prediction interval
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Author(s):  
Panagiotis Balermpas ◽  
Janita E. van Timmeren ◽  
David J. Knierim ◽  
Matthias Guckenberger ◽  
Ilja F. Ciernik

Abstract Objective To seek evidence for osteoradionecrosis (ORN) after dental extractions before or after intensity-modulated radiotherapy (IMRT) for head and neck cancer (HNC). Methods Medline/PubMed, Embase, and Cochrane Library were searched from 2000 until 2020. Articles on HNC patients treated with IMRT and dental extractions were analyzed by two independent reviewers. The risk ratios (RR) and odds ratios (OR) for ORN related to extractions were calculated using Fisher’s exact test. A one-sample proportion test was used to assess the proportion of pre- versus post-IMRT extractions. Forest plots were used for the pooled RR and OR using a random-effects model. Results Seven of 630 publications with 875 patients were eligible. A total of 437 (49.9%) patients were treated with extractions before and 92 (10.5%) after IMRT. 28 (3.2%) suffered from ORN after IMRT. ORN was associated with extractions in 15 (53.6%) patients, eight related to extractions prior to and seven cases related to extractions after IMRT. The risk and odds for ORN favored pre-IMRT extractions (RR = 0.18, 95% CI: 0.04–0.74, p = 0.031, I2 = 0%, OR = 0.16, 95% CI: 0.03–0.99, p = 0.049, I2 = 0%). However, the prediction interval of the expected range of 95% of true effects included 1 for RR and OR. Conclusion Tooth extraction before IMRT is more common than after IMRT, but dental extractions before compared to extractions after IMRT have not been proven to reduce the incidence of ORN. Extractions of teeth before IMRT have to be balanced with any potential delay in initiating cancer therapy.


Sensors ◽  
2022 ◽  
Vol 22 (2) ◽  
pp. 525
Author(s):  
Ran Duan ◽  
Jie Liu ◽  
Jianzhong Zhou ◽  
Pei Wang ◽  
Wei Liu

The prognostic is the key to the state-based maintenance of Francis turbine units (FTUs), which consists of performance state evaluation and degradation trend prediction. In practical engineering environments, there are three significant difficulties: low data quality, complex variable operation conditions, and prediction model parameter optimization. In order to effectively solve the above three problems, an ensemble prognostic method of FTUs using low-quality data under variable operation conditions is proposed in this study. Firstly, to consider the operation condition parameters, the running data set of the FTU is constructed by the water head, active power, and vibration amplitude of the top cover. Then, to improve the robustness of the proposed model against anomaly data, the density-based spatial clustering of applications with noise (DBSCAN) is introduced to clean outliers and singularities in the raw running data set. Next, considering the randomness of the monitoring data, the healthy state model based on the Gaussian mixture model is constructed, and the negative log-likelihood probability is calculated as the performance degradation indicator (PDI). Furthermore, to predict the trend of PDIs with confidence interval and automatically optimize the prediction model on both accuracy and certainty, the multiobjective prediction model is proposed based on the non-dominated sorting genetic algorithm and Gaussian process regression. Finally, monitoring data from an actual large FTU was used for effectiveness verification. The stability and smoothness of the PDI curve are improved by 3.2 times and 1.9 times, respectively, by DBSCAN compared with 3-sigma. The root-mean-squared error, the prediction interval normalized average, the prediction interval coverage probability, the mean absolute percentage error, and the R2 score of the proposed method achieved 0.223, 0.289, 1.000, 0.641%, and 0.974, respectively. The comparison experiments demonstrate that the proposed method is more robust to low-quality data and has better accuracy, certainty, and reliability for the prognostic of the FTU under complex operating conditions.


Author(s):  
Wassim R. Abou Ghaida ◽  
Ayman Baklizi

AbstractWe consider the prediction of future observations from the log-logistic distribution. The data is assumed hybrid right censored with possible left censoring. Different point predictors were derived. Specifically, we obtained the best unbiased, the conditional median, and the maximum likelihood predictors. Prediction intervals were derived using suitable pivotal quantities and intervals based on the highest density. We conducted a simulation study to compare the point and interval predictors. It is found that the point predictor BUP and the prediction interval HDI have the best overall performance. An illustrative example based on real data is given.


