Logarithm Of Probability Research Articles

Interaction between acceptability and probability: Evidence from predicate agreement with a coordinated subject in Russian

The study aims to establish whether language models trained on unlabeled text data can parametrize agreement variation. We compared the acceptability judgments made by native speakers and the probability metrics predicted by the language model ruBERT without fine-tuning. As a specific linguistic phenomenon, we considered predicate agreement with a coordinated subject in Russian. We analyzed in detail which syntactic, morphological, and semantic factors influenced sentence acceptability and probability. The experimental data enables us to reveal the role of each factor and their interaction. Besides the standard logarithmic probability, we considered sentence length and unigram probability. We assumed that the model would assign the highest probability to the most acceptable agreement strategy. However, our hypothesis was not confirmed: the correlation between probability and acceptability is lower for sentences with agreement variation than for sentences without variation. The linear position — the subject-predicate order and the conjuncts’ order — turned out to be the only factor which equally influences the acceptability and probability of a sentence. If the gender features of conjuncts match, the acceptability of singular agreement increases while the probability does not change. The animacy of conjuncts and the predicate symmetry influence neither acceptability nor probability. Our research demonstrates that ruBERT cannot be used to parametrize predicate agreement with a coordinated subject. The acceptability of a sentence is based on subtle linguistic contrasts which are not significant for the computer evaluation of its probability.

Automated derivation of diagnostic criteria for lung cancer using natural language processing on electronic health records: a pilot study

BackgroundThe digitisation of healthcare records has generated vast amounts of unstructured data, presenting opportunities for improvements in disease diagnosis when clinical coding falls short, such as in the recording of patient symptoms. This study presents an approach using natural language processing to extract clinical concepts from free-text which are used to automatically form diagnostic criteria for lung cancer from unstructured secondary-care data.MethodsPatients aged 40 and above who underwent a chest x-ray (CXR) between 2016 and 2022 were included. ICD-10 and unstructured data were pulled from their electronic health records (EHRs) over the preceding 12 months to the CXR. The unstructured data were processed using named entity recognition to extract symptoms, which were mapped to SNOMED-CT codes. Subsumption of features up the SNOMED-CT hierarchy was used to mitigate against sparse features and a frequency-based criteria, combined with univariate logarithmic probabilities, was applied to select candidate features to take forward to the model development phase. A genetic algorithm was employed to identify the most discriminating features to form the diagnostic criteria.Results75002 patients were included, with 1012 lung cancer diagnoses made within 12 months of the CXR. The best-performing model achieved an AUROC of 0.72. Results showed that an existing ‘disorder of the lung’, such as pneumonia, and a ‘cough’ increased the probability of a lung cancer diagnosis. ‘Anomalies of great vessel’, ‘disorder of the retroperitoneal compartment’ and ‘context-dependent findings’, such as pain, statistically reduced the risk of lung cancer, making other diagnoses more likely. The performance of the developed model was compared to the existing cancer risk scores, demonstrating superior performance.ConclusionsThe proposed methods demonstrated success in leveraging unstructured secondary-care data to derive diagnostic criteria for lung cancer, outperforming existing risk tools. These advancements show potential for enhancing patient care and results. However, it is essential to tackle specific limitations by integrating primary care data to ensure a more thorough and unbiased development of diagnostic criteria. Moreover, the study highlights the importance of contextualising SNOMED-CT concepts into meaningful terminology that resonates with clinicians, facilitating a clearer and more tangible understanding of the criteria applied.

