Statistical Estimation Approach Research Articles

Frequency analysis of droughts using historical information – new approach for probability plotting position: deceedance probability

This paper presents a new statistical approach for droughts estimation. The conducted frequency analysis uses for the first time the ‘Deceedance’ Probability using historical information. The developed approach was applied for the first time in Tunisia. The annual rainfall was fitted to eight distribution functions. A rigorous evaluation of the historical information, in terms of completeness and authenticity, is undertaken. It is shown that Weibull’s formula matched with the Log-Normal-III and Log-Pearson-III distributions gave the highest fit. These results are of practical relevance to water resources managers in arid and semi-arid regions for applications in droughts management and risk analysis.

Reading Between the Spikes of the Hypothalamic Neural Code

Reading the spike coding of hypothalamic neurones presents a considerable challenge because they exhibit highly irregular firing patterns. Electrophysiologists working in the motor and sensory systems, in which neurones fire more regularly, have devised satisfactory methods to describe the firing of cells, although the statistical assumptions that underlie the methods do not apply to hypothalamic neurones. Measurement of neural activity is nevertheless vital to characterise the activity of neuroendocrine cells. It has thus become necessary to develop methods suitable for the analysis of the highly irregular spike discharge patterns of both spontaneous and stimulus-evoked firing of hypothalamic neurones. We review techniques used to meet this challenge and demonstrate their considerable capacity to address important physiological questions. We also introduce a novel approach for valid statistical estimation of the information conveyed by the response of a single neurone to a periodic stimulus. The approach demonstrated significant diurnal rhythms of synaptic connectivity between hypothalamic nuclei.

On the impact of routing matrix inconsistencies on statistical path monitoring in overlay networks

Overlay networks can be used to find working paths when direct underlay paths are anomalously slow, e.g. because of a network fault. Overlay paths should not use links that are involved in a fault, so choosing which overlay path to use often requires path monitoring, which introduces an overhead. By using a routing matrix 'M' to define which links are used in each path, and sorting the matrix according to the degree of independence of paths, we can choose a reduced set of paths to monitor, and so reduce overheads. The state of the unmonitored paths are then predicted using statistical estimation techniques based on information inferred from the monitored paths. However, such methods assume knowledge of routing matrix. We investigate the impact on such methods when knowledge of the routing matrix is only approximate, e.g. as obtained using simple tools like traceroute which have been previously blamed for incorrect mapping of the topology of real world IP networks. This paper investigates the impact of routing matrix errors on such statistical path estimation approaches. We show that mitigation or removal of such errors leads to improved path metric prediction and anomaly detection.

Probabilistic Estimation of Multivariate Streamflow Using Independent Component Analysis and Climate Information

Abstract A statistical estimation approach is presented and applied to multiple reservoir inflow series that form part of Sydney’s water supply system. The approach involves first identifying sources of interannual and interdecadal climate variability using a combination of correlation- and wavelet-based methods, then using this information to construct probabilistic, multivariate seasonal estimates using a method based on independent component analysis (ICA). The attraction of the ICA-based approach is that, by transforming the multivariate dataset into a set of independent time series, it is possible to maintain the parsimony of univariate statistical methods while ensuring that both the spatial and temporal dependencies are accurately captured. Based on a correlation analysis of the reservoir inflows with the original sea surface temperature anomaly data, the principal sources of variability in Sydney’s reservoir inflows appears to be a combination of the El Niño–Southern Oscillation (ENSO) phenomenon and the Pacific decadal oscillation (PDO). A multivariate ICA-based estimation model was then used to capture this variability, and it was shown that this approach performed well in maintaining the temporal dependence while also accurately maintaining the spatial dependencies that exist in the 11-dimensional historical reservoir inflow dataset.

Bayesian strategy of accuracy estimation for characteristics retrieved from experimental data using base dynamic models of atmospheric photochemical systems

We develop a general approach for statistical estimation of accuracy of the characteristics of atmospheric photochemical systems retrieved from noisy time series of experimental data using base dynamic models. The practical value of such an approach was demonstrated by the example of retrieval of the spatio-temporal evolution of mesospheric photochemistry from satelliteborne measurements of ozone and hydroxyl concentrations. This made it possible, in particular, to determine the vertical profile of water-vapor concentration in this region of the atmosphere.