Forecasting ◽  
2021 ◽  
Vol 4 (1) ◽  
pp. 1-25
Author(s):  
Thabang Mathonsi ◽  
Terence L. van Zyl

Hybrid methods have been shown to outperform pure statistical and pure deep learning methods at forecasting tasks and quantifying the associated uncertainty with those forecasts (prediction intervals). One example is Exponential Smoothing Recurrent Neural Network (ES-RNN), a hybrid between a statistical forecasting model and a recurrent neural network variant. ES-RNN achieves a 9.4% improvement in absolute error in the Makridakis-4 Forecasting Competition. This improvement and similar outperformance from other hybrid models have primarily been demonstrated only on univariate datasets. Difficulties with applying hybrid forecast methods to multivariate data include (i) the high computational cost involved in hyperparameter tuning for models that are not parsimonious, (ii) challenges associated with auto-correlation inherent in the data, as well as (iii) complex dependency (cross-correlation) between the covariates that may be hard to capture. This paper presents Multivariate Exponential Smoothing Long Short Term Memory (MES-LSTM), a generalized multivariate extension to ES-RNN, that overcomes these challenges. MES-LSTM utilizes a vectorized implementation. We test MES-LSTM on several aggregated coronavirus disease of 2019 (COVID-19) morbidity datasets and find our hybrid approach shows consistent, significant improvement over pure statistical and deep learning methods at forecast accuracy and prediction interval construction.


Pharmaceutics ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2076
Author(s):  
Gust Nuytten ◽  
Susan Ríos Revatta ◽  
Pieter-Jan Van Bockstal ◽  
Ashish Kumar ◽  
Joris Lammens ◽  
...  

During the spin freezing step of a recently developed continuous spin freeze-drying technology, glass vials are rapidly spun along their longitudinal axis. The aqueous drug formulation subsequently spreads over the inner vial wall, while a cold gas flow is used for cooling and freezing the product. In this work, a mechanistic model was developed describing the energy transfer during each phase of spin freezing in order to predict the vial and product temperature change over time. The uncertainty in the model input parameters was included via uncertainty analysis, while global sensitivity analysis was used to assign the uncertainty in the model output to the different sources of uncertainty in the model input. The model was verified, and the prediction interval corresponded to the vial temperature profiles obtained from experimental data, within the limits of the uncertainty interval. The uncertainty in the model prediction was mainly explained (>96% of uncertainty) by the uncertainty in the heat transfer coefficient, the gas temperature measurement, and the equilibrium temperature. The developed model was also applied in order to set and control a desired vial temperature profile during spin freezing. Applying this model in-line to a continuous freeze-drying process may alleviate some of the disadvantages related to batch freeze-drying, where control over the freezing step is generally poor.


2021 ◽  
Author(s):  
Wei Zhang ◽  
Zhen He ◽  
Di WANG

Abstract Distribution regression is the regression case where the input objects are distributions. Many machine learning problems can be analysed in this framework, such as multi-instance learning and learning from noisy data. This paper attempts to build a conformal predictive system(CPS) for distribution regression, where the prediction of the system for a test input is a cumulative distribution function(CDF) of the corresponding test label. The CDF output by a CPS provides useful information about the test label, as it can estimate the probability of any event related to the label and be transformed to prediction interval and prediction point with the help of the corresponding quantiles. Furthermore, a CPS has the property of validity as the prediction CDFs and the prediction intervals are statistically compatible with the realizations. This property is desired for many risk-sensitive applications, such as weather forecast. To the best of our knowledge, this is the first work to extend the learning framework of CPS to distribution regression problems. We first embed the input distributions to a reproducing kernel Hilbert space using kernel mean embedding approximated by random Fourier features, and then build a fast CPS on the top of the embeddings. While inheriting the property of validity from the learning framework of CPS, our algorithm is simple, easy to implement and fast. The proposed approach is tested on synthetic data sets and can be used to tackle the problem of statistical postprocessing of ensemble forecasts, which demonstrates the effectiveness of our algorithm for distribution regression problems.


BMJ Open ◽  
2021 ◽  
Vol 11 (12) ◽  
pp. e050525
Author(s):  
Guttorm Raknes ◽  
Marianne Sørlie Strøm ◽  
Gerhard Sulo ◽  
Simon Øverland ◽  
Mathieu Roelants ◽  
...  

