FORUM STATISTIKA DAN KOMPUTASI
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Based on the six indicators provided by the State Ministry for Acceleration Development Backward Regions, the backward regions were clustered into 4 groups: fairly backward region, backward region, highly backward region, and severely backward region. This clustering used weighted average method. The weakness of this method was that the weight determination on each indicator was decided without distinct reference. Besides, there are many outlier in KNDPT data. The objectives of this research are to study the non-hierarchy cluster methods, that is C-Means and Fuzzy C-Means. Both methods have difference on membership value and weighted membership value. The result of this research showed that Fuzzy C-Means was more robust than C-Means.
Get PDFBased on the six indicators provided by the State Ministry for Acceleration Development Backward Regions, the backward regions were clustered into 4 groups: fairly backward region, backward region, highly backward region, and severely backward region. This clustering used weighted average method. The weakness of this method was that the weight determination on each indicator was decided without distinct reference. Besides, there are many outlier in KNDPT data. The objectives of this research are to study the non-hierarchy cluster methods, that is C-Means and Fuzzy C-Means. Both methods have difference on membership value and weighted membership value. The result of this research showed that Fuzzy C-Means was more robust than C-Means
Implementing Bayesian Inference using MCMC on MINITAB
No full textBayesian paradigm offers a conceptually simple and coherent system of statistical inference based on the simple data structure in representing uncertain knowledge by probability distribution for quantities of interest. The quantities of observed and unobserved data are then be manipulated by using laws of probability, in particular Bayes theorem, to obtain the posterior distribution of the quantity of interest. By using the pragmatic advantages of the Bayesian framework that allow to cope a very complex problems in analytic and dimension become simple in one dimension, this paper emphasize a stochastic simulation and the combination of mathematical analysis and simulation, in particular MCMC approach, as a general methods for summarizing distributions computationally.The methods of MCMC approaches with their stichastic simulation for Bayesian inference have been developed in macros of the MINITAB-based approaches. Some examples are presented to demonstrate the use of MINITAB for this Bayesian statistical inference. It is shown that for a single parameter the Package is useful for statistical computation, analysis and graphical presentation of the posterior densities. These capabilities show that the package is a suitable, a simple and an appropriate tool for implementing and teaching a computational Bayesian statistical inference using MCMC approach.Keywords: Markov Chain Monte Carlo, Bayesian methods, Rejection Sampling, Full conditional density, Marginal posterior density, MINITAB macros
PEMODELAN RESIKO PENYAKIT KAKI GAJAH (FILARIASIS) DI PROVINSI PAPUA DENGAN REGRESI ZERO-INFLATED POISSON
Get PDFThe goverment has established elimination of filariasis tropical disease as one of the priority programs. One of the districts that has become a target is Papua. The total amount of filariasis victim on every regency/city in Papua district can be assumed to follow a Poisson distribution. So Poisson regression method is a suitable method to know the influence factor of filariasis disease. Poisson regression model assumes equidispersion, that is equality of mean and variance of the response variable. Overdispersion test shows that the variance of the response variable exceeds its mean value. So the model is modified into zeroinflated Poisson (ZIP) regression model (logit and log). ZIP logit regression model shows that the quantity of filariasis victim in every regency/city in Papua district with zero count is influenced by the percentage of household members who sleep inside mosquito net, the percentage of household members who sleep inside insecticide musquito net, and the percentage of house-holds who keep pet (dog/cat/rabbit). While ZIP regression on log model shows that the increasing number of percentage household who keeps their pet will enhance the quantity of filariasis victim in Papua district as many as two people. Regencies/cities which need to get special attention through an elimination program of filariasis are Asmat, Tolikara, Supiori, Yapen Waropen, and Jayapura city
Penaksiran Dan Pengujian Model Regresi Beta-Logistik Heckman-Willis
No full textMethods are presented for modeling dose-related effects in proportion data when extra-binomial variability is a concern. Motivation is taken from experiments in developmental toxicology, where the observed proportions. Appeal is made to the well-known beta-binomial distribution to represent the overdispersion. From this, an exponential function of the linear predictor is used to model the dose-response relationship. The spesification was introduced previously for econometric applications by Heckman and Willis; it induces a form logistic regression for mean response, together with a reciprocal biexponential model for the intralitter correlation. For large sample, likelihood based methods for estimating and testing the joint proportion-correlation response are studied.Keywords: logistic regression, beta-binomial distributin, biexponential mode
