Search results for: maximum likelihood estimators

Authors: Raghunath Arnab

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The two-phase sampling which is also known as double sampling was introduced in 1938. In two-phase sampling, samples are selected in phases. In the first phase, a relatively large sample of size is selected by some suitable sampling design and only information on the auxiliary variable is collected. During the second phase, a sample of size is selected either from, the sample selected in the first phase or from the entire population by using a suitable sampling design and information regarding the study and auxiliary variable is collected. Evidently, two phase sampling is useful if the auxiliary information is relatively easy and cheaper to collect than the study variable as well as if the strength of the relationship between the variables and is high. If the sample is selected in more than two phases, the resulting sampling design is called a multi-phase sampling. In this article we will consider how one can use data collected at the first phase sampling at the stages of estimation of the parameter, stratification, selection of sample and their combinations in the second phase in a unified setup applicable to any sampling design and wider classes of estimators. The problem of the estimation of variance will also be considered. The variance of estimator is essential for estimating precision of the survey estimates, calculation of confidence intervals, determination of the optimal sample sizes and for testing of hypotheses amongst others. Although, the variance is a non-negative quantity but its estimators may not be non-negative. If the estimator of variance is negative, then it cannot be used for estimation of confidence intervals, testing of hypothesis or measure of sampling error. The non-negativity properties of the variance estimators will also be studied in details.

Keywords: auxiliary information, two-phase sampling, varying probability sampling, unbiased estimators

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Authors: Baladitya Swaika, Rahul Khatry

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Computer Adaptive Tests (CATs) is one of the most efficient ways for testing the cognitive abilities of students. CATs are based on Item Response Theory (IRT) which is based on item selection and ability estimation using statistical methods of maximum information selection/selection from posterior and maximum-likelihood (ML)/maximum a posteriori (MAP) estimators respectively. This study aims at combining both classical and Bayesian approaches to IRT to create a dataset which is then fed to a neural network which automates the process of ability estimation and then comparing it to traditional CAT models designed using IRT. This study uses python as the base coding language, pymc for statistical modelling of the IRT and scikit-learn for neural network implementations. On creation of the model and on comparison, it is found that the Neural Network based model performs 7-10% worse than the IRT model for score estimations. Although performing poorly, compared to the IRT model, the neural network model can be beneficially used in back-ends for reducing time complexity as the IRT model would have to re-calculate the ability every-time it gets a request whereas the prediction from a neural network could be done in a single step for an existing trained Regressor. This study also proposes a new kind of framework whereby the neural network model could be used to incorporate feature sets, other than the normal IRT feature set and use a neural network’s capacity of learning unknown functions to give rise to better CAT models. Categorical features like test type, etc. could be learnt and incorporated in IRT functions with the help of techniques like logistic regression and can be used to learn functions and expressed as models which may not be trivial to be expressed via equations. This kind of a framework, when implemented would be highly advantageous in psychometrics and cognitive assessments. This study gives a brief overview as to how neural networks can be used in adaptive testing, not only by reducing time-complexity but also by being able to incorporate newer and better datasets which would eventually lead to higher quality testing.

Keywords: computer adaptive tests, item response theory, machine learning, neural networks

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Authors: Sonal Budhiraja, Biswabrata Pradhan

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This work considers statistical inference based on progressive Type-I interval censored data with random removal. The scheme of progressive Type-I interval censoring with random removal can be described as follows. Suppose n identical items are placed on a test at time T0 = 0 under k pre-fixed inspection times at pre-specified times T1 < T2 < . . . < Tk, where Tk is the scheduled termination time of the experiment. At inspection time Ti, Ri of the remaining surviving units Si, are randomly removed from the experiment. The removal follows a binomial distribution with parameters Si and pi for i = 1, . . . , k, with pk = 1. In this censoring scheme, the number of failures in different inspection intervals and the number of randomly removed items at pre-specified inspection times are observed. Asymptotic properties of the maximum likelihood estimators (MLEs) are established under some regularity conditions. A β-content γ-level tolerance interval (TI) is determined for two parameters Weibull lifetime model using the asymptotic properties of MLEs. The minimum sample size required to achieve the desired β-content γ-level TI is determined. The performance of the MLEs and TI is studied via simulation.

Keywords: asymptotic normality, consistency, regularity conditions, simulation study, tolerance interval

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Authors: Dewi Retno Sari Saputro, Purnami Widyaningsih, Hendrika Handayani