Statistical Approach for Cycle Time Estimation in Semiconductor Packaging Factories

In the semiconductor industry, to enhance customer satisfactions and ability of quick responses, the development of cycle time estimation model is very important. Cycle time estimation is an essential planning basis, which has many applications, especially on the analyses of performance indexes, capacity planning, and the assignments of due dates. In this paper, we provide a statistical approach for cycle time estimation in semiconductor plastic ball grid array (PBGA) packaging factories. Due to today's fierce competitive environments in the semiconductor industry, planners involved in PBGA packaging factories need an approach to obtain estimated cycle times with different confidence to ensure the due date assignments more accurately. Therefore, upper confidence bounds of estimated cycle times at various confidence coefficients are also presented in this paper. We demonstrate the applicability of the proposed cycle time estimation model incorporating the upper confidence bounds by presenting a real-world example taken from a PBGA packaging shop floor in a semiconductor packaging factory located in the Science-Based Industrial Park in Hsinchu, Taiwan.

Joint penalized-likelihood reconstruction of time-activity curves and regions-of-interest from projection data in brain PET

This paper presents a novel statistical approach for joint estimation of regions-of-interest (ROIs) and the corresponding time–activity curves (TACs) from dynamic positron emission tomography (PET) brain projection data. It is based on optimizing the joint objective function that consists of a data log-likelihood term and two penalty terms reflecting the available a priori information about the human brain anatomy. The developed local optimization strategy iteratively updates both the ROI and TAC parameters and is guaranteed to monotonically increase the objective function. The quantitative evaluation of the algorithm is performed with numerically and Monte Carlo-simulated dynamic PET brain data of the 11C-Raclopride and 18F-FDG tracers. The results demonstrate that the method outperforms the existing sequential ROI quantification approaches in terms of accuracy, and can noticeably reduce the errors in TACs arising due to the finite spatial resolution and ROI delineation.

The statistical investigation of mechanical properties of PP/natural fibers composites

A systematic and statistical approach to evaluate and predict the properties of random discontinuous natural fiber reinforced composites. Different composites based on polypropylene and reinforced with natural fibers have been made and their mechanical properties are measured together with the distribution of the fiber size and the fiber diameter. The values obtained have been related to the theoretical predictions, using a combination of the Griffith theory for the effective properties of the natural fibers and the Halpin-Tsai equation for the elastic modulus of the composites. The relationships between experimental results and theoretical predictions are statistically analyzed using a probability density function estimation approach based on neural networks. The results show a more accurate expected value with respect to the traditional statistical function estimation approach. In order to point out the particular features of natural fibers, the same proposed method is also applied to PP-glass fiber composites.

Estimation of a Resilient Modulus Model for Cohesive Soils Using Joint Estimation and Mixed Effects

This paper presents the specification and estimation of a model based on the mechanistic empirical Pavement Design Guide (PDG) for estimating resilient modulus of fine-grained soils by using common soil parameters and by combining two different data sources: a database developed with Hawaiian fine-grained soils and data extracted from the Long Team Pavement Performance database for fine-grained subgrade soils. Two statistical techniques are combined to estimate the model parameters: joint estimation and mixed effects. Joint estimation considers multiple databases and allows identification of influential parameters that may be present only in some but not all databases whereas the mixed-effects statistical estimation approach is used to account for the within-group correlation between observations. The general structure of the PDG model is found acceptable if an allowance is made for the compaction level in addition to the saturation level in the PDG sigmoidal function. The resulting model contains parameters that are statistically significant and is more robust in that it can be used under a wider range of conditions than would have been possible if only one data source was available.

Syntactic Modeling and Signal Processing of Multifunction Radars: A Stochastic Context-Free Grammar Approach

Multifunction radars (MFRs) are sophisticated sensors with complex dynamical modes that are widely used in surveillance and tracking. This paper demonstrates that stochastic context-free grammars (SCFGs) are adequate models for capturing the essential features of the MFR dynamics. Specifically, MFRs are modeled as systems that ldquospeakrdquo a language that is characterized by an SCFG. The paper shows that such a grammar is modulated by a Markov chain representing radar's policy of operation. The paper also demonstrates how some well-known statistical signal processing techniques can be applied to MFR signal processing using these stochstic syntactic models. We derive two statistical estimation approaches for MFR signal processing-a maximum likelihood sequence estimator to estimate radar's policies of operation, and a maximum likelihood parameter estimator to infer the radar parameter values. Two layers of signal processing are introduced in this paper. The first layer is concerned with the estimation of MFR's policies of operation. It involves signal processing in the CFG domain. The second layer is concerned with identification of tasks the radar is engaged in. It involves signal processing in the finite-state domain. Both of these signal processing techniques are important elements of a bigger radar signal processing problem that is often encountered in electronic warfare applications-the problem of the estimation of the level of threat that a radar poses to each individual target at any point in time.