The search for DA double white dwarf binary candidates from SDSS DR14

Aims. Double white dwarf (DWD) binaries are one of the channels through which type Ia supernovae explosions occur. With the release of more and more sky survey data, the search for additional DWDs has become a possibility. We utilized the spectroscopic data from SDSS DR14 to search for DWD binaries based on variations in radial velocities (RVs). Methods. We obtained a sample of 4089 DA white dwarfs (WDs) with two or more spectra from SDSS DR14, and their RVs were derived using the cross-correlation function. Using the chi-squared (χ2) distribution of RVs as a base, we calculated the corresponding logarithmic probabilities (log p) for different degrees of freedom. Results. We selected the targets with log p < −3.0 and obtained 65 highly credible DWD candidates, of which 56 were newly discovered. We compared the distributions of the Teff, log g, and mass of the DWD candidates and found that the mass distribution of DWDs has two peaks. The primary peak, located at 0.45 M⊙, is lower than the peak of the total WD sample, while the secondary peak, located at 0.60 M⊙, is similar to the peak of the total sample. Finally, we crossmatched our sample with Zwicky Transient Facility (ZTF) photometry data and identified two targets with clear periodic variability. Based on the shape of their light curve, we think both could be white dwarf main-sequence binary stars

CatNorth: An Improved Gaia DR3 Quasar Candidate Catalog with Pan-STARRS1 and CatWISE

A complete and pure sample of quasars with accurate redshifts is crucial for quasar studies and cosmology. In this paper, we present CatNorth, an improved Gaia Data Release 3 (Gaia DR3) quasar candidate catalog with more than 1.5 million sources in the 3π sky built with data from Gaia, Pan-STARRS1, and CatWISE2020. The XGBoost algorithm is used to reclassify the original Gaia DR3 quasar candidates as stars, galaxies, and quasars. To construct training/validation data sets for the classification, we carefully built two different master stellar samples in addition to the spectroscopic galaxy and quasar samples. An ensemble classification model is obtained by averaging two XGBoost classifiers trained with different master stellar samples. Using a probability threshold of p QSO_mean > 0.95 in our ensemble classification model and an additional cut on the logarithmic probability density of zero proper motion, we retrieved 1,545,514 reliable quasar candidates from the parent Gaia DR3 quasar candidate catalog. We provide photometric redshifts for all candidates with an ensemble regression model. For a subset of 89,100 candidates, accurate spectroscopic redshifts are estimated with the convolutional neural network from the Gaia BP/RP spectra. The CatNorth catalog has a high purity of ∼90%, while maintaining high completeness, which is an ideal sample to understand the quasar population and its statistical properties. The CatNorth catalog is used as the main source of input catalog for the Large Sky Area Multi-Object Fiber Spectroscopic Telescope phase III quasar survey, which is expected to build a highly complete sample of bright quasars with i < 19.5.

On the Modification of Mellin Convolution Operator and Its Associated Information Potential

In this paper, we define a new generalization of Mellin-Gauss-Weierstrass operators that preserve logarithmic functions. We compute logarithmic moments of the new operators and describe the behavior of the modified operators in some weighted spaces. The weighted approximation properties of operators including weighted approximation and weighted quantitative type approximation properties, using weighted logarithmic modulus of continuity, are presented. Using the Mellin-Gauss-Weierstrass kernel as a logarithmic probability density, we study the associated information potential, the expected value and the variance .

Philosophy of thermodynamics.

Thermodynamics is regarded as a universal but not foundational theory because its laws for macroscopic quantities have not been derived from microscopic entities. Thus, to root thermodynamics into the fundamental substance, atomism is revived, thinking that the light quantum is the indivisible and permanent element. Assuming the same basic building blocks constitute everything, the state of any system can be quantified by entropy, the logarithmic probability measure multiplied by Boltzmann's constant. Then, the change in entropy expresses the system's evolution toward thermodynamic balance with its surroundings. These natural processes consuming free energy in the least time accumulate sigmoidally, resulting in skewed distributions found throughout nature. In this way, thermodynamics makes sense of phenomena across disciplines and provides a holistic worldview to address questions such as what the world is, how we know about it, what is the meaning of life and how we should live. This article is part of the theme issue ''Thermodynamics 2.0: Bridging the natural and social sciences (Part 1)'.

