A comparison of salmon escapement estimates using a hierarchical Bayesian approach versus separate maximum likelihood estimation of each year's return

2001 ◽  
Vol 58 (8) ◽  
pp. 1663-1671 ◽  
Author(s):  
Milo D Adkison ◽  
Zhenming Su
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Bayesian Approach ◽  
Count Data ◽  
Likelihood Estimation ◽  
Data Sets ◽  
Hierarchical Bayesian ◽  
Hierarchical Approach ◽  
Bayesian Hierarchical ◽  
The Bayesian Approach

In this simulation study, we compared the performance of a hierarchical Bayesian approach for estimating salmon escapement from count data with that of separate maximum likelihood estimation of each year's escapement. We simulated several contrasting counting schedules resulting in data sets that differed in information content. In particular, we were interested in the ability of the Bayesian approach to estimate escapement and timing in years where few or no counts are made after the peak of escapement. We found that the Bayesian hierarchical approach was much better able to estimate escapement and escapement timing in these situations. Separate estimates for such years could be wildly inaccurate. However, even a single postpeak count could dramatically improve the estimability of escapement parameters.

TREND-CYCLE DECOMPOSITIONS OF REAL GDP REVISITED: CLASSICAL AND BAYESIAN PERSPECTIVES ON AN UNSOLVED PUZZLE

2020 ◽  
pp. 1-25
Author(s):  
Chang-Jin Kim ◽  
Jaeho Kim
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Bayesian Approach ◽  
Stationary Process ◽  
Likelihood Estimation ◽  
Empirical Results ◽  
Real Gdp ◽  
Pile Up ◽  
Out Of Sample ◽  
The Bayesian Approach

While Perron and Wada (2009) maximum likelihood estimation approach suggests that postwar US real GDP follows a trend stationary process (TSP), our Bayesian approach based on the same model and the same sample suggests that it follows a difference stationary process (DSP). We first show that the results based on the approach should be interpreted with caution, as they are relatively more subject to the ‘pile-up problem’ than those based on the Bayesian approach. We then directly estimate and compare the two competing TSP and DSP models of real GDP within the Bayesian framework. Our empirical results suggest that a DSP model is preferred to a TSP model both in terms of in-sample fits and out-of-sample forecasts.

scholarly journals New class of Lindley distributions: properties and applications

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Duha Hamed ◽  
Ahmad Alzaghal
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Simulation Study ◽  
Likelihood Estimation ◽  
Statistical Properties ◽  
Data Sets ◽  
Lifetime Data ◽  
Unknown Parameters ◽  
Lindley Distribution ◽  
New Class

AbstractA new generalized class of Lindley distribution is introduced in this paper. This new class is called the T-Lindley{Y} class of distributions, and it is generated by using the quantile functions of uniform, exponential, Weibull, log-logistic, logistic and Cauchy distributions. The statistical properties including the modes, moments and Shannon’s entropy are discussed. Three new generalized Lindley distributions are investigated in more details. For estimating the unknown parameters, the maximum likelihood estimation has been used and a simulation study was carried out. Lastly, the usefulness of this new proposed class in fitting lifetime data is illustrated using four different data sets. In the application section, the strength of members of the T-Lindley{Y} class in modeling both unimodal as well as bimodal data sets is presented. A member of the T-Lindley{Y} class of distributions outperformed other known distributions in modeling unimodal and bimodal lifetime data sets.

scholarly journals Multivariate Hawkes processes: an application to financial data

2011 ◽  
Vol 48 (A) ◽  
pp. 367-378 ◽  
Author(s):  
Paul Embrechts ◽  
Thomas Liniger ◽  
Lu Lin
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Statistical Estimation ◽  
Goodness Of Fit ◽  
Likelihood Estimation ◽  
Financial Data ◽  
Data Sets ◽  
Hawkes Process ◽  
Science And Engineering ◽  
Hawkes Processes

A Hawkes process is also known under the name of a self-exciting point process and has numerous applications throughout science and engineering. We derive the statistical estimation (maximum likelihood estimation) and goodness-of-fit (mainly graphical) for multivariate Hawkes processes with possibly dependent marks. As an application, we analyze two data sets from finance.

scholarly journals Maximum likelihood estimation of the geometric niche preemption model

2021 ◽  
Author(s):  
Jan Graffelman
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Maximum Likelihood Estimator ◽  
Ecological Model ◽  
Likelihood Estimation ◽  
Data Sets ◽  
Likelihood Estimator ◽  
Two Samples ◽  
Multinomial Sampling ◽  
Geometric Decay

AbstractThe geometric series or niche preemption model is an elementary ecological model in biodiversity studies. The preemption parameter of this model is usually estimated by regression or iteratively by using May’s equation. This article proposes a maximum likelihood estimator for the niche preemption model, assuming a known number of species and multinomial sampling. A simulation study shows that the maximum likelihood estimator outperforms the classical estimators in this context in terms of bias and precision. We obtain the distribution of the maximum likelihood estimator and use it to obtain confidence intervals for the preemption parameter and to develop a preemption t test that can address the hypothesis of equal geometric decay in two samples. We illustrate the use of the new estimator with some empirical data sets taken from the literature and provide software for its use.

scholarly journals The Exponentiated Burr XII Power Series Distribution: Properties and Applications

Stats ◽  
2018 ◽  
Vol 2 (1) ◽  
pp. 15-31
Author(s):  
Arslan Nasir ◽  
Haitham Yousof ◽  
Farrukh Jamal ◽  
Mustafa Korkmaz
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Power Series ◽  
Likelihood Estimation ◽  
Real Data ◽  
Estimation Procedure ◽  
Model Parameters ◽  
Data Sets ◽  
Power Series Distributions ◽  
New Distribution

In this work, we introduce a new Burr XII power series class of distributions, which is obtained by compounding exponentiated Burr XII and power series distributions and has a strong physical motivation. The new distribution contains several important lifetime models. We derive explicit expressions for the ordinary and incomplete moments and generating functions. We discuss the maximum likelihood estimation of the model parameters. The maximum likelihood estimation procedure is presented. We assess the performance of the maximum likelihood estimators in terms of biases, standard deviations, and mean square of errors by means of two simulation studies. The usefulness of the new model is illustrated by means of three real data sets. The new proposed models provide consistently better fits than other competitive models for these data sets.

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