scholarly journals ANALISIS METODE BAYESIAN PADA SISTEM ANTREAN RAWAT JALAN DI RSUP Dr. KARIADI DENGAN DISTRIBUSI SAMPEL POISSON DAN GEOMETRIK

2021 ◽  
Vol 10 (3) ◽  
pp. 413-422
Author(s):  
Nur Azizah ◽  
Sugito Sugito ◽  
Hasbi Yasin
Keyword(s):  
Internal Medicine ◽  
Posterior Distribution ◽  
Prior Distribution ◽  
Bayesian Method ◽  
Likelihood Function ◽  
Queuing System ◽  
Hospital Service ◽  
Queuing Model ◽  
Sample Distribution ◽  
New Information

Hospital service facilities cannot be separated from queuing events. Queues are an unavoidable part of life, but they can be minimized with a good system. The purpose of this study was to find out how the queuing system at Dr. Kariadi. Bayesian method is used to combine previous research and this research in order to obtain new information. The sample distribution and prior distribution obtained from previous studies are combined with the sample likelihood function to obtain a posterior distribution. After calculating the posterior distribution, it was found that the queuing model in the outpatient installation at Dr. Kariadi Semarang is (G/G/c): (GD/∞/∞) where each polyclinic has met steady state conditions and the level of busyness is greater than the unemployment rate so that the queuing system at Dr. Kariadi is categorized as good, except in internal medicine poly. 

scholarly journals ANALISIS SISTEM PELAYANAN KERETA API DI STASIUN SEMARANG TAWANG MENGGUNAKAN PROSES BAYESIAN

2020 ◽  
Vol 9 (4) ◽  
pp. 495-504
Author(s):  
Lifana Nugraeni ◽  
Sugito Sugito ◽  
Dwi Ispriyanti
Keyword(s):  
Poisson Distribution ◽  
Posterior Distribution ◽  
Public Transportation ◽  
Bayesian Method ◽  
Service System ◽  
Likelihood Function ◽  
Performance Standard ◽  
Sample Distribution ◽  
Service Patterns ◽  
Transportation Facilities

Along with the times, transportation has progressed. Regarding the means of transportation, one of the phenomenon that is easily encountered in everyday life is the queue at public transportation facilities. One of the queues that occurred at public transportation facilities is  the train queue at Semarang Tawang Station. The number of trains that passes the station can cause the train service at the station busy. This study aims to see whether the train service system of Semarang Tawang Station is good or not. This can be consider by the queues method, determining the distribution of arrival patterns and service patterns to obtain a queues system model and a system performance standard. In this study, the distribution of arrival patterns and service patterns are determined by calculating the posterior distribution using the Bayesian method. The bayesian method was chosen because it is able to combine the sample distribution in the current study with the previous information for the same cases. The prior distribution and the likelihood function are the elements needed to obtain the posterior distribution. The distribution of arrival patterns and service patterns obtained from previous information follows the Poisson distribution. Based on the calculation of the posterior distribution, the result shows that the distribution of the arrival pattern is a discrete uniform distribution and the distribution of the service pattern is a Poisson distribution. The result shows that the train service system at Semarang Tawang Station has a model (Uniform Discrete / Gamma / 7: GD / ~ / ~) and has good service based on the performance values obtained.

Metropolis-Hastings Algorithms for DSGE Models

2015 ◽  
Author(s):  
Edward P. Herbst ◽  
Frank Schorfheide
Keyword(s):  
Random Walk ◽  
Posterior Distribution ◽  
Prior Distribution ◽  
Large Scale ◽  
Likelihood Function ◽  
Dsge Models ◽  
Posterior Distributions ◽  
Dsge Model ◽  
Alternative Proposal ◽  
Posterior Moments

This chapter talks about the most widely used method to generate draws from posterior distributions of a DSGE model: the random walk MH (RWMH) algorithm. The DSGE model likelihood function in combination with the prior distribution leads to a posterior distribution that has a fairly regular elliptical shape. In turn, the draws from a simple RWMH algorithm can be used to obtain an accurate numerical approximation of posterior moments. However, in many other applications, particularly those involving medium- and large-scale DSGE models, the posterior distributions could be very non-elliptical. Irregularly shaped posterior distributions are often caused by identification problems or misspecification. In lieu of the difficulties caused by irregularly shaped posterior surfaces, the chapter reviews various alternative MH samplers, which use alternative proposal distributions.

scholarly journals The Bühlmann–Straub Estimation of Claim Means in Random B-F Reserve Model

