Calibration Of Probability Research Articles

On Time-Dependent Trip Distance Distribution with For-Hire Vehicle Trips in Chicago

For transportation system analysis in a new space dimension with respect to individual trips’ remaining distances, vehicle trips demand has two main components: the departure time and the trip distance. In particular, the trip distance distribution (TDD) is a direct input to the bathtub model in the new space dimension, and is a very important variable to consider in many applications, such as the development of distance-based congestion pricing strategies or mileage tax. For a good understanding of the demand pattern, both the distribution of trip initiation and trip distance should be calibrated from real data. In this paper, it is assumed that the demand pattern can be described by the joint distribution of trip distance and departure time. In other words, TDD is assumed to be time-dependent, and a calibration and validation methodology of the joint probability is proposed, based on log-likelihood maximization and the Kolmogorov–Smirnov test. The calibration method is applied to empirical for-hire vehicle trips in Chicago, and it is concluded that TDD varies more within a day than across weekdays. The hypothesis that TDD follows a negative exponential, log-normal, or Gamma distribution is rejected. However, the best fit is systematically observed for the time-dependent log-normal probability density function. In the future, other trip distributions should be considered and also non-parametric probability density estimation should be explored for a better understanding of the demand pattern.

Artificial Intelligence: the Application of Machine Learning and Predictive Analytics in Credit Risk

In the last years Machine Learning (and the Artificial Intelligence), is experiencing a new rush thanks to the growth of volume and kind of data, the presence of tools / software with higher computational power and cheaper data storage size (e.g. cloud). In Credit Risk Management, the PD (Probability of Default) estimation has attracted lots of research interests in the past literature and recent studies have shown that advanced Artificial Intelligence (AI) methods achieved better performance than traditional statistical methods tied to simplified Machine Learning techniques. The study empirically investigates the results of applying different advanced machine learning techniques in estimation and calibration of Probability of Default. The study has been done on big data sample with more than 800,000 Retail customers of a panel European Banks under ECB Supervision, with 10 years of historical information (2006 - 2016) and 300 variables to be analyzed for each customer. The study shows that neural network produces a higher population riskiness ranking accuracy, with 71% of Accuracy Ratio. However, the authors’ idea is that classification tree is more interpretable from an economic and credit point of view. In terms of model calibration, cluster analysis produces rating classes more stable and with a predicted risk probability aligned with the observed default rate.

Validation and Calibration of Computer-simulated Probability of Detection Curves from Ultrasonic Inspection

Validation and Calibration of Computer-simulated Probability of Detection Curves from Ultrasonic Inspection

The theory, direction, and magnitude of ecosystem fire probability as constrained by precipitation and temperature.

The effects of climate on wildland fire confronts society across a range of different ecosystems. Water and temperature affect the combustion dynamics, irrespective of whether those are associated with carbon fueled motors or ecosystems, but through different chemical, physical, and biological processes. We use an ecosystem combustion equation developed with the physical chemistry of atmospheric variables to estimate and simulate fire probability and mean fire interval (MFI). The calibration of ecosystem fire probability with basic combustion chemistry and physics offers a quantitative method to address wildland fire in addition to the well-studied forcing factors such as topography, ignition, and vegetation. We develop a graphic analysis tool for estimating climate forced fire probability with temperature and precipitation based on an empirical assessment of combustion theory and fire prediction in ecosystems. Climate-affected fire probability for any period, past or future, is estimated with given temperature and precipitation. A graphic analyses of wildland fire dynamics driven by climate supports a dialectic in hydrologic processes that affect ecosystem combustion: 1) the water needed by plants to produce carbon bonds (fuel) and 2) the inhibition of successful reactant collisions by water molecules (humidity and fuel moisture). These two postulates enable a classification scheme for ecosystems into three or more climate categories using their position relative to change points defined by precipitation in combustion dynamics equations. Three classifications of combustion dynamics in ecosystems fire probability include: 1) precipitation insensitive, 2) precipitation unstable, and 3) precipitation sensitive. All three classifications interact in different ways with variable levels of temperature.

A spatial model of Wild Poliovirus Type 1 in Kano State, Nigeria: calibration and assessment of elimination probability