A statistical methodology for wire-length prediction

In this paper, the classic wire-length estimation problem is addressed and a new statistical wire-length estimation approach that captures the probability distribution function of net lengths after placement and before routing is proposed. These types of models are highly instrumental in formalizing a complete and consistent probabilistic approach to design automation and design closure where, along with optimizing the pertinent cost function, the associated prediction error is also considered. The wire-length prediction model was developed using a combination of parametric and nonparametric statistical techniques. The model predicts not only the length of the net using input parameters extracted from the floorplan of a design, but also probability distributions that a net with given characteristics after placement will have a particular length. The model is validated using the learn-and-test and resubstitution techniques. The model can be used for a variety of purposes, including the generation of a large number of statistically sound, and therefore realistic, instances of designs. The net models were applied to the probabilistic buffer-insertion problem and substantial improvement was obtained in net delay after routing (~ 20%) when compared to a traditional bounding box (BBOX)-based buffer-insertion strategy

Identifying best-practices: A Monte Carlo evaluation of quantile regression

The area of best practice research has only recently begun to embrace statistically based comparisons as a basis for identifying recommended practices. In part motivated by growing interest in performance measurement activities these new approaches hold significant potential for improvin our ability to identify and utilize true best practices. Unfortunately, little has been done to study how to apply statistical methods to this task appropriately. In this paper a Monte Carlo evaluation is developed to demonstrate that how Quantile Regression methods can be used to identify best practice. After a brief literature review and a summary of the Quantile Regression technique, the paper develops a specific monte carle simulation design based on statistical situations with varying numbers of high, medium and low performing organizations. Next, we apply quantile regression to the simulated data and attempts to develop some reasonable guidance about how to apply quantile regressions to real world data. The results demonstrate that quantile regression can accurately estimate different models for different types of organizations (e.g. high and low performing) and should be considered as an effective tool for the empirical study of these practices when samples of similar organizations are available. As an order based statistical estimation approach, it also has the virtue of being more robust than typical moment apporoaches.

A Statistical Approach for Estimation of Process Flow Data from Production of Chemicals of Fossil Origin (6 pp)

The life cycles of many products including textiles contain chemicals for which process flow data are not known or are too time consuming to collect. Although each chemical may not contribute significantly to the LCA results of the product, which might justify excluding them, but together their contribution could be significant. Similarly, rough estimates of the process flows for the production of a single chemical may be very uncertain and considered meaningless, while the estimates of the cumulative data of process flows for several chemicals may be less uncertain and be a meaningful contribution to the quality of the LCA results. There are methods for estimation of process flows for different types of products, with varying demands regarding input data and time and with varying accuracy of the results. This work contributes to the available methods, focusing on simple estimations for production of chemical substances. The goal was to create a fast method for estimation of emissions, resource and energy flows (process flows) for the production of chemicals, based on easily available data on the properties of the chemicals. The process flows investigated were limited to those normally associated with process industries and contributing most to depletion of resources, to global warming, acidification, eutrophication and photochemical ozone production, i.e. use of energy, crude oil, coal, natural gas, uranium in ore and emissions of CO2, SOx, NOx, NMVOC, methane, BOD, COD and total N. Toxic substances were excluded, since toxic emissions are substance specific and cannot be included in a generalization. Available data for the process flows for the production of chemicals of mainly fossil origin were correlated to properties of chemicals such as amount of carbon in the molecule, heat of formation and average number of chemical reaction steps in the production. The production procedures were found in readily available literature. Up to about six reaction steps were evaluated in the correlation study. The variations in the process flows among the chemicals studied were calculated. There were weak correlations between average number of chemical reaction steps in the production and energy use, COD measured in water emissions, and SOx and NOx emissions to air. For the remaining properties of chemicals and process flows, there were only weak correlations for share of double bonding in the molecule if only molecules containing double bondings were included. The precision in estimation of the process flows increases non-significantly when adding information on the number of reaction steps or share of double bonding for chemicals containing double bonding is added. It seems reasonable to start with a simple grouping method to estimate the process flows for the production of a chemical of fossil origin. Further investigations might investigate whether there is a correlation between process flows and the costs of chemicals, and further study the correlations between process flows and share of double bonding for chemicals containing double bondings.

