form is common practice in order to assess the uncertainty in hydrocarbon prospecting. It gives interpreters the ability to measure how sure they are about prospect they dealing with by looking at most probable value. In another side pre-stack data is now commonly available; it changes the paradigm about seismic inversion from just post-stack inversion turn into pre-stack inversion. The reason is obvious, by inverting pre-stack data will allow interpreter to obtain not only lithology information but fluid as well.The Bayes? Rule is extension of conditional probability, it has been utilizes in many disciplines such us remote sensing, broadcasting, marketing and medical science to support in decision making. Bayes? Rule is used to revise a probability value based on additional information that is later obtained. The same concept can also be applied to help decision making in hydrocarbon prospect evaluation where the output of pre-stack inversion can be transformed to probability volume supervised by well log data.This study uses P-Impedance and VP/VS as inputs because their combination is good indicator of lithology and hydrocarbon. Using training set from well log the volumes then transformed into four most probable classes: (1) shale, (2) wet sand, (3) compacted sand, and (4) hydrocarbon sand., Presenting seismic data in probability form is common practice in order to assess the uncertainty in hydrocarbon prospecting. It gives interpreters the ability to measure how sure they are about prospect they dealing with by looking at most probable value. In another side pre-stack data is now commonly available; it changes the paradigm about seismic inversion from just post-stack inversion turn into pre-stack inversion. The reason is obvious, by inverting pre-stack data will allow interpreter to obtain not only lithology information but fluid as well.The Bayes’ Rule is extension of conditional probability, it has been utilizes in many disciplines such us remote sensing, broadcasting, marketing and medical science to support in decision making. Bayes’ Rule is used to revise a probability value based on additional information that is later obtained. The same concept can also be applied to help decision making in hydrocarbon prospect evaluation where the output of pre-stack inversion can be transformed to probability volume supervised by well log data.This study uses P-Impedance and VP/VS as inputs because their combination is good indicator of lithology and hydrocarbon. Using training set from well log the volumes then transformed into four most probable classes: (1) shale, (2) wet sand, (3) compacted sand, and (4) hydrocarbon sand.]"

"ABSTRAKMenampilkan data seismic dalam bentuk probabilitas merupakan cara yang umum dilakukan untuk mengikutsertakan informasi ketidak pastian dari pekerjaan pemetaan prospek hidrokarbon Hal tersebut memberikan interpreter peluang untuk mengukur seberapa yakin mereka terhadap prospek yang sudah dibuat dengan memanfaatkan informasi nilai ldquo most probable rdquo Pada sisi lain ketersediaan pre stack data sudah sangat umum dijumpai sehingga hal ini merubah cara pandang terhadap inversi seismic yang semula hanya dilakukan terhadap data post stack menjadi inversi pre stack Hal tersebut memang beralasan karena dengan inversi pre stack interpreter tidak hanya dimungkinkan mendapatkan informasi litologi namun juga informasi tentang fluida Aturan Bayes adalah merupakan bentuk lain dari probabilitas terkondisi aturan ini telah banyak dimanfaatkan oleh berbagai disiplin ilmu seperti penginderaan jauh peramalan cuaca pemasaran dan ilmu medis untuk membantu dalam meminimalkan resiko saat pengambilan keputusan Hal yang sama juga bias kita terapkan pada bidang ilmu bumi dimana keluaran dari proses inversi pre stack dapat ditransformasi menjadi bentuk volum probabilitas dengan supervisi data sumuran Penelitian ini menggunakan Acoustic impedance dan VP VS sebagai input karena kombinasi keduanya merupakan indikator yang baik untuk memisahkan litologi maupun hidrokarbon Dengan menggunakan supervisi dari data sumuran kedua volume tersebut kemudian di transformasi menjadi bentuk kelas most probable 1 shale 2 wet sand 3 compacted sand dan 4 hydrocarbon sand

