Impacts of atypical data on Bayesian inference and robust Bayesian approach in fisheries

1999 ◽  
Vol 56 (9) ◽  
pp. 1525-1533 ◽  
Author(s):  
Y Chen ◽  
D Fournier
Keyword(s):  
Bayesian Inference ◽  
Bayesian Method ◽  
Mixture Distribution ◽  
Posterior Distributions ◽  
Bayesian Analyses ◽  
Probability Of Occurrence ◽  
Likelihood Functions ◽  
The Mean ◽  
Atypical Values ◽  
Simple Growth

Bayesian inference is increasingly used in fisheries. In formulating likelihood functions in Bayesian inference, data have been analyzed as if they are normally, identically, and independently distributed. It has come to be believed that the first two of the assumptions are frequently inappropriate in fisheries studies. In fact, data distributions are likely to be leptokurtic and (or) contaminated by occasional bad values giving rise to outliers in many fisheries studies. Despite the likelihood of having outliers in fisheries studies, the impacts of outliers on Bayesian inference have received little attention. In this study, using a simple growth model as an example, we evaluate the impacts of outliers on the derivation of posterior distributions in Bayesian analyses. Posterior distributions derived from the Bayesian method commonly used in fisheries are found to be sensitive to outliers. The distributions are severely biased in the presence of atypical values. The sensitivity of normality-based Bayesian analyses on atypical data may result from small "tails" of normal distribution so that the probability of occurrence of an event drops off quickly as one moves away from the mean a distance of a few standard deviations. A robust Bayesian method can be derived by including a mixture distribution that increases the size of tail so that the probability of occurrence of an event does not drop off too quickly as one moves away from the mean. The posterior distributions derived from this proposed approach are found to be robust to atypical data in this study. The proposed approach offers a potentially useful addition to Bayesian methods used in fisheries.

scholarly journals BAYESIAN INFERENCE FOR THE TANGENT PORTFOLIO

2018 ◽  
Vol 21 (08) ◽  
pp. 1850054 ◽  
Author(s):  
DAVID BAUDER ◽  
TARAS BODNAR ◽  
STEPAN MAZUR ◽  
YAREMA OKHRIN
Keyword(s):  
Bayesian Inference ◽  
Point Of View ◽  
Posterior Distributions ◽  
Conditional Distributions ◽  
Linear Combinations ◽  
Conjugate Priors ◽  
Mean And Variance ◽  
The Mean ◽  
Stochastic Representations ◽  
Mean Vector

In this paper, we consider the estimation of the weights of tangent portfolios from the Bayesian point of view assuming normal conditional distributions of the logarithmic returns. For diffuse and conjugate priors for the mean vector and the covariance matrix, we derive stochastic representations for the posterior distributions of the weights of tangent portfolio and their linear combinations. Separately, we provide the mean and variance of the posterior distributions, which are of key importance for portfolio selection. The analytic results are evaluated within a simulation study, where the precision of coverage intervals is assessed.

Bayesian Estimation of Stimulus Responses in Poisson Spike Trains

2004 ◽  
Vol 16 (7) ◽  
pp. 1325-1343 ◽  
Author(s):  
Sidney R. Lehky
Keyword(s):  
Bayesian Method ◽  
Significant Degree ◽  
Spike Trains ◽  
Neural Responses ◽  
Interval Estimates ◽  
Poisson Statistics ◽  
Likelihood Functions ◽  
Bayesian Estimates ◽  
Mean And Variance ◽  
The Mean

A Bayesian method is developed for estimating neural responses to stimuli, using likelihood functions incorporating the assumption that spike trains follow either pure Poisson statistics or Poisson statistics with a refractory period. The Bayesian and standard estimates of the mean and variance of responses are similar and asymptotically converge as the size of the data sample increases. However, the Bayesian estimate of the variance of the variance is much lower. This allows the Bayesian method to provide more precise interval estimates of responses. Sensitivity of the Bayesian method to the Poisson assumption was tested by conducting simulations perturbing the Poisson spike trains with noise. This did not affect Bayesian estimates of mean and variance to a significant degree, indicating that the Bayesian method is robust. The Bayesian estimates were less affected by the presence of noise than estimates provided by the standard method.

scholarly journals Adaptive Gaussian Process Approximation for Bayesian Inference with Expensive Likelihood Functions

2018 ◽  
Vol 30 (11) ◽  
pp. 3072-3094 ◽  
Author(s):  
Hongqiao Wang ◽  
Jinglai Li
Keyword(s):  
Bayesian Inference ◽  
Gaussian Process ◽  
Adaptive Algorithm ◽  
Posterior Density ◽  
Unknown Parameters ◽  
Likelihood Functions ◽  
Inference Problems ◽  
Active Learning Method ◽  
Computationally Intensive ◽  
Process Approximation