Mechanical properties of polypropylene matrix composites reinforced with natural fibers: A statistical approach

AbstractThis work presents a systematic and statistical approach to evaluate and predict the properties of random discontinuous natural fiber reinforced composites. Different composites based on polypropylene and reinforced with natural fibers were produced and their mechanical properties are measured together with the distribution of the fiber size and the fiber diameter. The values obtained were related to the theoretical predictions, using a combination of the Griffith theory for the effective properties of the natural fibers and the Halpin‐Tsai equation for the elastic modulus of the composites. The relationships between experimental results and theoretical predictions were statistically analyzed using a probability density function estimation approach based on neural networks. The results show a more accurate expected value with respect to the traditional statistical function estimation approach. In order to point out the particular features of natural fibers, the same proposed method is also applied to PP–glass fiber composites.

Distributions-Oriented Verification of Probability Forecasts for Small Data Samples

Abstract The distributions-oriented approach to forecast verification uses an estimate of the joint distribution of forecasts and observations to evaluate forecast quality. However, small verification data samples can produce unreliable estimates of forecast quality due to sampling variability and biases. In this paper, new techniques for verification of probability forecasts of dichotomous events are presented. For forecasts of this type, simplified expressions for forecast quality measures can be derived from the joint distribution. Although traditional approaches assume that forecasts are discrete variables, the simplified expressions apply to either discrete or continuous forecasts. With the derived expressions, most of the forecast quality measures can be estimated analytically using sample moments of forecasts and observations from the verification data sample. Other measures require a statistical modeling approach for estimation. Results from Monte Carlo experiments for two forecasting examples sho...

Cross-Calibration of Stroke Disability Measures

It is common to assess disability of stroke patients using standardized scales, such as the Rankin Stroke Outcome Scale (RS) and the Barthel Index (BI). The RS, which was designed for applications to stroke, is based on assessing directly the global conditions of a patient. The BI, which was designed for more general applications, is based on a series of questions about the patient's ability to carry out 10 basic activities of daily living. Because both scales are commonly used, but few studies use both, translating between scales is important in gaining an overall understanding of the efficacy of alternative treatments, and in developing prognostic models that combine several datasets. The objective of our analysis is to provide a tool for translating between BI and RS. Specifically, we estimate the conditional probability distributions of each given the other. Subjects consisted of 459 individuals who sustained a stroke and who were recruited for the Kansas City Stroke Study from 1995 to 1998. We assessed patients with BI and RS measures 1, 3, and 6 months after stroke. In addition, we included data from the Framingham study, in the form of a table cross-classifying patients by RS and coarsely aggregated BI. Our statistical estimation approach is motivated by several goals: (a) overcoming the difficulty presented by the fact that our two sources report data at different resolutions; (b) smoothing the empirical counts to provide estimates of probabilities in regions of the table that are sparsely populated; (c) avoiding estimates that would conflict with medical knowledge about the relationship between the two measures; and (d) estimating the relationship between RS and BI at three months after the stroke, while borrowing strength from measurements made at 1 month and 6 months. We address these issues via a Bayesian analysis combining data augmentation and constrained semiparametric inference. Our results provide the basis for comparing and integrating the results of clinical trials using different disability measures, and integrating clinical trials results into a comprehensive decision model for the assessment of long-term implications and cost-effectiveness of stroke prevention and acute treatment interventions. In addition, our results indicate that the degree of agreement between the two measures is less strong than commonly reported, and emphasize the importance of trial designs that include multiple assessments of outcome.

A probability model for the meiosis I non-disjunction fraction in numerical chromosomal anomalies.