Leakage detection in natural gas pipeline based on unsupervised learning and stress perception

Natural gas pipeline leakage can cause serious financial losses to natural gas transportation and pose accidents to the environmental safety. Currently-used supervised learning methods heavily rely on sufficient pipeline failure historical data for their training. Therefore, we propose a novel detection approach based on unsupervised learning and stress perception for determining the leakage situation in pipelines. In this study, pipeline stress signals are first acquired based on residual magnetic effect. The relationship between residual magnetic and stress is built using improved sparrow search algorithm (ISSA) and extreme learning machine (ELM). Then, the Wasserstein generative adversarial network with gradient penalty (WGAN-GP) is deployed to learn suitable features from the stress signals under the pipeline normal condition, generating high-quality stress data features. Finally, the generated stress features are supplied to the Bayesian Gaussian mixture model (BGMM). And the weighted logarithm probability (WLP) is used as the health indicator for examining pipeline status. The results demonstrate that the relative error of residual magnetic stress model is controlled within 3 %, and the WLP value of fault samples is smaller than − 100, so that the proposed method can discriminate the normal and leak conditions as well as the risk and severity of leakage. This study provides a theoretical basis and new perspective for pipeline leakage detection.

A Logarithmic Bayesian Approach to Quantum Error Detection

We consider the problem of continuous quantum error correction from a Bayesian perspective, proposing a pair of digital filters using logarithmic probabilities that are able to achieve near-optimal performance on a three-qubit bit-flip code, while still being reasonable to implement on low-latency hardware. These practical filters are approximations of an optimal filter that we derive explicitly for finite time steps, in contrast with previous work that has relied on stochastic differential equations such as the Wonham filter. By utilizing logarithmic probabilities, we are able to eliminate the need for explicit normalization and can reduce the Gaussian noise distribution to a simple quadratic expression. The state transitions induced by the bit-flip errors are modeled using a Markov chain, which for log-probabilties must be evaluated using a LogSumExp function. We develop the two versions of our filter by constraining this LogSumExp to have either one or two inputs, which favors either simplicity or accuracy, respectively. Using simulated data, we demonstrate that the single-term and two-term filters are able to significantly outperform both a double threshold scheme and a linearized version of the Wonham filter in tests of error detection under a wide variety of error rates and time steps.

Livelihood resilience and strategies of rural residents of earthquake-threatened areas in Sichuan Province, China.

Natural disasters are increasing in frequency in China. Enhancing residents' livelihood resilience and adjusting their livelihood strategies have gradually become effective means of dealing with disaster risk. Therefore, it is of great significance to explore the livelihood strategies and livelihood resilience of rural residents in earthquake-stricken areas to help them cope with disaster risks. However, few studies have explored the correlation between residents' livelihood resilience and livelihood strategies from the perspective of residents' livelihood resilience. Based on a survey of 327 households in four districts and counties of Sichuan Province, China that were affected by the Wenchuan and Lushan earthquakes, we construct a framework for analyzing livelihood resilience and livelihood strategy selection. We comprehensively analyze the characteristics of livelihood resilience and livelihood strategy and explore their correlation using an ordinal multi-classification logistic regression model. The results show that: (1) Among 327 sample households, 90.21% were non-farming, 3.67% were part-time households and 6.12% were farming households. Residents' livelihood resilience is mainly based on their disaster prevention and mitigation capacity. (2) As far as the correlation between livelihood resilience and livelihood strategies is concerned, the stronger the buffer capacity in livelihood resilience, the more rural residents tend to engage in non-farming activities to obtain income. When other conditions remain unchanged, the logarithmic probability of choosing an agricultural livelihood strategy decreases by 21.814 for each unit of buffer capacity. From the perspective of residents' livelihood resilience, this study deepens our understanding of the relationship between livelihood resilience and livelihood strategy in earthquake-stricken areas. It also provides useful information for the formulation of policies to improve residents' resilience in disaster-threatened areas.

A Semantics-Assisted Video Captioning Model Trained With Scheduled Sampling.

