Informal statistical models and modeling

Enhanced understanding of historical climate impacts on crop yield is critical for adaptation and mitigations within the context of global warming. Previous impact assessments rely on statistical or process‐based models, each with its own strength and weakness. To date, a global‐scale comparison between process‐based and statistical models in assessing climate impacts on yield variability and trends is lacking. Here, we leverage both statistical and process models to estimate global impacts of climate variability and trend on maize yield between 1980 and 2010. To allow for reasonable comparability, we develop a novel emulator to mimic each of eight global process‐based maize models, based on which the common set of climate scenarios are used for driving both statistical and process models. Results show that climate variability controls 42% of global maize yield variations in statistical model, while large discrepancy is found in process‐based models with R2 ranging from 0.22 to 0.61, especially at the country scale. Both statistical and most process models suggest that historical climate trend has led to a yield loss by 1.51–3.80% during the period 1980–1990. As for the period 1991–2000, however, the observed negative climate impacts are only captured by two process models. In contrast to the positive climate impact in statistical model, most of process‐based models simulated negative climate effects for the period 2001–2010, due to large yield sensitivity to maximum temperature in process models. This study highlights the large discrepancies not only among the eight process‐based models but also between statistical and process‐based models in simulating yield response to climate variation and trends, which has great implications for projecting future crop yields under climate change.

In OBS networks, the delay of control packets in the switch control unit (SCU) of core nodes influences burst loss performance in the optical switching and should be constrained. Furthermore, the end-to-end (E2E) delay requirements of premium services need queueing delay guarantee in network nodes throughout the transmission path. For this purpose, a framework for deterministic delay guarantee is proposed in this article. It incorporates the deterministic delay model in the ingress edge node as well as in the SCUs of core nodes. On this basis, the configuration of the assembler and the offset time is addressed by means of an optimization problem under the delay constraints. Scenario studies are carried out with reference to realistic transport network topologies. Compared to statistical delay models in the literature, the deterministic model has advantages in rendering robust absolute delay guarantee for individual FEC flows, which is especially appreciated in the provisioning of premium services. By performance evaluation in comparison with the statistical models, it is shown that the adopted deterministic delay models lead to practical delay bounds in a magnitude that is close to the delay estimations by stochastic analysis.

BackgroundIrreversible electroporation (IRE) is a minimally invasive tissue ablation technique which utilizes electric pulses delivered by electrodes to a targeted area of tissue to produce high amplitude electric fields, thus inducing irreversible damage to the cell membrane lipid bilayer. An important application of this technique is for cancer tissue ablation. Mathematical modelling is considered important in IRE treatment planning. In the past, IRE mathematical modelling used a deterministic single value for the amplitude of the electric field required for causing cell death. However, tissue, particularly cancerous tissue, is comprised of a population of different cells of different sizes and orientations, which in conventional IRE are exposed to complex electric fields; therefore, using a deterministic single value is overly simplistic.MethodsWe introduce and describe a new methodology for evaluating IRE induced cell death in tissue. Our approach employs a statistical Peleg-Fermi model to correlate probability of cell death in heterogeneous tissue to the parameters of electroporation pulses such as the number of pulses, electric field amplitude and pulse length. For treatment planning, the Peleg-Fermi model is combined with a numerical solution of the multidimensional electric field equation cast in a dimensionless form. This is the first time in which this concept is used for evaluating IRE cell death in multidimensional situations.ResultsWe illustrate the methodology using data reported in literature for prostate cancer cell death by IRE. We show how to fit this data to a Fermi function in order to calculate the critical statistic parameters. To illustrate the use of the methodology, we simulated 2-D irreversible electroporation protocols and produced 2-D maps of the statistical distribution of cell death in the treated region. These plots were compared to plots produced using a deterministic model of cell death by IRE and the differences were noted.ConclusionsIn this work we introduce a new methodology for evaluation of tissue ablation by IRE using statistical models of cell death. We believe that the use of a statistical model rather than a deterministic model for IRE cell death will improve the accuracy of treatment planning for cancer treatment with IRE.

Accurately estimating the return values of significant wave height is essential for marine and coastal infrastructure, particularly as climate change intensifies the frequency and intensity of extreme wave events. Traditional models, which assume stationarity in wave data, often underestimate future risks by neglecting the impacts of climate change on wave dynamics. Combining time series decomposition and recurrence analysis, the research develops a nonstationary framework to predict significant wave height. The stochastic component is modelled using a stationary probability distribution, while the deterministic component is predicted based on sea surface temperature projections from CMIP6 climate scenarios. The model evaluation demonstrates strong predictive capability for both stochastic and deterministic components. Application of the model to China’s coastal waters reveals significant discrepancies between stationary and nonstationary return value estimates. Compared to conventional distribution models, the nonstationary model predicts substantial increases in extreme wave heights. These findings underscore the importance of adopting nonstationary models to more accurately assess future risks posed by extreme wave events in a changing climate.