We consider Bayesian inference problems with computationally intensive likelihood functions. We propose a Gaussian process (GP)–based method to approximate the joint distribution of the unknown parameters and the data, built on recent work (Kandasamy, Schneider, & Póczos, 2015 ). In particular, we write the joint density approximately as a product of an approximate posterior density and an exponentiated GP surrogate. We then provide an adaptive algorithm to construct such an approximation, where an active learning method is used to choose the design points. With numerical examples, we illustrate that the proposed method has competitive performance against existing approaches for Bayesian computation.

scholarly journals Estimating Rainfall Design Values for the City of Oslo, Norway—Comparison of Methods and Quantification of Uncertainty

Water ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 1735 ◽  
Author(s):  
Julia Lutz ◽  
Lars Grinde ◽  
Anita Verpe Dyrrdal
Keyword(s):  
Bayesian Inference ◽  
Goodness Of Fit ◽  
Bayesian Method ◽  
Gumbel Distribution ◽  
Likelihood Estimation ◽  
Current Method ◽  
Credible Interval ◽  
Computational Method ◽  
Goodness Of Fit Tests ◽  
Idf Curves

Due to its location, its old sewage system, and the channelling of rivers, Oslo is highly exposed to urban flooding. Thus, it is crucial to provide relevant and reliable information on extreme precipitation in the planning and design of infrastructure. Intensity-Duration-Frequency (IDF) curves are a frequently used tool for that purpose. However, the computational method for IDF curves in Norway was established over 45 years ago, and has not been further developed since. In our study, we show that the current method of fitting a Gumbel distribution to the highest precipitation events is not able to reflect the return values for the long return periods. Instead, we introduce the fitting of a Generalised Extreme Value (GEV) distribution for annual maximum precipitation in two different ways, using (a) a modified Maximum Likelihood estimation and (b) Bayesian inference. The comparison of the two methods for 14 stations in and around Oslo reveals that the estimated median return values are very similar, but the Bayesian method provides upper credible interval boundaries that are considerably higher. Two different goodness-of-fit tests favour the Bayesian method; thus, we suggest using the Bayesian inference for estimating IDF curves for the Oslo area.

Accuracy of predicting the vancomycin concentration in Japanese cancer patients by the Sawchuk–Zaske method or Bayesian method

2019 ◽  
Vol 26 (3) ◽  
pp. 543-548
Author(s):  
Toshihisa Nakashima ◽  
Takayuki Ohno ◽  
Keiichi Koido ◽  
Hironobu Hashimoto ◽  
Hiroyuki Terakado
Keyword(s):  
Cancer Patients ◽  
Prediction Error ◽  
Bayesian Method ◽  
Predictive Accuracy ◽  
Pharmacokinetic Parameters ◽  
Population Pharmacokinetic ◽  
Squared Prediction Error ◽  
Trough Concentrations ◽  
The Mean ◽  
Mean Prediction Error

Background In cancer patients treated with vancomycin, therapeutic drug monitoring is currently performed by the Bayesian method that involves estimating individual pharmacokinetics from population pharmacokinetic parameters and trough concentrations rather than the Sawchuk–Zaske method using peak and trough concentrations. Although the presence of malignancy influences the pharmacokinetic parameters of vancomycin, it is unclear whether cancer patients were included in the Japanese patient populations employed to estimate population pharmacokinetic parameters for this drug. The difference of predictive accuracy between the Sawchuk–Zaske and Bayesian methods in Japanese cancer patients is not completely understood. Objective To retrospectively compare the accuracy of predicting vancomycin concentrations between the Sawchuk–Zaske method and the Bayesian method in Japanese cancer patients. Methods Using data from 48 patients with various malignancies, the predictive accuracy (bias) and precision of the two methods were assessed by calculating the mean prediction error, the mean absolute prediction error, and the root mean squared prediction error. Results Prediction of the trough and peak vancomycin concentrations by the Sawchuk–Zaske method and the peak concentration by the Bayesian method showed a bias toward low values according to the mean prediction error. However, there were no significant differences between the two methods with regard to the changes of the mean prediction error, mean absolute prediction error, and root mean squared prediction error. Conclusion The Sawchuk–Zaske method and Bayesian method showed similar accuracy for predicting vancomycin concentrations in Japanese cancer patients.

scholarly journals Bayesian Inference for the Difference of Two Proportion Parameters in Over-Reported Two-Sample Binomial Data Using the Doubly Sample

Stats ◽  
2019 ◽  
Vol 2 (1) ◽  
pp. 111-120 ◽  
Author(s):  
Dewi Rahardja
Keyword(s):  
Bayesian Inference ◽  
Closed Form ◽  
Bayesian Approach ◽  
Interval Estimation ◽  
Real Data ◽  
Simulation Studies ◽  
Posterior Distributions ◽  
Binomial Data ◽  
The Difference ◽  
Data Subject

We construct a point and interval estimation using a Bayesian approach for the difference of two population proportion parameters based on two independent samples of binomial data subject to one type of misclassification. Specifically, we derive an easy-to-implement closed-form algorithm for drawing from the posterior distributions. For illustration, we applied our algorithm to a real data example. Finally, we conduct simulation studies to demonstrate the efficiency of our algorithm for Bayesian inference.