Given the features of a video, recurrent neural networks can be used to automatically generate a caption for the video. Existing methods for video captioning have at least three limitations. First, semantic information has been widely applied to boost the performance of video captioning models, but existing networks often fail to provide meaningful semantic features. Second, the Teacher Forcing algorithm is often utilized to optimize video captioning models, but during training and inference, different strategies are applied to guide word generation, leading to poor performance. Third, current video captioning models are prone to generate relatively short captions that express video contents inappropriately. Toward resolving these three problems, we suggest three corresponding improvements. First of all, we propose a metric to compare the quality of semantic features, and utilize appropriate features as input for a semantic detection network (SDN) with adequate complexity in order to generate meaningful semantic features for videos. Then, we apply a scheduled sampling strategy that gradually transfers the training phase from a teacher-guided manner toward a more self-teaching manner. Finally, the ordinary logarithm probability loss function is leveraged by sentence length so that the inclination of generating short sentences is alleviated. Our model achieves better results than previous models on the YouTube2Text dataset and is competitive with the previous best model on the MSR-VTT dataset.

Abstract PR07: Development of a biomarker-based nomogram to predict the pathologic response to neoadjuvant pembrolizumab in muscle-invasive urothelial bladder cancer (MIBC)

Abstract Background: The possibility to predict the pathologic complete response (pT0) or pT≤1 after neoadjuvant immunotherapy may deeply impact the management of MIBC and orient clinical trials. The PURE01 study (Necchi A et al., J Clin Oncol 2018) evaluated preoperative pembrolizumab before radical cystectomy (RC) in T2-3bN0MO patients (pts). The trial is ongoing after an amendment to increase the sample size and includes cT4a pts. Methods: Pts received 3 cycles of pembrolizumab, q3 weeks, prior to RC. Tumor samples from baseline tissue (TURB) and post-therapy tissue (RC) have been assayed. The reported analyses included hybrid capture-based comprehensive genomic profiling (CGP) to evaluate all classes of genomic alterations (GA). Tumor mutational burden (TMB) was determined on up to 1.1 Mbp of sequenced DNA; PD-L1 expression was assayed with immunohistochemistry and reported with the combined positive score (CPS, Dako 22C3 mAb). Pre- vs. post-therapy GA frequencies, and their association with pT0 response, have been compared via Fisher's exact tests. Logarithmic probabilities of pT0 were plotted according to the continuously coded value of the TMB. A nomogram against pT0 and pT≤1 response was developed that included clinical T-stage and baseline PD-L1 CPS (dichotomized as &amp;lt; or ≥10) plus TMB. Performance testing of the nomogram is herein reported in terms of discrimination (Harrell's c index). Results: From 02/17 to 11/18, 87 pts were enrolled and completed treatment with RC. Selected baseline GA more frequently observed in nonresponders (pT≥2) vs. pT0 were: CCND1 (17.1 vs. 6.7%, p=0.27) and TSC1 (20 vs. 3.3%, p=0.06). Of note, GA of KRAS and SMARCA4 were not seen in pT0 pts but in 11.4% and 14.2% of pT≥2 pts instead, respectively. Increasing TMB values featured a linear association with pT0 probabilities (p=0.03). The c-indexes of the nomogram were 0.78 and 0.75 for pT0 and pT≤1 endpoints, respectively. Pts presenting with cT3-4 stage, CPS≥10, and TMB≥20 mut/mb had a median nomogram-derived probability of achieving pT0 = 79.5% and of achieving pT≤1 = 98%. These probabilities substantially decreased with lower TMB values (10 mut/mb cut-off) for cT3-4 stages, while for cT2 pts they were maintained as high as 76.3% and 98.5% for pT0 and pT≤1, respectively. Conclusion: The first nomogram including key biomarker information, derived from the ongoing PURE-01 study, may be a suitable tool to select patients who deserve single-agent pembrolizumab as preoperative approach. Pending validation with additional prospective data from the ongoing trials, this tool is proposed with the aim of developing new personalized neoadjuvant immunotherapy studies. Key genomic biomarker features may characterize nonresponding residual disease and help refine postoperative targeted therapy strategies. This abstract is also being presented as Poster B24. Citation Format: Andrea Necchi, Marco Bandini, Daniele Raggi, Alberto Briganti, Elena Farè, Andrea Gallina, Renzo Colombo, Marco Bianchi, Maurizio Colecchia, Roberta Lucianò, Andrea Salonia, Filippo Pederzoli, Jeffrey S. Ross, Russell Madison, Francesco Montorsi, Siraj M. Ali, Jon H. Chung. Development of a biomarker-based nomogram to predict the pathologic response to neoadjuvant pembrolizumab in muscle-invasive urothelial bladder cancer (MIBC) [abstract]. In: Proceedings of the AACR Special Conference on Bladder Cancer: Transforming the Field; 2019 May 18-21; Denver, CO. Philadelphia (PA): AACR; Clin Cancer Res 2020;26(15_Suppl):Abstract nr PR07.

