scholarly journals Frequentist Method

2020 ◽  
Author(s):  
Keyword(s):  
Frequentist Method

scholarly journals Comparing Parameter Estimation of Random Coefficient Autoregressive Model by Frequentist Method

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 62 ◽  
Author(s):  
Autcha Araveeporn
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Mean Square Error ◽  
Maximum Likelihood Method ◽  
Least Squares Method ◽  
Likelihood Function ◽  
Likelihood Method ◽  
Mean Square ◽  
Average Mean Square Error ◽  
Frequentist Method

This paper compares the frequentist method that consisted of the least-squares method and the maximum likelihood method for estimating an unknown parameter on the Random Coefficient Autoregressive (RCA) model. The frequentist methods depend on the likelihood function that draws a conclusion from observed data by emphasizing the frequency or proportion of the data namely least squares and maximum likelihood methods. The method of least squares is often used to estimate the parameter of the frequentist method. The minimum of the sum of squared residuals is found by setting the gradient to zero. The maximum likelihood method carries out the observed data to estimate the parameter of a probability distribution by maximizing a likelihood function under the statistical model, while this estimator is obtained by a differential parameter of the likelihood function. The efficiency of two methods is considered by average mean square error for simulation data, and mean square error for actual data. For simulation data, the data are generated at only the first-order models of the RCA model. The results have shown that the least-squares method performs better than the maximum likelihood. The average mean square error of the least-squares method shows the minimum values in all cases that indicated their performance. Finally, these methods are applied to the actual data. The series of monthly averages of the Stock Exchange of Thailand (SET) index and daily volume of the exchange rate of Baht/Dollar are considered to estimate and forecast based on the RCA model. The result shows that the least-squares method outperforms the maximum likelihood method.

Determining Uncertainty in NMR T2 Distribution Using Frequentist Method

2016 ◽  
Vol 47 (10) ◽  
pp. 1081-1094
Author(s):  
Youlong Zou ◽  
Ranhong Xie ◽  
Yejiao Ding ◽  
Alon Arad
Keyword(s):  
T2 Distribution ◽  
Nmr T2 Distribution ◽  
Frequentist Method

scholarly journals Rainfall thresholds for the possible occurrence of landslides in Italy

2010 ◽  
Vol 10 (3) ◽  
pp. 447-458 ◽  
Author(s):  
M. T. Brunetti ◽  
S. Peruccacci ◽  
M. Rossi ◽  
S. Luciani ◽  
D. Valigi ◽  
...  
Keyword(s):  
Slope Failure ◽  
Central Italy ◽  
Economic Damage ◽  
Small Data ◽  
Data Sets ◽  
Rainfall Thresholds ◽  
Campania Region ◽  
Landslide Occurrence ◽  
Abruzzo Region ◽  
Frequentist Method

Abstract. In Italy, rainfall is the primary trigger of landslides that frequently cause fatalities and large economic damage. Using a variety of information sources, we have compiled a catalogue listing 753 rainfall events that have resulted in landslides in Italy. For each event in the catalogue, the exact or approximate location of the landslide and the time or period of initiation of the slope failure is known, together with information on the rainfall duration D, and the rainfall mean intensity I, that have resulted in the slope failure. The catalogue represents the single largest collection of information on rainfall-induced landslides in Italy, and was exploited to determine the minimum rainfall conditions necessary for landslide occurrence in Italy, and in the Abruzzo Region, central Italy. For the purpose, new national rainfall thresholds for Italy and new regional rainfall thresholds for the Abruzzo Region were established, using two independent statistical methods, including a Bayesian inference method and a new Frequentist approach. The two methods proved complementary, with the Bayesian method more suited to analyze small data sets, and the Frequentist method performing better when applied to large data sets. The new regional thresholds for the Abruzzo Region are lower than the new national thresholds for Italy, and lower than the regional thresholds proposed in the literature for the Piedmont and Lombardy Regions in northern Italy, and for the Campania Region in southern Italy. This is important, because it shows that landslides in Italy can be triggered by less severe rainfall conditions than previously recognized. The Frequentist method experimented in this work allows for the definition of multiple minimum rainfall thresholds, each based on a different exceedance probability level. This makes the thresholds suited for the design of probabilistic schemes for the prediction of rainfall-induced landslides. A scheme based on four probabilistic thresholds is proposed. The four thresholds separate five fields, each characterized by different rainfall intensity-duration conditions, and corresponding different probability of possible landslide occurrence. The scheme can be implemented in landslide warning systems that operate on rainfall thresholds, and on precipitation measurements or forecasts.