Modifikasi Teknik Tsay Dalam Analisis Intervensi
No full textAda dua kelemahanan dalam analisis intervensi dengan teknik Tsay yaitu keterbatasannya dalam mendeteksi perubahan ragam yang terjadi dekat dengan ujung seri dan ketiadaan ujiawal untuk mendeteksi keberadaan intervensi. Dalam studi ini, kelemahan tersebut dikaji dan alternatif pemecahannya disarankan.Kajian ini mendapatkan bahwa kuasa uji yang dikembangkan oleh Inclan & Tiao lebih besar dari kuasa uji Tsay dan dapat digunakan untuk mendeteksi perubahan ragam yang terjadi dekat dengan ujung seri. Untuk ujiawal, kajian ini mengusulkan penggunaan test kurtosis dan kecondongan. Oleh karena itu disimpulkan bahwa uji perubahan ragam dalam analisis intervensi dengan teknik Tsay perlu digantikan dengan uji Inclan & Tiao dan uji kecondongan dan kurtosis perlu diintroduksikan sebagai ujiawal kehadiran intervensi di dalam seri.Kata kunci: analisis intervensi, uji perubahan ragam, kecondongan, kurtosi
Multi-locations trials play an important role in plant breeding and agronomic research. Study concerning genotype-environment interaction is needed in the selection of genotype to be released. AMMI (Additive Main Effect and Multiplicative Interaction) is one of the statistical techniques used to analyze data from multi-locations trials. The analysis of AMMI is a combination of analysis between additive main effect and principal component analysis. Multi-location sampling data which were collected several years on several planting season used these analyzed separately. To obtain more comprehensive information of multi-location sampling data, an analysis which combines all of the information through out the years are needed. One of the alternatives is the Bayesian approach. This method utilizes initial information on the estimated parameters and information from samples. The simulation states that prediction with Bayesian methods will produce a better estimator, because the MSE of the Bayesian estimator is smaller than the MSE estimator generated using least squares method.
Get PDFMulti-locations trials play an important role in plant breeding and agronomic research. Study concerning genotype-environment interaction is needed in the selection of genotype to be released. AMMI (Additive Main Effect and Multiplicative Interaction) is one of the statistical techniques used to analyze data from multi-locations trials. The analysis of AMMI is a combination of analysis between additive main effect and principal component analysis. Multi-location sampling data which were collected several years on several planting season used these analyzed separately. To obtain more comprehensive information of multi-location sampling data, an analysis which combines all of the information through out the years are needed. One of the alternatives is the Bayesian approach. This method utilizes initial information on the estimated parameters and information from samples. The simulation states that prediction with Bayesian methods will produce a better estimator, because the MSE of the Bayesian estimator is smaller than the MSE estimator generated using least squares method
REGRESI TERBOBOTI GEOGRAFIS DENGAN PEMBOBOT KERNEL KUADRAT GANDA UNTUK DATA KEMISKINAN DI KABUPATEN JEMBER
Get PDFThe determination of whether rural areas are considered poor or no are usually based on the average cost per capita with a global analysis that needs independent observations and the results are applied to all villages. But it is very likely that poverty would be influenced by space and neighboring areas, so the data between observations are rarely independent. One of the statistical analysis that encounters this spatial problem is Geographically Weighted Regression (GWR), which gives different weights to each geographical observation. In this paper, the weighting used for the GWR model is kernel bi-square, with its bandwidth values respectively. Optimal bandwidth can be obtained by minimizing the value of cross validation coefficient (CV). The results showed that the GWR model is more effective than the regression to analyze the data on average expenditure per capita in Jember
Additive Main Effects Multiplicative Interaction (AMMI) is a widely known analysis used in understanding genotype and environment interaction (GEI) in plant breeding research. The interpretation of AMMI based on biplot visualizes the first two component of principle components analysis. Biplot of AMMI is only an exploration analysis and it does not provide the hypothesis testing, so it can conduct different interpretation by plant breeding researchers. The aim of this research is to find a systematic approach through bootstrap resampling method. Bootstrap resampling method in AMMI model produces confidence region of the first two interaction principle component ( and ) for genotype and environment respectively. Bootstrap confidence region of and estimated the stability of genotype, thus making AMMI analysis more precise and realiable for characterization and selection of genetic environment.