Stationary response probability density of nonlinear random vibrating systems: a data-driven method

A data-driven method is established to derive the (approximately) analytical expression of the stationary response probability density of nonlinear random vibrating system, which explicitly includes system features and intensity of excitation. The stationary response probability density is first assumed as an exponential form by using the principle of maximum entropy. Through the rule of dimensional consistency, the power of exponential function is expressed as a linear combination of a set of nondimensional parameter clusters which are constituted by system features, intensity of excitation, and state variables. By comparing the power of exponential function with the approximate logarithm probability density evaluated from simulated data statistically, the determination of unknown coefficients comes down to the solution of (overdetermined) simultaneous linear algebraic equations. The data-driven method rediscovers the exact stationary response probability density of random-excited Duffing oscillator and derives an approximately analytical expression of stationary response probability density of van der Pol system from the simulated data of six cases with different values of system features and intensity of excitation. This data-driven method is a unique method which can explicitly include the information of system and excitation in the analytical expression of stationary response probability density. It avoids the solution of simultaneous nonlinear algebraic equations encountered in the maximum entropy method and closure methods and, in the meanwhile, avoids the sophisticated selection of weighting functions in closure methods.

The research of dust dispersed composition of urban environment

Introduction. Presently, the atmosphere of urban environments needs protection due to excessive ambient air pollutant concentrations. Each year these concentrations go up, triggered by environmental factors and anthropogenic processes, such as industry, transport, housing and utilities infrastructure. Dust is one of the main ecological factors that have a negative impact on the air. The co-authors have analyzed theoretical regularities governing the fractional composition of dust in the urban atmosphere, field tested the air polluted by the atmospheric aerosol in urban areas, and studied the applicability of truncated normal distribution law to particle size distribution in the atmospheric aerosol.&#x0D; Materials and methods. The co-authors employed a set of conventional and advanced information collection and processing methods that enable researchers to deliver novelty-intensive results, including methods of dust particle size distribution assessment, experimental design, mathematical modeling, etc. The co-authors have benchmarked the earlier results against the findings of this research to identify their qualitative and quantitative compliance with the results published in independent sources.&#x0D; Results. The co-authors have found that integral curves describing dust particle distribution over equivalent diameters, constructed in the coordinate system of logarithmic probability, represent truncated normal distribution, derived from classical normal distribution by limiting the interval of possible variables for random values. These integral curves are an implementation of a random function where a random function parameter represents dparticle, um.&#x0D; Conclusions. Size distribution of dust particles is an important characteristic of air pollutions that can help to reduce concentration of the atmospheric aerosol in the air. Studies of dust particle size regularities, typical for an urban atmosphere, are particularly relevant because they contribute to the resolution of several problems of environmental safety in an urban environment.