ObjectiveTo explore the potential impact of the first wave of COVID-19 pandemic on all cause and cause-specific mortality in Norway.DesignPopulation-based register study.SettingThe Norwegian cause of Death Registry and the National Population Register of Norway.ParticipantsAll recorded deaths in Norway from March to May from 2010 to 2020.Main outcome measuresRate (per 100 000) of all-cause mortality and causes of death in the European Shortlist for Causes of Death from March to May 2020. The rates were age standardised and adjusted to a 100% register coverage and compared with a 95% prediction interval (PI) from linear regression based on corresponding rates for 2010–2019.Results113 710 deaths were included, of which 10 226 were from 2020. We did not observe any deviation from predicted total mortality. There were fewer than predicted deaths from chronic lower respiratory diseases excluding asthma (11.4, 95% PI 11.8 to 15.2) and from other non-ischaemic, non-rheumatic heart diseases (13.9, 95% PI 14.5 to 20.2). The death rates were higher than predicted for Alzheimer’s disease (7.3, 95% PI 5.5 to 7.3) and diabetes mellitus (4.1, 95% PI 2.1 to 3.4).ConclusionsThere was no significant difference in the frequency of the major causes of death in the first wave of the 2020 COVID-19 pandemic in Norway compared with corresponding periods 2010–2019. There was an increase in diabetes mellitus and Alzheimer’s deaths. Reduced mortality due to some heart and lung conditions may be linked to infection control measures.


Entropy ◽  
2021 ◽  
Vol 23 (12) ◽  
pp. 1608
Author(s):  
Benjamin Kompa ◽  
Jasper Snoek ◽  
Andrew L. Beam

Uncertainty quantification for complex deep learning models is increasingly important as these techniques see growing use in high-stakes, real-world settings. Currently, the quality of a model’s uncertainty is evaluated using point-prediction metrics, such as the negative log-likelihood (NLL), expected calibration error (ECE) or the Brier score on held-out data. Marginal coverage of prediction intervals or sets, a well-known concept in the statistical literature, is an intuitive alternative to these metrics but has yet to be systematically studied for many popular uncertainty quantification techniques for deep learning models. With marginal coverage and the complementary notion of the width of a prediction interval, downstream users of deployed machine learning models can better understand uncertainty quantification both on a global dataset level and on a per-sample basis. In this study, we provide the first large-scale evaluation of the empirical frequentist coverage properties of well-known uncertainty quantification techniques on a suite of regression and classification tasks. We find that, in general, some methods do achieve desirable coverage properties on in distribution samples, but that coverage is not maintained on out-of-distribution data. Our results demonstrate the failings of current uncertainty quantification techniques as dataset shift increases and reinforce coverage as an important metric in developing models for real-world applications.


2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
G. Ramkumar ◽  
Satyajeet Sahoo ◽  
T. M. Amirthalakshmi ◽  
S. Ramesh ◽  
R. Thandaiah Prabu ◽  
...  

Solar energy conversion efficiency has improved by the advancement technology of photovoltaic (PV) and the involvement of administrations worldwide. However, environmental conditions influence PV power output, resulting in randomness and intermittency. These characteristics may be harmful to the power scheme. As a conclusion, precise and timely power forecast information is essential for the power networks to engage solar energy. To lessen the negative impact of PV electricity usage, the offered short-term solar photovoltaic (PV) power estimate design is based on an online sequential extreme learning machine with a forgetting mechanism (FOS-ELM) under this study. This approach can replace existing knowledge with new information on a continuous basis. The variance of model uncertainty is computed in the first stage by using a learning algorithm to provide predictable PV power estimations. Stage two entails creating a one-of-a-kind PI based on cost function to enhance the ELM limitations and quantify noise uncertainty in respect of variance. As per findings, this approach does have the benefits of short training duration and better reliability. This technique can assist the energy dispatching unit list producing strategies while also providing temporal and spatial compensation and integrated power regulation, which are crucial for the stability and security of energy systems and also their continuous optimization.


2021 ◽  
Vol 9 ◽  
Author(s):  
Mao Yang ◽  
Tian Peng ◽  
Xin Su ◽  
Miaomiao Ma

The periodicity and non-stationary nature of photovoltaic (PV) output power make the point prediction result contain very little information, increase the difficulty of describing the prediction uncertainty, and it is difficult to ensure the most efficient operation of the power system. Effectively predicting the PV power range will greatly improve the economics and stability of the grid. Therefore, this paper proposes an improved generalized based on the combination of wavelet packet (WP) and least squares support vector machine (LSSVM) to obtain higher accuracy point prediction results. The error mixed distribution function is used to fit the probability distribution of the prediction error, and the probability prediction is performed to obtain the prediction interval. The coverage rate and average width of the prediction interval are used as indicators to evaluate the prediction results of the interval. By comparing with the results of conventional methods based on normal distribution, at 95 and 90% confidence levels, the method proposed in this paper achieves higher coverage while reducing the average bandwidth by 5.238 and 3.756%, which verifies the effectiveness of the proposed probability interval prediction method.


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