Numerical chromosome abnormalities (aneuploidies) are among the most common known causes of mental retardation and the leading cause of pregnancy loss in humans. They primarily arise by the process of meiotic non-disjunction. We still know very little about the contribution of genetic and environmental causes for non-disjunction in humans. In order to increase our understanding of the epidemiology of human trisomies, it is necessary to establish the proportion of cases occurring in the first or second division of meiosis. Trisomic patients will display, in study of microsatellite typed by the polymerase chain reaction (PCR), three fragment peaks of equal intensity, two fragments at an average 2:1 dosage or one individual fragment. In this work we describe a statistical approach for estimation of the fraction of meiosis I non-disjunctions (F) in the absence of the parental information. First we determine a probability model for the number of peaks in a polymorphic microsatellite locus, which is a function of F. Based on this model, we obtain a maximum likelihood estimator for F, using the observed proportion of one, two and three allele patterns in trisomic individuals. Relying on the properties of maximum likelihood theory, we also calculate the asymptotic variance and confidence intervals for F. Owing to the fact that the samples of trisomic patients are limited in number, the use of asymptotic theory may be compromised. Thus, we employ the bootstrap technique to build confidence intervals for F and compare the results with those obtained from the normal theory. This estimator that dispenses the need to study parents opens the possibility of using archival material for comparative epidemiological studies of Down's syndrome and other aneuploidies. In this paper we propose a probability model to estimate the fraction of meiosis I non-disjunction, F, by only using the proportion of allele patterns of trisomy individuals, while traditional methods require typing pericentromeric markers from those affected and their parents.

Identifying Best-Practices: A Monte Carlo Evaluation of Quantile Regression

The area of best practice research has only rcccntly begun to embrace statistically based comparisons as a basis for ying recommended practices. In part motivated by growing interest in performance measurement activities these new hes hold significant potential for improving out ability to identify and utilize true best practices. Unfortunately, little been done to study how to apply statistical methods to this task appropriately. In this paper a Monte Carlo evaluation is loped to demonstrate that how Quantile Regression methods can be used to identify best practice. After a brief literature and a summary of the Quantile Regression technique, the paper develops a specific monte carlo simulation design statistical situations with varying numbers of high, medium and low performing organizations. Next, we apply quan regression to the simulated data and attempts to develop some reasonable guidance about how to apply quantile rcgres to real world data. The results demonstrate that quantile regression can accurately estimate different models for different types of organizations (e.g. high and low performing) and should be considered as an effective tool for the empirical study of practices when samples of similar organizations are available. As an order based statistical estimation approach, it also the virtue of being more robust than typical moment approaches. This paper is based on a working paper developed at The Maxwell School in June 2001, which was partially funded by doctoral research grant from the Dean of The Maxwell School and the Center for Technology and Information Policy.

Binding of pyrene on lake aquatic humic matter: the role of structural descriptors

Partition coefficients for the binding affinities of pyrene to 28 different humic materials were determined by the solubility enhancement method. The humic materials used in the present study were isolated by different methods from different environmental sources, and characterized by various methods including spectroscopic and pyrolysis (Py) approaches. Several structural descriptors were derived for testing the binding affinity of pyrene. A significant correlation was observed, supporting the earlier literature results, between the pyrene binding coefficient and the molecular weights, molar absorptivities at 280 nm, and aromaticity of the aquatic humic solutes. Also other structural descriptors, e.g. nitrogen and especially aliphatic moieties, have their own importance to the binding affinity of pyrene. The results confirm the fact that it is not meaningful to treat aquatic and terrestrial humic material as an integrated whole. The results also disclosed that the isolation and fractionation procedures of aquatic humic probes will strengthen, as a result of breaking hydrophobic bondings of aggregates between different humic solutes, the binding affinities of pyrene on different humic isolates compared with the original situation predominating in the water sample. One has to be very careful in the light of the forthcoming predictions what kind of humic probe has been adopted for representing aquatic humic matter (HM). A statistical approach for estimation of the most probable carbon distribution in a humus sample proved quite workable for the prediction of binding affinity of pyrene on aquatic humic materials.

Aviation infrastructure performance and airline cost: a statistical cost estimation approach

Abstract The relationship between the performance of the US National Airspace System (NAS) and airline costs is examined by estimating airline cost functions that include NAS performance metrics as arguments, using quarterly data for 10 US domestic airlines. Performance metrics that vary by airline and quarter are developed by applying principal component analysis to seven underlying variables, including average delay, delay variance, and the proportion of flights that is cancelled. This analysis reveals that variation in the seven variables can be adequately captured by three or fewer factors, which we term NAS performance factors. If three factors are used, they can be interpretted as “delay”, “variability”, and “disruption”, the latter two of which are merged into a single “irregularity” factor in the two-factor model. Cost function estimation results confirm the anticipated link between NAS performance and airline cost. In the cost models with two and three performance factors, the irregularity and disruption factors are found to have the strongest cost impacts. These results challenge the prevailing assumption that delay reduction is the most important benefit from NAS enhancements. Using the estimated cost models, we predict airline cost savings from substantially improved NAS performance in the range $1–4 billion annually.