The intraday seasonal variance pattern contains stochastic as well as deterministic components. Therefore, the estimation of information arrivals in the associated volatility process requires the proper filtering of both of these seasonal components. However, popular current models remove only the deterministic part of the typical U‐shape volatility. Here, we provide the first empirical results of the importance of the stochastic component, as developed by Cho and Daigler (2012). We show that a highly significant additional 8.5% to 12.9% of the total seasonal variance is explained by the stochastic seasonal variance component for S&P500 futures, live cattle futures, and the Japanese yen‐U.S. dollar spot exchange rate. Moreover, we show that the stochastic seasonal filtering model implemented here does not create any statistical distortions of the filtered series, as occurs with deterministic‐based seasonal adjustment processes, as well as comparing the model examined here with the most popular current deterministic model. As part of our analysis we examine the application of the model to macroeconomic news and out‐of‐sample results for the model. © 2012 Wiley Periodicals, Inc. Jrl Fut Mark 34:479–495, 2014

The most widely accepted and used definition of probability is the relative-frequency definition. Strict adherence to this interpretation of probability requires the empirical development of statistical models from measured data. Using this definition of probability usually results in statistical models that are adequate for predicting the occurrence of the most common events, i.e., events near the mean. However, experience has shown that the resulting statistical models are often not adequate for predicting the occurrence of rare or extreme events, for which little or no data exist. In electrical engineering and the other physical sciences, an alternative approach exists for developing the statistical models. This approach is predicated on the existence of valid deterministic models of the phenomena or interaction of interest. The statistical models are derived from the deterministic models by making assumptions about the behavior of the parameters in the deterministic models. Physics-based statistical modeling can be applied to derive both strength and stress distributions. In the present paper, a strength example is developed-the thermal failure of semiconductor devices subjected to electrical overstress. Typical comparisons of predicted failure, based on the derived distributions, to measured data are presented.

Producing predictions of the probabilistic risks of operating materials for given lengths of time at stated operating conditions requires the assimilation of existing deterministic creep life prediction models (that only predict the average failure time) with statistical models that capture the random component of creep. To date, these approaches have rarely been combined to achieve this objective. The first half of this paper therefore provides a summary review of some statistical models to help bridge the gap between these two approaches. The second half of the paper illustrates one possible assimilation using 1Cr1Mo-0.25V steel. The Wilshire equation for creep life prediction is integrated into a discrete hazard based statistical model—the former being chosen because of its novelty and proven capability in accurately predicting average failure times and the latter being chosen because of its flexibility in modelling the failure time distribution. Using this model it was found that, for example, if this material had been in operation for around 15 years at 823 K and 130 MPa, the chances of failure in the next year is around 35%. However, if this material had been in operation for around 25 years, the chance of failure in the next year rises dramatically to around 80%.

The importance of the stochastic component of climatic variables in simulating the thermal behaviour of domestic dwellings

To effectively dimension and rollout a cellular network, accurate site-specific field strength predictions are required. Traditionally, operators make use of high-speed statistical propagation models for each proposed base site. Today's advanced cellular networks place a greater emphasis on urban microcellular deployment. It is well known that statistical models perform poorly in such environments. To overcome these limitations, the use of deterministic propagation modelling is common. However, although such models enhance prediction accuracy, they also require excessive computation time. A new hybrid statistical/deterministic field strength prediction model is proposed that combines the speed of a statistical model with the site-specific accuracy of a deterministic ray model. Results indicate that the new hybrid model can produce very accurate field strength prediction grids with computing times reduced by one to two orders of magnitude. For the example considered, the computing time for a one square kilometer grid comprising 10000 points (100 by 100) has been reduced from 20 mins to just over 4 minutes (running on an 800 MHz Pentium III). For more complex ray models and/or higher grid densities, even higher speed-up factors can be achieved.

In recent decades, warming temperatures have caused sharp reductions in the volume of sea ice in the Arctic Ocean. Predicting changes in Arctic sea ice thickness is vital in a changing Arctic for making decisions about shipping and resource management in the region. We propose a statistical spatio-temporal two-stage model for sea ice thickness and use it to generate probabilistic forecasts up to three months into the future. Our approach combines a contour model to predict the ice-covered region with a Gaussian random field to model ice thickness conditional on the ice-covered region. Using the most complete estimates of sea ice thickness currently available, we apply our method to forecast Arctic sea ice thickness. Point predictions and prediction intervals from our model offer comparable accuracy and improved calibration compared with existing forecasts. We show that existing forecasts produced by ensembles of deterministic dynamic models can have large errors and poor calibration. We also show that our statistical model can generate good forecasts of aggregate quantities such as overall and regional sea ice volume. Supplementary materials accompanying this paper appear on-line.