Aridity and Risk Calculations in Saudi Arabian Wadis: Wadi Fatimah Case

BackgroundInfrequent rainfall and rare flash floods are the primary sources of water in semi-arid and arid regions and are the key aspects in the management of water supply. In these regions, rainfall varies temporally and spatially with infrequent high intensities and sporadic occurrences, making it impossible to systematically record measurements as a proper time series.PurposeThe main purpose of this paper is to present temporal (risk assessment) and spatial (isohyet maps) methods for the evaluation of monthly rainfall water volumes and infiltration rates. Additionally, an aridity index based on rainfall and temperature measurements is proposed for use in semi-arid and arid regions.MethodThe limited data available for semi-arid and arid regions are treated using effective probabilistic and statistical methods. Calculation of the volume of rainfall is achieved through a simple hydrological procedure which involves examining monthly isohyet maps based on a set of rainfall measurements from weather stations in scattered locations. Calculation of rainfall and infiltration risks are performed according to the logarithmic normal probability distribution function. Furthermore, the potential monthly rainfall and infiltration rates are calculated using a set of pre-selected risk percentages.Results Aridity index, rainfall volume, and risk values are presented for Wadi Fatimah, which is located in the western Saudi Arabia. Potential rainfall and infiltration rates are calculated on a monthly scale using a set of pre-selected risk percentages. These simple calculations provide a sound basis for future studies on groundwater resource storage strategy, operation, and management.ConclusionsWater management studies can be best advanced through simple but effective assessment methods, as presented in this paper with specific applications to the Wadi Fatimah drainage basin that joins the Red Sea.

A three-class change detection methodology for SAR-data based on hypothesis testing and Markov Random field modelling

ABSTRACTThis study presents a new automatic change detection process chain based on bi-temporal co-registered and calibrated Sentinel-1 level-1 Interferometric Wide Ground Range Detected C-band synthetic aperture radar intensity imagery. The whole processor contains three main components: firstly, a preprocessing step is used to perform geometrical and radiometrical calibration. Secondly, an automatic coarse detection step is applied based on a statistical hypothesis test to obtain an initial classification. Thirdly, a post-classification step is introduced to optimize the initial classification result in the form of minimizing a global energy function defined on a Markov Random Field. In this study, a graph-cut algorithm is applied iteratively to solve the global optimization problem. At each iteration, the data energy function for the current classification is set by the logarithmic probability density function. The relevant parameters are estimated by the method of logarithmic cumulants. Supplemental data is presented to explain the formulae used in this study. Experiments are performed using a flood event which occurred in 2015 along the coastline of Greece near Kavala region and the Evros River at the border between Greece and Turkey. The proposed method shows a satisfying classification result with overall accuracy above 95% and kappa coefficient () above 0.87.

Are there common mathematical structures in economics and physics?

Economics is a field that looks into the future. We may know a few things ahead (ex ante), but most things we only know, afterwards (ex post). How can we work in a field, where much of the important information is missing? Mathematics gives two answers: 1. Probability theory leads to microeconomics: the Lagrange function optimizes utility under constraints of economic terms (like costs). The utility function is the entropy, the logarithm of probability. The optimal result is given by a probability distribution and an integrating factor. 2. Calculus leads to macroeconomics: In economics we have two production factors, capital and labour. This requires two dimensional calculus with exact and not-exact differentials, which represent the “ex ante” and “ex post” terms of economics. An integrating factor turns a not-exact term (like income) into an exact term (entropy, the natural production function). The integrating factor is the same as in microeconomics and turns the not-exact field of economics into an exact physical science.

Solution of classical evolutionary models in the limit when the diffusion approximation breaks down.

The discrete time mathematical models of evolution (the discrete time Eigen model, the Moran model, and the Wright-Fisher model) have many applications in complex biological systems. The discrete time Eigen model rather realistically describes the serial passage experiments in biology. Nevertheless, the dynamics of the discrete time Eigen model is solved in this paper. The 90% of results in population genetics are connected with the diffusion approximation of the Wright-Fisher and Moran models. We considered the discrete time Eigen model of asexual virus evolution and the Wright-Fisher model from population genetics. We look at the logarithm of probabilities and apply the Hamilton-Jacobi equation for the models. We define exact dynamics for the population distribution for the discrete time Eigen model. For the Wright-Fisher model, we express the exact steady state solution and fixation probability via the solution of some nonlocal equation then give the series expansion of the solution via degrees of selection and mutation rates. The diffusion theories result in the zeroth order approximation in our approach. The numeric confirms that our method works in the case of strong selection, whereas the diffusion method fails there. Although the diffusion method is exact for the mean first arrival time, it provides incorrect approximation for the dynamics of the tail of distribution.