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ABSTRACTPresenting seismic data in probability form is common practice in order to assess the uncertainty in hydrocarbon prospecting. It gives interpreters the ability to measure how sure they are about prospect they dealing with by looking at most probable value. In another side pre-stack data is now commonly available; it changes the paradigm about seismic inversion from just post-stack inversion turn into pre-stack inversion. The reason is obvious, by inverting pre-stack data will allow interpreter to obtain not only lithology information but fluid as well.The Bayes’ Rule is extension of conditional probability, it has been utilizes in many disciplines such us remote sensing, broadcasting, marketing and medical science to support in decision making. Bayes’ Rule is used to revise a probability value based on additional information that is later obtained. The same concept can also be applied to help decision making in hydrocarbon prospect evaluation where the output of pre-stack inversion can be transformed to probability volume supervised by well log data.This study uses P-Impedance and VP/VS as inputs because their combination is good indicator of lithology and hydrocarbon. Using training set from well log the volumes then transformed into four most probable classes: (1) shale, (2) wet sand, (3) compacted sand, and (4) hydrocarbon sand."

"ABSTRAKTugas akhir ini membahas mengenai metode Bayes dalam penaksiran parameter skala dari distribusi Nakagami menggunakan dua fungsi loss, yaitu Square Error Loss Function dan Precautionary Loss Function. Pada tugas akhir ini juga akan dicari Resiko Posterior dari masing-masing taksiran. Sebagai pembanding untuk taksiran dengan menggunakan metode Bayes, akan dicari juga taksiran parameter skala dari distribusi Nakagami menggunakan metode Maksimum Likelihood. Sebagai ilustrasi, akan dilakukan simulasi dengan data yang berdistribusi Nakagami ( ). Setelah taksiran telah didapatkan, akan dihitung Mean Square Error dari masing-masing taksiran. Hal tersebut dilakukan untuk mengetahui seberapa baik taksiran yang dihasilkan oleh metode Bayes.

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ABSTRACT

This paper discusses about Bayesian Method in estimating the scale parameter of Nakagami Distribution using two loss function, that is Square Error Loss Function and Precautionary Loss Function. This paper will also find the posterior risk from each of the estimator. As the comparison of the Bayesian estimate, the estimator using Maximum Likelihood method will also be considered. For the illustration, simulation with Nakagami distributed data ( ) will be performed. Once the estimate have been obtained, Mean Square Error on each estimate will be calculated. This is done to measure the performance of the estimate produced by Bayesian method."

"Ketika mengamati suatu adverse event, subjek penelitian dapat keluar di tengah pengamatan karena adanya penyebab-penyebab lain yang dinamakan sebagai competing event. Misalkan dalam sebuah studi observasi, adverse event yang ingin diamati adalah kematian karena kanker otak. Namun, seperti yang diketahui, kematian individu yang diamati boleh jadi disebabkan oleh hal lain, seperti kecelakaan, atau penyakit lain selain kanker. Oleh karena itu, competing event perlu dipertimbangkan juga agar dapat ditentukan probabilitas adverse event yang lebih akurat. Terdapat beberapa estimator untuk suatu data survival yang dapat digunakan untuk menaksir probabilitas adverse event, diantaranya estimator Nelson-Aalen dan estimator Kaplan-Meier. Akan tetapi, kedua estimator ini masih memiliki kekurangan dimana probabilitas adverse event yang diukur dengan kedua estimator tersebut mengalami over-estimation dikarenakan tidak mempertimbangkan competing event. Berdasarkan penelusuran literatur, terdapat sebuah estimator lain yang diusulkan oleh Aalen-Johansen, yaitu estimator Aalen-Johansen. Estimator ini mampu memperhitungkan competing event dalam menaksir probabilitas adverse event dengan menggunakan multi-state model dalam perhitungannya. Pada tugas akhir ini akan dibahas penurunan estimator Aalen Johansen beserta penerapan estimator tersebut ke dalam beberapa dataset. Hasil estimasi yang diperoleh kemudian dibandingkan dengan hasil estimasi menggunakan estimator Kaplan-Meier. Didapatkan bahwa hasil probabilitas menggunakan estimator Aalen-Johansen lebih tepat.