scholarly journals Bayesian modeling and simulation to inform rare disease drug development early decision-making: application to Duchenne muscular dystrophy

2021 ◽  
Author(s):  
Janelle L. Lennie ◽  
John T. Mondick ◽  
Marc R. Gastonguay
Keyword(s):  
Decision Making ◽  
Natural History ◽  
Drug Development ◽  
Rare Disease ◽  
Bayesian Model ◽  
Short Term ◽  
Decision Accuracy ◽  
Model Based ◽  
Term Trial ◽  
Frequentist Method

AbstractRare disease clinical trials are constrained to small sample sizes and may lack placebo-control, leading to challenges in drug development. This paper proposes a Bayesian model-based framework for early go/no-go decision making in rare disease drug development, using Duchenne muscular dystrophy (DMD) as an example. Early go/no-go decisions were based on projections of long-term functional outcomes from a Bayesian model-based analysis of short-term trial data informed by prior knowledge based on 6MWT natural history literature data in DMD patients. Frequentist hypothesis tests were also applied as a reference analysis method. A number of combinations of hypothetical trial designs, drug effects and cohort comparison methods were assessed.The proposed Bayesian model-based framework was superior to the frequentist method for making go/no-go decisions across all trial designs and cohort comparison methods in DMD. The average decision accuracy rates across all trial designs for the Bayesian and frequentist analysis methods were 45.8 and 8.98%, respectively. A decision accuracy rate of at least 50% was achieved for 42 and 7% of the trial designs under the Bayesian and frequentist analysis methods, respectively. The frequentist method was limited to the short-term trial data only, while the Bayesian methods were informed with both the short-term data and prior information. The specific results of the DMD case study were limited due to incomplete specification of individual-specific covariates in the natural history literature data and should be reevaluated using a full natural history dataset. These limitations aside, the framework presented provides a proof of concept for the utility of Bayesian model-based methods for decision making in rare disease trials.

scholarly journals Confidence in confidence distributions!

2020 ◽  
Vol 476 (2237) ◽  
pp. 20190781
Author(s):  
Céline Cunen ◽  
Nils Lid Hjort ◽  
Tore Schweder
Keyword(s):  
Bayesian Analysis ◽  
Recent Article ◽  
Exact Analysis ◽  
Set Up ◽  
Conjunction Analysis ◽  
Frequentist Method

The recent article ‘Satellite conjunction analysis and the false confidence theorem’ (Balch et al . 2019, Satellite conjunction analysis and the false confidence theorem. Proc. R. Soc. A 475 , 20180565) points to certain difficulties with Bayesian analysis when used for models for satellite conjuntion and ensuing operative decisions. Here, we supplement these previous analyses and findings with further insights, uncovering what we perceive of as being the crucial points, explained in a prototype set-up where exact analysis is attainable. We also show that a different and frequentist method, involving confidence distributions, is free of the false confidence syndrome.

scholarly journals Forecasting Using Information and Entropy Based on Belief Functions

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Woraphon Yamaka ◽  
Songsak Sriboonchitta
Keyword(s):  
Objective Function ◽  
Likelihood Function ◽  
Prediction Interval ◽  
Empirical Studies ◽  
Simulated Data ◽  
Belief Function ◽  
Prediction Intervals ◽  
Belief Functions ◽  
Acceptable Range ◽  
Frequentist Method