BackgroundSince the launch of the Global Polio Eradication Initiative, all but three countries (Nigeria, Pakistan, and Afghanistan) have apparently interrupted all wild poliovirus (WPV) transmission, and only one of three wild serotypes has been reported globally since 2012. Countrywide supplemental immunization campaigns in Nigeria produced dramatic reduction in WPV Type 1 paralysis cases since 2010 compared to the 2000’s, and WPV1 has not been observed in Nigeria since July 24, 2014. This article presents the development and calibration of a spatial metapopulation model of wild poliovirus Type 1 transmission in Kano State, Nigeria, which was the location of the most recent WPV1 case and 5 out of 6 of the reported WPV1 paralytic cases in Nigeria in 2014.MethodsThe model is calibrated to data on the case counts and age at onset of paralysis from 2003–2009. The features of the data drive model development from a simple susceptible-exposed-infective-recovered (SEIR) model to a spatial metapopulation model featuring seasonal forcing and age-dependent transmission. The calibrated parameter space is then resampled, projected forward, and compared to more recent case counts to estimate the probability that Type 1 poliovirus has been eliminated in Kano state.ResultsThe model indicates a 91 % probability that Type 1 poliovirus has been eliminated from Kano state as of October 2015. This probability rises to >99 % if no WPV1 paralysis cases are detected for another year. The other states in Nigeria have experienced even longer case-free periods (the only other state with a WPV1 case was Yobe, on April 19, 2014), and Nigeria is the last remaining country in Africa to experience endemic WPV1 transmission, so these results can be interpreted as an upper bound on the probability that WPV1 transmission is currently interrupted continent-wide.ConclusionsWhile the results indicate optimism that WPV1 transmission has been interrupted in Kano state, the model also assumes that frequent SIAs with high coverage continue to take place in Kano state through the end of the certification period. We conclude that though WPV1 appears to be on the brink of continent-wide elimination (WHO officially removed Nigeria from the list of polio-endemic countries on September 25, 2015), it is important for the polio program to maintain vigilance in surveillance and vaccination activities to prevent WPV1 resurgence through the WHO’s 3-year eradication certification period.Electronic supplementary materialThe online version of this article (doi:10.1186/s12879-016-1817-3) contains supplementary material, which is available to authorized users.

Multiple Forms of Endocannabinoid and Endovanilloid Signaling Regulate the Tonic Control of GABA Release.

Tonic cannabinoid signaling plays a critical role in the regulation of synaptic transmission. However, the mechanistic details of how persistent CB1 cannabinoid receptor activity inhibits neurotransmitter release have remained elusive. Therefore, electrophysiological recordings, lipid measurements, and super-resolution imaging were combined to elucidate those signaling molecules and mechanisms that underlie tonic cannabinoid signaling. The findings indicate that constitutive CB1 activity has pivotal function in the tonic control of hippocampal GABA release. Moreover, the endocannabinoid 2-arachidonoylglycerol (2-AG) is continuously generated postsynaptically, but its synaptic effect is regulated strictly by presynaptic monoacylglycerol lipase activity. Finally, anandamide signaling antagonizes tonic 2-AG signaling via activation of postsynaptic transient receptor potential vanilloid TRPV1 receptors. This unexpected mechanistic diversity may be necessary to fine-tune GABA release probability under various physiological and pathophysiological conditions.

Joint probabilistic forecasting of wind speed and temperature using Bayesian model averaging

Ensembles of forecasts are typically employed to account for the forecast uncertainties inherent in predictions of future weather states. However, biases and dispersion errors often present in forecast ensembles require statistical post‐processing. Univariate post‐processing models such as Bayesian model averaging (BMA) have been successfully applied for various weather quantities. Nonetheless, BMA and many other standard post‐processing procedures are designed for a single weather variable, thus ignoring possible dependencies among weather quantities. In line with recently upcoming research to develop multivariate post‐processing procedures, for example, BMA for bivariate wind vectors, or flexible procedures applicable for multiple weather quantities of different types, a bivariate BMA model for joint calibration of wind speed and temperature forecasts is proposed on the basis of the bivariate truncated normal distribution. It extends the univariate truncated normal BMA model designed for post‐processing ensemble forecast of wind speed by adding a normally distributed temperature component with a covariance structure representing the dependency among the two weather quantities.The method is applied to wind speed and temperature forecasts of the eight‐member University of Washington mesoscale ensemble and of the 11‐member Aire Limitée Adaptation dynamique Développement International‐Hungary Ensemble Prediction System (ALADIN‐HUNEPS) ensemble of the Hungarian Meteorological Service, and its predictive performance is compared to that of the independent BMA calibration of these weather quantities and the general Gaussian copula method. The results indicate improved calibration of probability and accuracy of point forecasts in comparison to the raw ensemble and the independent BMA approach, and the overall performance of this bivariate model is able to keep up with that of the Gaussian copula method. Copyright © 2014 John Wiley & Sons, Ltd.

Measurement of photon correlations with multipixel photon counters

Development of reliable photon number resolving detectors (PNRD), devices which are capable to distinguish 1,2,3.. photons, is of a great importance for quantum optics and its applications. A new class of affordable PNRD is based on multipixel photon counters (MPPC). Here we review results of experiments on using MPPCs for direct characterization of squeezed vacuum (SV) states, generated via parametric downconversion (PDC). We use MPPCs to measure the second order normalized intensity correlation function (g^(2)) and directly detect the two-mode squeezing of SV states. We also present a method of calibration of crosstalk probability in MPPCs based on g^(2) measurements of coherent states.

Crosstalk calibration of multi-pixel photon counters using coherent states

We present a novel method of calibration of crosstalk probability for multi-pixel photon counters (MPPCs) based on the measurement of the normalized second-order intensity correlation function of coherent light. The method was tested for several MPPCs, and was shown to be advantageous over the traditional calibration method based on the measurements of the dark noise statistics. The method can be applied without the need of modification for different kinds of spatially resolved single photon detectors.