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Upon observing an adverse event, subject of research may walk out of the observation because of other events, called as competing events. For example, a brain cancer death study. We want to observe this adverse event, specifically death because of brain cancer. However, as we know, death has many causes, accidents, or even other diseases except brain cancer. Which is why, competing events need to be considered prior calculating an adverse event probability, to get a more accurate and reliable result. There are some estimators for survival data that can be used to estimate adverse event probability, such as Nelson-Aalen estimator and Kaplan-Meier estimator. However, both estimators have a weakness, in which these estimators do not consider competing events during estimating an adverse event, resulting in over estimation. Based on literature research, there is another estimator that is proposed by Aalen Johansen, called Aalen-Johansen Estimator. This estimator can put competing event into account upon estimating an adverse event probability by applying multi-state model. In this thesis, Aalen-Johansen formula will be outlined, explained, and applied in several datasets. Results obtained from the simulation will be compared with the results from Kaplan-Meier estimator. The results show that probability that is estimated by Aalen-Johansen estimator is more accurate to the real data on field."

"Kinerja mahasiswa adalah bagian penting dari suatu perguruan tinggi. Hal ini dikarenakan salah satu kriteria  perguruan tinggi yang berkualitas didasarkan pada  prestasi akademik yang baik. Tahun pertama perkuliahan adalah periode mahasiswa untuk meletakkan dasar atau fondasi yang selanjutnya akan mempengaruhi keberhasilan akademik karena tahun pertama memainkan peran penting dalam membentuk sikap dan kinerja siswa di tahun-tahun berikutnya. Pada Penelitian ini, pendekatan Semi-supevised Learning digunakan dalam mengklasifikasi kinerja mahasiswa tahun pertama di Departemen Matematika, Universitas Indonesia. Kinerja Mahasiswa dibagi menjadi dua kategori, yaitu sedang dan tinggi. Sampel pada penelitian ini adalah 140 mahasiswa tahun pertama dengan menggunakan 27 fitur. Ada dua proses yang digunakan, yaitu proses clustering dan klasifiksi. Pada proses clustering, mahasiswa dibagi menjadi tiga cluster/kelompok menggunakan K-Means Clustering. Sedangkan dalam proses klasifikasinya menggunakan Naïve Bayes Classifier. Kinerja algoritma yang diusulkan menghasilkan nilai akurasi 96.67% dan sensitifitas 94.44%.

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Students performance is an essential part of a higher learning institution because one of the criteria for a high-quality university is based on its excellent record of academic achievements. The first- year of the lecture is the student period in laying the foundation that will affect academic success because first-year plays an important role in shaping the attitudes and performance of students in the following years. In this study, a semi-supervised learning approach is used to classify the performance of first-year students in the Department of Mathematics, Universitas Indonesia. Student performance will be divided into two categories, namely medium and high. The sample in this study consist of 140 first-year students with 27 features. There are two processes used i.e. clustering and the classification process. In the clustering process, the data is divided into three clusters using K-Means Clustering and the Naïve Bayes Classifier is chosen to classify it. The performance of the proposed algorithms is stated by accuracy and sensitivity value i.e. 96.67% and 94.44% respectively."

"Dalam pengujian hipotesis berganda, dilakukan pengujian lebih darisatu hipotesis, yang diuji pada satu waktu secara simultan. Apabila masingmasingpengujian dalam suatu family hipotesis mempunyai probabilitasmelakukan kesalahan tipe 1, maka secara keseluruhan pada pengujianhipotesis berganda akan terjadi penggandaan probabilitas kesalahan tipe 1.Probabilitas melakukan kesalahan tipe1 pada pengujian hipotesis bergandaakan semakin membesar seiring dengan meningkatnya jumlah pengujian.Untuk mengatasi hal itu, ada beberapa cara untuk mengukur kesalahan tipe1dalam family hipotesis diantaranya Family Wise Error Rate (FWER), FalseDiscovery Rate (FDR), dan positif False Discovery Rate (pFDR). Untukmengontrol kesalahan tersebut, diperlukan suatu metode sedemikiansehingga probabilitas kesalahan tipe 1 keseluruhan ≤ α. Pada tugas akhir ini,akan dibahas metode - metode pengujian untuk hipotesis berganda yaitumetode Bonferroni yang merupakan salah satu metode untuk FWER, metodeBenjamin-Hochberg untuk FDR yang memperbaiki Metode Bonferroni danmetode Storey untuk pFDR yang memperbaiki Metode Benjamin-Hochberg."