Get PDFAdditive Main Effects Multiplicative Interaction (AMMI) is a widely known analysis used in understanding genotype and environment interaction (GEI) in plant breeding research. The interpretation of AMMI based on biplot visualizes the first two component of principle components analysis. Biplot of AMMI is only an exploration analysis and it does not provide the hypothesis testing, so it can conduct different interpretation by plant breeding researchers. The aim of this research is to find a systematic approach through bootstrap resampling method. Bootstrap resampling method in AMMI model produces confidence region of the first two interaction principle component ( and ) for genotype and environment respectively. Bootstrap confidence region of and estimated the stability of genotype, thus making AMMI analysis more precise and realiable for characterization and selection of genetic environment
Indeks Harga Saham Gabungan (IHSG) merupakan salah satu indikator yang digunakan pemerintah dalam mengambil kebijakan dalam bidang ekonomi. Selain itu pemerintah menganggap pentingnya pasar modal sebagai alternatif pembiayaan selain perbankan. Fluktuasi yang sangat besar terjadi di pasar bursa, karena setiap transaksi tercatat dengan skala waktu yang kecil sehingga perubahan nilai yang terjadi begitu cepat. Pada kasus ini asumsi kehomogenan ragam tidak terpenuhi. Pada pasar bursa juga memperlihatkan adanya pengaruh asimetrik(leverage), yaitu hubungan yang negatif antara perubahan nilai return dengan pergerakan volatilitasnya. Model EGARCH yang memodelkan ragam bersyarat sebagai fungsi log-linear digunakan sebagai fungsi ragam dalam memodelkan nilai harian IHSG, sehingga nilai ragam bersyarat yang diprediksi tidak akan pernah negatif. Model EGARCH terpilih adalah MA(1)-EGARCH(1,1). Model EGARCH terbukti sangat baik dalam memodelkan nilai harian IHSG, tetapi belum cukup baik untuk meramalkan nilai IHSG yang akan datang. Selain ramalan terhadap nilai harian IHSG, pemodelan fungsi ragam juga menghasilkan peramalan terhadap ragam bersyaratnya. Ramalan ragam bersyarat sangat berguna bagi pemegang aset dalam melihat perilaku pergerakan IHSG dan untuk menghitung besarnya resiko memegang suatu aset di masa yang akan datang.
No full textIndeks Harga Saham Gabungan (IHSG) merupakan salah satu indikator yang digunakan pemerintah dalam mengambil kebijakan dalam bidang ekonomi. Selain itu pemerintah menganggap pentingnya pasar modal sebagai alternatif pembiayaan selain perbankan. Fluktuasi yang sangat besar terjadi di pasar bursa, karena setiap transaksi tercatat dengan skala waktu yang kecil sehingga perubahan nilai yang terjadi begitu cepat. Pada kasus ini asumsi kehomogenan ragam tidak terpenuhi. Pada pasar bursa juga memperlihatkan adanya pengaruh asimetrik(leverage), yaitu hubungan yang negatif antara perubahan nilai return dengan pergerakan volatilitasnya. Model EGARCH yang memodelkan ragam bersyarat sebagai fungsi log-linear digunakan sebagai fungsi ragam dalam memodelkan nilai harian IHSG, sehingga nilai ragam bersyarat yang diprediksi tidak akan pernah negatif. Model EGARCH terpilih adalah MA(1)-EGARCH(1,1). Model EGARCH terbukti sangat baik dalam memodelkan nilai harian IHSG, tetapi belum cukup baik untuk meramalkan nilai IHSG yang akan datang. Selain ramalan terhadap nilai harian IHSG, pemodelan fungsi ragam juga menghasilkan peramalan terhadap ragam bersyaratnya. Ramalan ragam bersyarat sangat berguna bagi pemegang aset dalam melihat perilaku pergerakan IHSG dan untuk menghitung besarnya resiko memegang suatu aset di masa yang akan datang
PEMODELAN KALIBRASI PEUBAH GANDA DENGAN PENDEKATAN REGRESI SINYAL P-SPLINE
Get PDFModel kalibrasi peubah ganda merupakan suatu fungsi hubungan antara satuan pengukuran yang dapat diperoleh melalui proses yang relatif mudah atau murah dengan satuan pengukuran yang memerlukan waktu lama dan biaya mahal. Secara umum data kalibrasi memiliki multikolinearitas yang tinggi antar peubah penjelas dan dimensinya jauh lebih besar daripada banyaknya contoh yang dimiliki. Oleh karena itu, sebagian besar pendekatan model kalibrasi memerlukan pereduksian data terlebih dulu. Solusi alternatif bagi pemodelan kalibrasi adalah regresi sinyal P-spline (RSP). RSP merupakan salah satu pendekatan nonparametrik yang mensyaratkan bahwa koefisien regresi berada dalam ruang fungsi mulus. Hal ini dilakukan dengan cara merepresentasikan koefisien regresi sebagai kombinasi linear dari basis B-spline. Penambahan penalti dilakukan untuk mengatasi multikolinearitas pada model serta meningkatkan kemulusan koefisien regresi. Indeks dari bilangan gelombang yang terukur oleh FTIR digunakan sebagai domain B-spline. Spektra gingerol diidentifikasi memiliki pengaruh pencaran multiplikatif, sehingga perlu dilakukan koreksi pencaran. Model RSP dengan koreksi pencaran multiplikatif pada senyawa aktif gingerol memberikan hasil prediksi yang lebih baik. Hal ini ditunjukkan oleh nilai RMSEP dan R2y vs ŷ masing-masing sebesar 0.06867 dan 95.73 %. Nilai-nilai tersebut jauh lebih kecil dari hasil yang diberikan oleh model regresi komponen utama dengan pra-pemrosesan koreksi pencaran maupun transformasi wavelet