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Zhang Yi ◽  
Wen Limin ◽  
Li Zhilong
Keyword(s):  
Prior Distribution ◽  
Personal Experience ◽  
Bayesian Method ◽  
Historical Data ◽  
Credibility Theory ◽  
Empirical Bayesian ◽  
Sample Distribution ◽  
Empirical Bayesian Method ◽  
Chain Ladder ◽  
Bayesian Estimators

In the B-F reserve model, it is a very critical step to estimate the claim means of the accident year. However, the traditional method uses the prior estimators of the claim means based on the personal experience of actuaries or historical data. This method inevitably carries the subjectivity of the actuary himself. In this paper, a stochastic B-F model is established, and a prior distribution is constructed for the claim means in the accident year. The idea of the credibility theory is used to derive the linear Bayesian estimators of claim means. Finally, the empirical Bayesian method is used to estimate the first two moments of the prior distribution, and the empirical Bayesian estimators of the claim means and the corresponding reserves are derived. The estimators obtained in this paper do not depend on the specific forms of the sample distribution and the prior distribution and can be used directly in practice. In the numerical simulation, our estimates are compared with the traditional B-F estimates and the chain ladder estimates. It is verified that the estimates given in this paper have small mean square error.

scholarly journals Impact of Prioritization on the Outpatient Queuing System in the Emergency Department with Limited Medical Resources

Symmetry ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 796 ◽  
Author(s):  
Ao Zhang ◽  
Xiaomin Zhu ◽  
Qian Lu ◽  
Runtong Zhang
Keyword(s):  
Emergency Department ◽  
Emergency Services ◽  
Service System ◽  
Queuing System ◽  
Hospital Service ◽  
Key Factors ◽  
Queuing Model ◽  
Medical Resources ◽  
Proposed Model

The emergency department has an irreplaceable role in the hospital service system because of the characteristics of its emergency services. In this paper, a new patient queuing model with priority weight is proposed to optimize the management of emergency department services. Compared with classical queuing rules, the proposed model takes into consideration the key factors of service and the first-come-first-served queuing rule in emergency services. According to some related queuing indicators, the optimization of emergency services is discussed. Finally, a case study and some compared analysis are conducted to illustrate the practicability of the proposed model.

scholarly journals An Accurate Asymptotic Approximation for Experience Rated Premiums

2004 ◽  
Vol 34 (01) ◽  
pp. 113-124
Author(s):  
Riccardo Gatto
Keyword(s):  
Numerical Methods ◽  
Posterior Distribution ◽  
Prior Distribution ◽  
Asymptotic Approximation ◽  
Good Accuracy ◽  
Likelihood Function ◽  
Analytical Calculation ◽  
Expected Loss ◽  
Exact Calculations ◽  
The Bayesian Approach

In the Bayesian approach, the experience rated premium is the value which minimizes an expected loss with respect to a posterior distribution. The posterior distribution is conditioned on the claim experience of the risk insured, represented by a n-tuple of observations. An exact analytical calculation for the experience rated premium is possible under restrictive circumstances only, regarding the prior distribution, the likelihood function, and the loss function. In this article we provide an analytical asymptotic approximation as n → ∞ for the experience rated premium. This approximation can be obtained under more general circumstances, it is simple to compute, and it inherits the good accuracy of the Laplace approximation on which it is based. In contrast with numerical methods, this approximation allows for analytical interpretations. When exact calculations are possible, some analytical comparisons confirm the good accuracy of this approximation, which can even lead to the exact experience rated premium.

scholarly journals Making Better Decisions: Can Minimizing Frequentist Risk Help?

2016 ◽  
Vol 5 (3) ◽  
pp. 80 ◽  
Author(s):  
Rose D. Baker ◽  
Ian G. McHale
Keyword(s):  
Decision Making ◽  
Posterior Distribution ◽  
Prior Distribution ◽  
Likelihood Function ◽  
Bayesian Decision Theory ◽  
Bayesian Decision ◽  
Risk Minimization ◽  
Likelihood Principle ◽  
Complete Class ◽  
Bet Size

The concept of shrinking bet size in Kelly betting to minimize estimated frequentist risk has recently been mooted. This rescaling appears to conflict with Bayesian decision theory through the likelihood principle and the complete class theorem; the Bayesian solution should already be optimal. We show theoretically and through examples that when the modeldetermining the likelihood function is correct, the prior distribution (if not dominated by data) is `correct' in a frequentist sense, and the posterior distribution is proper, then no further rescaling is required. However, if the model or the prior distribution is incorrect, or the posterior distribution improper, frequentist risk minimization can be a useful technique. We discuss how it might best be exploited. Another example, from maintenance, is used to show the wider applicability of the methodology; these conclusionsapply generally to decision-making.