This paper introduces an entropy-based belief function to the forecasting problem. While the likelihood-based belief function needs to know the distribution of the objective function for the prediction, the entropy-based belief function does not. This is because the observed data likelihood is somewhat complex in practice. We, thus, replace the likelihood function with the entropy. That is, we propose an approach in which a belief function is built from the entropy function. As an illustration, the proposed method is compared to the likelihood-based belief function in the simulation and empirical studies. According to the results, our approach performs well under a wide array of simulated data models and distributions. There are pieces of evidence that the prediction interval obtained from the frequentist method has a much narrower prediction interval, while our entropy-based method performs the widest. However, our entropy-based belief function still produces an acceptable range for prediction intervals as the true prediction value always lay in the prediction intervals.

scholarly journals Uncertainty analysis of the estimation of stony debris flow rainfall threshold: the application to the Backward Dynamical Approach

2020 ◽  
Author(s):  
Marta Martinengo ◽  
Daniel Zugliani ◽  
Giorgio Rosatti
Keyword(s):  
Debris Flow ◽  
Uncertainty Analysis ◽  
Flow Characteristics ◽  
Warning System ◽  
Rainfall Threshold ◽  
Rainfall Condition ◽  
Dynamical Approach ◽  
Critical Issues ◽  
Frequentist Method ◽  
The Impact

Abstract. Rainfall thresholds, namely rainfall intensity-duration conditions beyond which the probability of debris flow occurrence is considered significant, can be used as a forecasting tool in debris-flow early warning system. Many uncertainties may affect the thresholds calibration and, in turn, the reliability and effectiveness of this tool. The purpose of this study is to assess the uncertainty in the determination of the rainfall threshold for stony debris flow based on the Back Dynamical Approach (BDA) (Rosatti et al., 2019), an innovative method to estimate the rainfall duration and averaged intensity strictly related to measured debris flow. The uncertainty analysis has been computed performing two Monte Carlo cascade simulations: (i) to assess the variability in the estimate of rainfall conditions due to the uncertainty of some of the BDA parameters and (ii) to quantify the impact of this variability on the threshold parameters, obtained by using the frequentist method. Then, the deviation between these analysis outcomes and the values obtained in Rosatti et al. (2019) has been examined. The results highlight that the variability in the rainfall condition estimate is strongly related to the debris flow characteristics and the hyetograph shape. Depending on these features, the spreading of the obtained distributions can take both low and high values. Instead, the threshold parameters are characterised by a low statistical spreading. Finally, the consistency between the outcome of this study and the results obtained in Rosatti et al. (2019) has been proved and the critical issues related to the rainfall condition estimation have been discussed.

scholarly journals A network meta-analysis for neoadjuvant and adjuvant treatments for resectable squamous cell carcinoma of esophagus

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Yunpeng Zhao ◽  
Yongqiang Wang ◽  
Lei Shan ◽  
Chuanliang Peng ◽  
Wenhao Zhang ◽  
...  
Keyword(s):  
Squamous Cell Carcinoma ◽  
Cell Carcinoma ◽  
Squamous Cell ◽  
Meta Analysis ◽  
Multimodality Treatment ◽  
Extensive Literature ◽  
Significant Survival ◽  
Resectable Esophageal ◽  
Carcinoma Of Esophagus ◽  
Frequentist Method

AbstractThe optimal treatment for resectable esophageal squamous cell carcinoma (ESCC) is still a debatable point; however, randomized trials for strategies including neoadjuvant or adjuvant chemotherapy (CT), radiotherapy, or chemoradiotherapy (CRT) are not always available. This network meta-analysis aimed to identify an effective approach through indirect comparisons. An extensive literature search comparing multimodality treatment and surgery was performed, and a network meta-analysis was conducted with the frequentist method. Twenty-three trials including a total of 3636 ESCC patients were included. Neoadjuvant CRT and neoadjuvant CT, which were recommended by most guidelines for esophageal cancer, were associated with an overall survival advantage compared with surgery alone (HR = 0.43, 95% CI 0.26–0.73; HR = 0.71, 95% CI 0.32–1.59). A statistically significant survival benefit from neoadjuvant CRT compared with neoadjuvant CT could not be demonstrated in our study (HR = 0.61, 95% CI 0.32–1.17, P = 0.08). Our network meta-analysis showed that both neoadjuvant CRT and neoadjuvant CT were effective in improving the survival of patients with ESCC. Individual clinical decisions need further study in the future.

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