Probabilistic Forecasting with Stationary VAR Models

I use a set of vector autoregressive models to forecast some of the main macroeconomic variables in a wide range of countries. The goal is to provide some insight about different forecast accuracy measures in a probabilistic forecasting framework. The countries are selected based on their available data in the International Financial Statistics (IFS) database. The target variables are GDP, CPI and exchange rate growth in yearly, quarterly and monthly frequencies. I specify the model sets by using a list of potentially relevant variables from IFS database. The results are available up to four forecast horizons and for two different classes of forecast accuracy measures: The probabilistic class which contains linear, logarithmic, quadratic, Hyvarinen and continuous ranked probability score rules, and the non-probabilistic class which contains mean absolute and mean square error measures. The results show that the forecasts are sensitive to the choice of a forecast accuracy class, in sense of Hellinger distance. However, within each class, the choice is not critical. Among different probabilistic measures, the logarithmic and quadratic rules are more reliable in practice. The results also show that the forecast power of stationary multivariate models is higher than the univariate ones, for both probabilistic and non-probabilistic accuracy measures.

Estimation of the Predictive Ability of Ecological Models

The conventional criteria for predictive model selection do not indicate the absolute goodness of models. For example, the quantity of Akaike Information Criterion (AIC) has meanings only when we compare AIC of different models for a given amount of data. Thus, the existing criteria do not tell us whether the quantity and quality of data is satisfactory, and hence we cannot judge whether we should collect more data to further improve the model or not. To solve such a practical problem, we propose a criterion RD that lies between 0 and 1. RD is an asymptotic estimate of the proportion of improvement in the predictive ability under a given error structure, where the predictive ability is defined by the expected logarithmic probability by which the next dataset (2nd dataset) occurs under a model constructed from the current dataset (1st dataset). That is, the predictive ability is defined by the expected logarithmic probability of the 2nd dataset evaluated at the model constructed from the 1st dataset. Appropriate choice of error structures is important in the calculation of RD. We illustrate examples of calculations of RD by using a small dataset about the moth abundance.

Probabilistic Models for Forecasting Earthquakes in the Northeast Region of India

Northeast India and its adjoining areas are characterized by very high seismic activity. According to the Indian seismic code, the region falls under seismic zone V, which represents the highest seismic-hazard level in the country. This region has experienced a number of great earthquakes, such as the Assam (1950) and Shillong (1897) earthquakes, that caused huge devastation in the entire northeast and adjacent areas by flooding, landslides, liquefaction, and damage to roads and buildings. In this study, an attempt has been made to find the probability of occurrence of a major earthquake (M-w > 6) in this region using an updated earthquake catalog collected from different sources. Thereafter, dividing the catalog into six different seismic regions based on different tectonic features and seismogenic factors, the probability of occurrences was estimated using three models: the lognormal, Weibull, and gamma distributions. We calculated the logarithmic probability of the likelihood function (ln L) for all six regions and the entire northeast for all three stochastic models. A higher value of ln L suggests a better model, and a lower value shows a worse model. The results show different model suits for different seismic zones, but the majority follows lognormal, which is better for forecasting magnitude size. According to the results, Weibull shows the highest conditional probabilities among the three models for small as well as large elapsed time T and time intervals t, whereas the lognormal model shows the lowest and the gamma model shows intermediate probabilities. Only for elapsed time T = 0, the lognormal model shows the highest conditional probabilities among the three models at a smaller time interval (t = 3-15 yrs). The opposite result is observed at larger time intervals (t = 15-25 yrs), which show the highest probabilities for the Weibull model. However, based on this study, the IndoBurma Range and Eastern Himalaya show a high probability of occurrence in the 5 yr period 2012-2017 with >90% probability.