The Maple Syrup Problem: The Normal-Normal Conjugate

2019 ◽  
pp. 172-190
Author(s):  
Therese M. Donovan ◽  
Ruth M. Mickey
Keyword(s):  
Normal Distribution ◽  
Posterior Distribution ◽  
Prior Distribution ◽  
Unknown Parameter ◽  
Distributed Data ◽  
Maple Syrup ◽  
New Information ◽  
The Mean ◽  
Two Parameters ◽  
Parameter Values

In this chapter, Bayesian methods are used to estimate the two parameters that identify a normal distribution, μ‎ and σ‎. Many Bayesian analyses consider alternative parameter values as hypotheses. The prior distribution for an unknown parameter can be represented by a continuous probability density function when the number of hypotheses is infinite. In the “Maple Syrup Problem,” a normal distribution is used as the prior distribution of μ‎, the mean number of millions of gallons of maple syrup produced in Vermont in a year. The amount of syrup produced in multiple years is determined, and assumed to follow a normal distribution with known σ‎. The prior distribution is updated to the posterior distribution in light of this new information. In short, a normal prior distribution + normally distributed data → normal posterior distribution.

Interval Estimation of Bivariate Correlations With Missing Data on Both Variables: A Bayesian Approach

1997 ◽  
Vol 22 (4) ◽  
pp. 407-424 ◽  
Author(s):  
Alan L. Gross
Keyword(s):  
Missing Data ◽  
Posterior Distribution ◽  
Prior Distribution ◽  
Bayesian Method ◽  
Interval Estimation ◽  
Data Set ◽  
Interval Estimates ◽  
Bivariate Correlation ◽  
Missing Completely At Random ◽  
Sample Correlation

The posterior distribution of the bivariate correlation ( ρxy) is analytically derived given a data set consisting N1 cases measured on both x and y, N2 cases measured only on x, and N3 cases measured only on y. The posterior distribution is shown to be a function of the subsample sizes, the sample correlation ( rxy) computed from the N1 complete cases, a set of four statistics which measure the extent to which the missing data are not missing completely at random, and the specified prior distribution for ρxy. A sampling study suggests that in small ( N = 20) and moderate ( N = 50) sized samples, posterior Bayesian interval estimates will dominate maximum likelihood based estimates in terms of coverage probability and expected interval widths when the prior distribution for ρxy is simply uniform on (0, 1). The advantage of the Bayesian method when more informative priors based on beta densities are employed is not as consistent.

The White House Problem: The Beta-Binomial Conjugate

2019 ◽  
pp. 133-149
Author(s):  
Therese M. Donovan ◽  
Ruth M. Mickey
Keyword(s):  
Posterior Distribution ◽  
Beta Distribution ◽  
Prior Distribution ◽  
Unknown Parameter ◽  
Fixed Number ◽  
Binomial Data ◽  
White House ◽  
New Information ◽  
Famous Person ◽  
Special Cases

This chapter introduces the beta-binomial conjugate. There are special cases where a Bayesian prior probability distribution for an unknown parameter of interest can be quickly updated to a posterior distribution of the same form as the prior. In the “White House Problem,” a beta distribution is used to set the priors for all hypotheses of p, the probability that a famous person can get into the White House without an invitation. Binomial data are then collected, and provide the number of times a famous person gained entry out of a fixed number of attempts. The prior distribution is updated to a posterior distribution (also a beta distribution) in light of this new information. In short, a beta prior distribution for the unknown parameter + binomial data → beta posterior distribution for the unknown parameter, p. The beta distribution is said to be “conjugate to” the binomial distribution.

scholarly journals An Accurate Asymptotic Approximation for Experience Rated Premiums

2004 ◽  
Vol 34 (1) ◽  
pp. 113-124
Author(s):  
Riccardo Gatto
Keyword(s):  
Numerical Methods ◽  
Posterior Distribution ◽  
Prior Distribution ◽  
Asymptotic Approximation ◽  
Good Accuracy ◽  
Likelihood Function ◽  
Analytical Calculation ◽  
Expected Loss ◽  
Exact Calculations ◽  
The Bayesian Approach

In the Bayesian approach, the experience rated premium is the value which minimizes an expected loss with respect to a posterior distribution. The posterior distribution is conditioned on the claim experience of the risk insured, represented by a n-tuple of observations. An exact analytical calculation for the experience rated premium is possible under restrictive circumstances only, regarding the prior distribution, the likelihood function, and the loss function. In this article we provide an analytical asymptotic approximation as n → ∞ for the experience rated premium. This approximation can be obtained under more general circumstances, it is simple to compute, and it inherits the good accuracy of the Laplace approximation on which it is based. In contrast with numerical methods, this approximation allows for analytical interpretations. When exact calculations are possible, some analytical comparisons confirm the good accuracy of this approximation, which can even lead to the exact experience rated premium.

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