scholarly journals Assessing fracture occurrence using "weighted fracturing density": a step towards estimating rock instability hazard

2004 ◽  
Vol 4 (1) ◽  
pp. 83-93 ◽  
Author(s):  
M. Jaboyedoff ◽  
F. Baillifard ◽  
F. Philippossian ◽  
J.-D. Rouiller
Keyword(s):  
Fracture Density ◽  
Probability Of Occurrence ◽  
Major Class ◽  
Line Parallel ◽  
Digital Elevation ◽  
Discontinuity Sets ◽  
The Mean ◽  
Slope Instabilities ◽  
Elevation Model ◽  
Effective Use

Abstract. Based on the assumption that major class of rock instabilities are created by discontinuities, a method is proposed to estimate the fracture density by means of a digital elevation model (DEM). By using the mean orientation, the mean spacing and the mean trace length of discontinuity sets potentially involved in slope instabilities and a DEM, it is possible to calculate the mean number of discontinuities of a given set per cell of the DEM. This would allow for an estimation of the probability of the presence of at least one discontinuity in a given area or simply in a topographic cell of the DEM. This analysis highlights sites potentially affected by rockslides within a region. Depending on the available data, the mean number can be calculated either by area, or along a line parallel to the mean apparent spacing. The effective use of the probability of occurrence is dependent on the size of the discontinuities because short and closely spaced discontinuities will have a 100% probability of occurrence in each favorable location. The a posteriori prediction of a recent rockslide is discussed as an example.

scholarly journals The estimation of the uncertainty associated with rating curves of the river Ivinhema in the state of Paraná/Brazil

2018 ◽  
Vol 40 ◽  
pp. 06029
Author(s):  
Luiz Henrique Maldonado ◽  
Daniel Firmo Kazay ◽  
Elio Emanuel Romero Lopez
Keyword(s):  
Bayesian Inference ◽  
Likelihood Function ◽  
The State ◽  
Likelihood Estimator ◽  
Likelihood Functions ◽  
Important Impact ◽  
Rating Curves

The estimation of the uncertainty associated with stage-discharge relations is a challenge to the hydrologists. Bayesian inference with likelihood estimator is a promissory approach. The choice of the likelihood function has an important impact on the capability of the model to represent the residues. This paper aims evaluate two likelihood functions with DREAM algorithm to estimate specific non-unique stage-discharge rating curves: normal likelihood function and Laplace likelihood function. The result of BaRatin is also discussed. The MCMC of the DREAM and the BaRatin algorithm have been compared and its results seem consistent for the studied case. The Laplace likelihood function presented as good results as normal likelihood function for the residues. Other gauging stations should be evaluated to attend more general conclusions.

Investigating the Effect of Prior Distributions on Posterior Estimates of Common Cause Failure Parameters Using Bayesian Method

2020 ◽  
Vol 6 (3) ◽  
Author(s):  
Edward Shitsi ◽  
Emmanuel K. Boafo ◽  
Felix Ameyaw ◽  
H. C. Odoi
Keyword(s):  
Bayesian Analysis ◽  
Confidence Level ◽  
Bayesian Method ◽  
Jeffreys Prior ◽  
Uncertainty Interval ◽  
Prior Distributions ◽  
Common Cause ◽  
Common Cause Failure ◽  
Dirichlet Prior ◽  
The Mean

Abstract Quantification of common cause failure (CCF) parameters and their application in multi-unit PSA are important to the safety and operation of nuclear power plants (NPPs) on the same site. CCF quantification mainly involves the estimation of potential failure of redundant components of systems in a NPP. The components considered in quantification of CCF parameters include motor operated valves, pumps, safety relief valves, air-operated valves, solenoid-operated valves, check valves, diesel generators, batteries, inverters, battery chargers, and circuit breakers. This work presents the results of the CCF parameter quantification using check valves and pumps. The systems considered as case studies for the demonstration of the proposed methodology are auxiliary feedwater system (AFWS) and high-pressure safety injection (HPSI) systems of a pressurized water reactor (PWR). The posterior estimates of alpha factors assuming two different prior distributions (Uniform Dirichlet prior and Jeffreys prior) using the Bayesian method were investigated. This analysis is important due to the fact that prior distributions assumed for alpha factors may affect the shape of posterior distribution and the uncertainty of the mean posterior estimates. For the two different priors investigated in this study, the shape of the posterior distribution is not influenced by the type of prior selected for the analysis. The mean of the posterior distributions was also analyzed at 90% confidence level. These results show that the type of prior selected for Bayesian analysis could have effects on the uncertainty interval (or the confidence interval) of the mean of the posterior estimates. The longer the confidence interval, the better the type of prior selected at a particular confidence level for Bayesian analysis. These results also show that Jeffreys prior is preferred over Uniform Dirichlet prior for Bayesian analysis because it yields longer confidence intervals (or shorter uncertainty interval) at 90% confidence level discussed in this work.

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