4-D lesion detection using expectation-maximization and hidden Markov model

2005 ◽  
Author(s):  
J. Solomon ◽  
A. Sood
Keyword(s):  
Markov Model ◽  
Hidden Markov Model ◽  
Expectation Maximization ◽  
Hidden Markov ◽  
Lesion Detection

Point and Figure Portfolio Optimization using Hidden Markov Models and Its Application on the Bumi Resources Tbk Shares

2021 ◽  
Vol 3 (1) ◽  
pp. 44-52
Author(s):  
Kastolan Kastolan ◽  
Berlian Setiawaty ◽  
N. K. Kutha Ardana
Keyword(s):  
Markov Model ◽  
Hidden Markov Model ◽  
Portfolio Optimization ◽  
Expectation Maximization ◽  
Stock Prices ◽  
Stock Price ◽  
Hidden Markov ◽  
Expectation Maximization Algorithm ◽  
Percentage Error ◽  
Time Sampling

AbstractThe problem of portfolio optimization is to select a trading strategy which maximizes the expected terminal wealth. Since the stocks are traded at discrete random times in a real-world market, we are interested in a time sampling method. The sampling of stock price is obtained from the process of time sampling which is used in a point and figure chart. Point and figure (PF) chart displays the up and down movements of unbalanced stock prices. The basic idea is to describe essential movements of the unbalanced stock prices using a hidden Markov model. The model parameters are transition probability matrices. They are estimated using maximum likelihood method and expectation maximization algorithm. The estimation procedure involves change of measure. The model is then applied to the stock price of Bumi Resources Tbk. collected on a daily basis. The estimated parameters are used to calculate the optimal portfolio using a recursive algorithm. The results show that the discrete hidden Markov model can be applied to describe essential movements of the stock price. The best result gives 93.63% accuracy of the estimate of observation sequence with mean absolute percentage error (MAPE) 3.63%. The numerical calculation shows that the optimal logarithmic PF-portfolio increases the wealth.Keywords: point and figure portfolio; optimization portfolio; discrete hidden Markov model; expectation maximization algorithm; stock price of Bumi Resources Tbk. AbstrakMasalah pengoptimalan portofolio adalah pemilihan strategi perdagangan yang dapat memaksimalkan kekayaan terminal yang diharapkan. Karena di pasar dunia nyata, saham diperdagangkan pada waktu acak yang berbeda, sehingga kami tertarik pada metode pengambilan sampel waktu. Proses pengambilan sampel waktu diperoleh sampling harga saham yang digunakan dalam diagram point and figure (PF-chart). Grafik point and figure hanya menampilkan pergerakan naik atau turun harga saham yang tidak seimbang. Ide dasarnya adalah untuk mendeskripsikan pergerakan esensial dari harga saham yang tidak seimbang menggunakan model hidden Markov. Parameter dari model ini adalah matriks probabilitas transisi. Parameter diestimasi menggunakan metode maximum likelihood dan algoritma expectation maximization. Prosedur estimasi melibatkan perubahan ukuran. Model ini kemudian diaplikasikan pada harga saham Bumi Resources Tbk. dari tanggal 2 Januari 2007 sampai dengan 31 Januari 2011. Hasil estimasi parameter tersebut digunakan untuk menghitung portofolio optimal menggunakan algoritma rekursif. Hasil penelitian ini menunjukkan bahwa model hidden Markov diskrit dapat diterapkan untuk menggambarkan pergerakan esensial dari harga saham. Model terbaik memberikan akurasi 93.63% dari estimasi deretan observasi dengan mean absolute percentage error (MAPE) 3,63% dan 5 faktor penyebab kejadian. Perhitungan numerik menunjukkan bahwa logaritma portofolio-PF yang optimal dapat meningkatkan kekayaan.Kata kunci: portofolio point and figure; optimalisasi portofolio; model hidden Markov diskrit; algoritma expectation maximization; harga saham PT Bumi Resources.

scholarly journals Estimasi Parameter Model Poisson Hidden Markov Pada Data Banyaknya Kedatangan Klaim Asuransi Jiwa

2020 ◽  
Vol 1 (2) ◽  
pp. 65
Author(s):  
Vieri Koerniawan ◽  
Nurtiti Sunusi ◽  
Raupong Raupong
Keyword(s):  
Markov Model ◽  
Hidden Markov Model ◽  
Life Insurance ◽  
Expectation Maximization ◽  
Numerical Solutions ◽  
Likelihood Function ◽  
Hidden Markov ◽  
Information Criterion ◽  
Model Parameters ◽  
Insurance Data

The Poisson hidden Markov model is a model that consists of two parts. The first part is the cause of events that are hidden or cannot be observed directly and form a Markov chain, while the second part is the process of observation or observable parts that depend on the cause of the event and following the Poisson distribution. The Poisson hidden Markov model parameters are estimated using the Maximum Likelihood Estimator (MLE). But it is difficult to find analytical solutions from the ln-likelihood function. Therefore, the Expectation Maximization (EM) algorithm is used to obtain its numerical solutions which are then applied to life insurance data. The best model is obtained with 2 states or m = 2 based on the smallest Bayesian Information Criterion (BIC) value of 338,778 and the average predicted number of claims arrivals is 0.385 per day.

Prediction of Facies Distribution in a Clastic Reservoir Using a Hidden Markov Model Combined With an Expectation-Maximization Algorithm

2016 ◽  
Author(s):  
Hwasoo Suk ◽  
Baehyun Min ◽  
Joe M. Kang ◽  
Cheolkyun Jeong
Keyword(s):  
Probability Distribution ◽  
Markov Model ◽  
Hidden Markov Model ◽  
Expectation Maximization ◽  
Hidden Markov ◽  
Transition Probability ◽  
Expectation Maximization Algorithm ◽  
Model Parameters ◽  
Facies Distribution ◽  
Clastic Reservoir

This study determines facies distribution in a clastic reservoir using a hidden Markov model combined with an Expectation-Maximization algorithm. Iterating expectation and maximization steps of the algorithm builds the hidden Markov model by tuning the model parameters including initial state distribution, state transition probability distribution, and observable symbol probability distribution. Optimized model parameters contribute to improving the predictability of facies distribution along the well trajectory using core and logging data.

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