Propagation conditions in an underwater acoustic channel are known to vary in time, causing the received signal strength to deviate from the nominal value predicted by a deterministic propagation model. To facilitate large-scale system design in such conditions (e.g. power allocation), we develop a statistical propagation model in which the transmission loss is treated as a random variable. By repetitive computation of acoustic field using ray tracing for a set of varying environmental conditions (surface height, wave activity, small displacements of transmitter and receiver around nominal locations), an ensemble of transmission losses is compiled which is then used to infer the statistical model parameters. A reasonable agreement is found with log-normal distribution, whose mean obeys a log-distance increases, and whose variance appears to be constant for a certain range of inter-node distances in a given deployment location. The statistical model is deemed useful for higher-level system planning, where simulation is needed to assess the performance of candidate network protocols under various resource allocation policies, i.e. to determine the transmit power and bandwidth allocation necessary to achieve a desired level of performance (connectivity, throughput, reliability, etc.).

Spectral modeling synthesis (SMS) has been used as a powerful tool for musical sound modeling. This technique considers a sound as a combination of a deterministic plus a stochastic component. The deterministic component is represented by the series of sinusoids that are described by amplitude, frequency, and phase functions and the stochastic component is represented by a series of magnitude spectrum envelopes that functions as a time varying filter excited by white noise. These representations make it possible for a synthesized sound to attain all the perceptual characteristics of the original sound. However, sometimes considerable phase variations occur in the deterministic component by using the conventional SMS for the complex sound such as whale sounds when the partial frequencies in successive frames differ. This is because it utilizes the calculated phase to synthesize deterministic component of the sound. As a result, it does not provide a good spectrum matching between original and synthesized spectrum in higher frequency region. To overcome this problem, we propose a modified SMS that provides good spectrum matching of original and synthesized sound by calculating complex residual spectrum in frequency domain and utilizing original phase information to synthesize the deterministic component of the sound. Analysis and simulation results for synthesizing whale sounds suggest that the proposed method is comparable to the conventional SMS in both time and frequency domain. However, the proposed method outperforms the SMS in better spectrum matching.

The modes' reconstruction into the stochastic and deterministic components is proposed for forecasting the crude oil prices with the concept of “divide and conquer” and modes reconstruction. It is to reduce the complexity in the computation and to enhance the forecasting accuracy of the decomposition ensemble technique. Under the framework of “divide and conquer”, the decomposition and ensemble methodologies of forecasting power successfully improves with the proposed model based on the modes' reconstruction. The corresponding reconstruction is using average mutual information (AMI). The proposed procedure is based on four layers i.e., complex data decomposition, reconstruction of modes into components, the prediction of each individual component and assembling the final prediction. In the proposed procedure, the modes of the stochastic component are analyzed thoroughly as it influences the prediction results significantly. For verification and illustration purposes, the case study of Brent and West Texas Intermediate (WTI) daily crude oil prices data are used, and the empirical study confirms that the outcomes outperform all the considered benchmark models, including auto-regressive integrated moving average (ARIMA) model, generalized autoregressive conditional heteroscedasticity (GARCH) model, NAIVE model, ARIMA Kalman Filter model. This outcome is achieved, with the reconstruction decomposition ensemble (RDE) model along stochastic and deterministic components. Hence, it is concluded that the proposed model achieved higher forecasting accuracy and takes less computational time with the modes' reconstruction as opposed to using all the decompose modes.

Wind power prediction based on numerical and statistical models

Many of the available solar radiation databases only provide global horizontal irradiance (GHI) while there is a growing need of extensive databases of direct normal radiation (DNI) mainly for the development of concentrated solar power and concentrated photovoltaic technologies. In the present work, we propose a methodology for the generation of synthetic DNI hourly data from the hourly average GHI values by dividing the irradiance into a deterministic and stochastic component intending to emulate the dynamics of the solar radiation. The deterministic component is modeled through a simple classical model. The stochastic component is fitted to measured data in order to maintain the consistency of the synthetic data with the state of the sky, generating statistically significant DNI data with a cumulative frequency distribution very similar to the measured data. The adaptation and application of the model to the location of Seville shows significant improvements in terms of frequency distribution over the classical models. The proposed methodology applied to other locations with different climatological characteristics better results than the classical models in terms of frequency distribution reaching a reduction of the 50% in the Finkelstein-Schafer (FS) and Kolmogorov-Smirnov test integral (KSI) statistics.