Maximum Likelihood Estimation

Scholz, Fritz

doi:10.1002/0471667196.ess1571.pub2

Cited by 94 publications

(21 citation statements)

References 45 publications

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“…Then, we use maximum likelihood estimation (MLE) to estimate the order p and q together with the coefficients. The MLE technique finds the values of the parameters that maximize the probability of obtaining the data that we have observed (Scholz, ). MLE estimates are obtained by minimizing Akaike information criteria (AIC) (Akaike, ):

AIC = - 2 log ((), L) + 2 k

where L is the likelihood of pollutants.…”

Section: Methodsmentioning

confidence: 99%

Time Series Forecasting of Air Quality Based On Regional Numerical Modeling in Hong Kong

et al. 2018

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Based on prevailing numerical forecasting models (Community Multiscale Air Quality [CMAQ] model , Comprehensive Air Quality Model with Extensions, and Nested Air Quality Prediction Modeling System) and observations from monitoring stations in Hong Kong, we employ a set of autoregressive integrated moving average (ARIMA) models with numerical forecasts (ARIMAX) to improve the forecast of air pollutants including PM2.5, NO2, and O3. The results show significant improvements in multiple evaluation metrics for daily (1–3 days) and hourly (1–72 hr) forecast. Forecasts on daily 1‐hr and 8‐hr maximum O3 are also improved. For instance, compared with CMAQ, applying CMAQ‐ARIMA reduces average root‐mean‐square errors (RMSEs) at all stations for daily average PM2.5, NO2, and O3 in the next 3 days by 14.3–21.0%, 41.2–46.3%, and 47.8–49.7%, respectively. For hourly forecasts in the next 72 hr, reductions in RMSEs brought by ARIMAX using CMAQ are 18.2% for PM2.5, 32.1% for NO2, and 36.7% for O3. Large improvements in RMSEs are achieved for nonrural PM2.5 and rural NO2 using ARIMAX with three numerical models. Dynamic hourly forecast shows that ARIMAX can be applied for forecast of 7‐ to 72‐hr PM2.5, 4‐ to 72‐hr NO2, and 4‐ to 6‐hr O3. Besides applying ARIMAX for NO2, we recommend a mixed forecast strategy to ARIMAX for normal values of PM2.5 and O3 and employ numerical models for outputs above 75th percentile of historical observations. Our hybrid ARIMAX method can combine the advantage of ARIMA and numerical modeling to assist real‐time air quality forecasting efficiently and consistently.

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AIC = - 2 log ((), L) + 2 k

where L is the likelihood of pollutants.…”

Section: Methodsmentioning

confidence: 99%

Time Series Forecasting of Air Quality Based On Regional Numerical Modeling in Hong Kong

et al. 2018

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“…If x has a Rician distribution with parameters s and ϑ, then (x/ϑ) 2 has a non-central chi-square distribution with two degrees of freedom and non-centrality parameter (s/ϑ) 2 . The parameters (θ) of the presented models were estimated using the method of maximum likelihood [38].…”

Section: Speckle Modelingmentioning

confidence: 99%

Assessment of corneal properties based on statistical modeling of OCT speckle

Jesus¹,

Iskander²

2016

Biomed. Opt. Express

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A new approach to assess the properties of the corneal micro-structure based on the statistical modeling of speckle obtained from Optical Coherence Tomography (OCT) is presented. A number of statistical models were proposed to fit the corneal speckle data obtained from OCT raw image. Short-term changes in corneal properties were studied by inducing corneal swelling whereas age-related changes were observed analyzing data of sixty-five subjects aged between twenty-four and seventy-three years. Generalized Gamma distribution has shown to be the best model, in terms of the Akaike's Information Criterion, to fit the OCT corneal speckle. Its parameters have shown statistically significant differences (Kruskal-Wallis, < 0.001) for short and age-related corneal changes. In addition, it was observed that age-related changes influence the corneal biomechanical behaviour when corneal swelling is induced. This study shows that Generalized Gamma distribution can be utilized to modeling corneal speckle in OCT providing complementary quantified information where micro-structure of corneal tissue is of essence.

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“…We will be using exponential, gamma, Rayleigh, log-normal, Mittag-Leffler, generalised Pareto and Weibull distibutions. All of these will have best fit parameters chosen using by three different methodsmethod of moments [2], maximum likelihood estimators [20], and the curve fitting tool in MAT-LAB (non-linear least squares) -and then compared to the empirical complementary cumulative distribution functions (eCCDFs) of the original data to determine which one is most optimal.…”

Section: B Properties Identified From Original Datamentioning

confidence: 99%

“…The use of networks to model contact patterns or interactions between individuals has proved to be a step change in how epidemics and other spreading processes are modelled [3,10,12,15,27,28]. The basic ingredient of such models is to represent individuals by nodes and contacts between these as links between nodes.…”

Section: Introductionmentioning

confidence: 99%

The Mathematics of Human Contact: Developing a Model for Social Interaction in School Children

et al. 2018

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In this paper, we provide a statistical analysis of high-resolution contact pattern data within primary and secondary schools as collected by the SocioPatterns collaboration. Students are graphically represented as nodes in a temporally evolving network, in which links represent proximity or interaction between students.This article focuses on link-and node-level statistics, such as the on-and off-durations of links as well as the activity potential of nodes and links.Parametric models are fitted to the on-and off-durations of links, inter-event times and node activity potentials and, based on these, we propose a number of theoretical models that are able to reproduce the collected data within varying levels of accuracy. By doing so, we aim to identify the minimal network-level properties that are needed to closely match the real-world data, with the aim of combining this contact pattern model with epidemic models in future work.

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Maximum Likelihood Estimation

Cited by 94 publications

References 45 publications

Time Series Forecasting of Air Quality Based On Regional Numerical Modeling in Hong Kong

Time Series Forecasting of Air Quality Based On Regional Numerical Modeling in Hong Kong

Assessment of corneal properties based on statistical modeling of OCT speckle

The Mathematics of Human Contact: Developing a Model for Social Interaction in School Children

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