A model-based approach for the analysis of the calibration of probability judgments

AbstractThe calibration of probability or confidence judgments concerns the association between the judgments and some estimate of the correct probabilities of events. Researchers rely on estimates using relative frequencies computed by aggregating data over observations. We show that this approach creates conceptual problems, and may result in the confounding of explanatory variables or unstable estimates. To circumvent these problems we propose using probability estimates obtained from statistical models—specifically mixed models for binary data—in the analysis of calibration. We illustrate this methodology by re-analyzing data from a published study and comparing the results from this approach to those based on relative frequencies. The model-based estimates avoid problems with confounding variables and provided more precise estimates, resulting in better inferences.

Incomplete Validation of Risk Stratification Indices

University of Utah, Salt Lake City, Utah. n.l.pace@utah.eduUsing 2001–2006 Medicare hospital data (Medicare Provider Analysis and Review [MEDPAR]) in approximately 17 million patients aged 65 yr and older, Sessler and colleagues1have proposed four risk stratification indices (RSIs) for mortality and duration of hospital stay. With a complex, stepwise hierarchical-selection algorithm, the authors1chose a parsimonious set of statistically significant predictors from the approximately 20,500 International Classification of Diseases, Ninth Revision, diagnostic and procedure codes. For example, in-hospital mortality was modeled on 184 predictor codes with odds ratios varying from 0.131 to 57.821. Using a split sample design, these RSIs were internally validated on MEDPAR data for another 17 million patients and were externally validated on 100,000 patient records from the Cleveland Clinic (Ohio; Perioperative Health Documentation System). Working in the parameter space (β coefficients), validation of the RSIs was demonstrated on the development, validation, and external datasets by the c (concordance) statistic,2which revealed very good discrimination in all datasets.However, the performance of these RSIs has not been adequately justified. To do so requires calculation of the prediction probability for each patient by exponentiation of the RSI (inverse logit; P i= 1/[1 +e −RSI]); P iranges from 0 to 1 (open interval). For each patient, prediction probability P iis compared with the observed dichotomous outcome Y i= 0 (dead) or Y i= 1 (alive). Overall performance of RSI is measured by the distance of the predicted outcome (P i) from the actual outcome (Y i); a good model of risk will have a short average distance. The accepted measures for overall performance in the validation datasets are the Brier score and the Nagelkerke R2statistic.2Overall performance can be partitioned into two characteristics: discrimination and calibration. Statistical software tools for estimation of overall performance, discrimination, and calibration are readily available.The c statistic is a measure of discrimination; it is a rank order statistic for predictions versus actual outcomes and is equivalent to the area under the receiver operating characteristic curve. As rank order statistics are invariant under monotonic transformations, the c statistic of RSI is identical to the c statistic of P i. Perfect discrimination corresponds with a c statistic of 1 and is achieved if the P ior RSI scores for all patients dying are higher than those for all patients not dying, with no overlap. A c statistic value of 0.5 indicates an RSI without discrimination (i.e. , no better than flipping a coin). While a good risk model will have high discrimination, by itself the c statistic is not optimal in assessing or comparing risk models.3The third aspect of performance measures is calibration (i.e. , the agreement between observed outcomes and predictions). For example, if an RSI score has a predicted probability of 20% for in-hospital mortality, then approximately 20% of inpatients with that RSI score are expected to die. The calibration of prediction probability can be assessed by regression plots of Y iversus P i, with patients grouped by deciles; there is also a specialized binary regression method.4Sessler et al. 1should be congratulated for their statistical models of risk that may, in the future, allow comparisons of outcomes of health care across institutions. I hope that they will provide supplementary analyses to demonstrate that, besides good discrimination, their RSIs also have good calibration and overall performance.University of Utah, Salt Lake City, Utah. n.l.pace@utah.edu

Allocation of Monte Carlo Resources for the Iterated Bootstrap

Use of the iterated bootstrap is often recommended for calibration of bootstrap intervals, using either direct calibration of the nominal coverage probability (prepivoting), or additive correction of the interval endpoints. Monte Carlo resampling is a straightforward, but computationally expensive way to approximate the endpoints of bootstrap intervals. Booth and Hall examined the case of coverage calibration of Efron's percentile interval, and developed an asymptotic approximation for the error in the Monte Carlo approximation of the endpoints. Their results can be used to determine an approximately optimal allocation of resamples to the first and second level of the bootstrap. An extension of this result to the case of the additively corrected percentile interval shows that the bias of the Monte Carlo approximation to the additively corrected endpoints is of smaller order than in the case of direct coverage calibration, and the asymptotic variance is the same. Because the asymptotic bias is controlled by the number of second level resamples, and the asymptotic variance by the number of first level resamples, this indicates that comparable Monte Carlo accuracy can be achieved with far less computational effort for the additively corrected interval than for the coverage calibrated interval. For both methods of calibration, these results and supporting simulations show that, for an optimal allocation of computing resources, the number of second level resamples should generally be considerably less than the number of first level resamples. This is in contrast to the usual practice in the literature. Also, the number of first level resamples needed to achieve reasonable Monte Carlo accuracy for double bootstrap confidence intervals is roughly times greater than for single stage bootstrap confidence intervals, and again is generally underestimated in the literature.