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Extreme data on an observation can occur due to unusual circumstances in the observation. The data can provide important information that can’t be provided by other data so that its existence needs to be further investigated. The method for obtaining extreme data is one of them using maxima block method. The distribution of extreme data sets taken with the maxima block method is called the distribution of extreme values. Distribution of extreme values is Gumbel distribution with two parameters. The parameter estimation of Gumbel distribution with maximum likelihood method (ML) is difficult to determine its exact value so that it is necessary to solve the approach. The purpose of this study was to determine the parameter estimation of Gumbel distribution with quasi-Newton BFGS method. The quasi-Newton BFGS method is a numerical method used for nonlinear function optimization without constraint so that the method can be used for parameter estimation from Gumbel distribution whose distribution function is in the form of exponential doubel function. The quasi-New BFGS method is a development of the Newton method. The Newton method uses the second derivative to calculate the parameter value changes on each iteration. Newton's method is then modified with the addition of a step length to provide a guarantee of convergence when the second derivative requires complex calculations. In the quasi-Newton BFGS method, Newton's method is modified by updating both derivatives on each iteration. The parameter estimation of the Gumbel distribution by a numerical approach using the quasi-Newton BFGS method is done by calculating the parameter values that make the distribution function maximum. In this method, we need gradient vector and hessian matrix. This research is a theory research and application by studying several journals and textbooks. The results of this study obtained the quasi-Newton BFGS algorithm and estimation of Gumbel distribution parameters. The estimation method is then applied to daily rainfall data in Purworejo District to estimate the distribution parameters. This indicates that the high rainfall that occurred in Purworejo District decreased its intensity and the range of rainfall that occurred decreased.

Keywords: parameter estimation, Gumbel distribution, maximum likelihood, broyden fletcher goldfarb shanno (BFGS)quasi newton

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Authors: Mohamed Raouf Benmakrelouf, Joseph Rynkiewicz

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Targeted maximum likelihood estimation (TMLE) is well-established method for causal effect estimation with desirable statistical properties. TMLE is a doubly robust maximum likelihood based approach that includes a secondary targeting step that optimizes the target statistical parameter. A causal interpretation of the statistical parameter requires assumptions of the Rubin causal framework. The causal effect of binary variable, E, on outcomes, Y, is defined in terms of comparisons between two potential outcomes as E[YE=1 − YE=0]. Our aim in this paper is to present an adaptation of TMLE methodology to estimate the causal effect of a non-binary categorical variable, providing a large application. We propose coding on the initial data in order to operate a binarization of the interest variable. For each category, we get a transformation of the non-binary interest variable into a binary variable, taking value 1 to indicate the presence of category (or group of categories) for an individual, 0 otherwise. Such a dummy variable makes it possible to have a pair of potential outcomes and oppose a category (or a group of categories) to another category (or a group of categories). Let E be a non-binary interest variable. We propose a complete disjunctive coding of our variable E. We transform the initial variable to obtain a set of binary vectors (dummy variables), E = (Ee : e ∈ {1, ..., |E|}), where each vector (variable), Ee, takes the value of 0 when its category is not present, and the value of 1 when its category is present, which allows to compute a pairwise-TMLE comparing difference in the outcome between one category and all remaining categories. In order to illustrate the application of our strategy, first, we present the implementation of TMLE to estimate the causal effect of non-binary variable on outcome using simulated data. Secondly, we apply our TMLE adaptation to survey data from the French Political Barometer (CEVIPOF), to estimate the causal effect of education level (A five-level variable) on a potential vote in favor of the French extreme right candidate Jean-Marie Le Pen. Counterfactual reasoning requires us to consider some causal questions (additional causal assumptions). Leading to different coding of E, as a set of binary vectors, E = (Ee : e ∈ {2, ..., |E|}), where each vector (variable), Ee, takes the value of 0 when the first category (reference category) is present, and the value of 1 when its category is present, which allows to apply a pairwise-TMLE comparing difference in the outcome between the first level (fixed) and each remaining level. We confirmed that the increase in the level of education decreases the voting rate for the extreme right party.

Keywords: statistical inference, causal inference, super learning, targeted maximum likelihood estimation

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Authors: Ariful Islam, Showkat Ahmad Lone

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Statistical distributions have long been employed in the assessment of semiconductor devices and product reliability. The power function-distribution is one of the most important distributions in the modern reliability practice and can be frequently preferred over mathematically more complex distributions, such as the Weibull and the lognormal, because of its simplicity. Moreover, it may exhibit a better fit for failure data and provide more appropriate information about reliability and hazard rates in some circumstances. This study deals with estimating information about failure times of items under step-stress partially accelerated life tests for competing risk based on adoptive type-I progressive hybrid censoring criteria. The life data of the units under test is assumed to follow Mukherjee-Islam distribution. The point and interval maximum-likelihood estimations are obtained for distribution parameters and tampering coefficient. The performances of the resulting estimators of the developed model parameters are evaluated and investigated by using a simulation algorithm.

Keywords: adoptive progressive hybrid censoring, competing risk, mukherjee-islam distribution, partially accelerated life testing, simulation study

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Authors: Gubhinder Kundhi, Paul Rilstone

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Refined procedures for higher-order asymptotic theory for non-linear models are developed. These include a new method for deriving stochastic expansions of arbitrary order, new methods for evaluating the moments of polynomials of sample averages, a new method for deriving the approximate moments of the stochastic expansions; an application of these techniques to gather improved inferences with the weak instruments problem is considered. It is well established that Instrumental Variable (IV) estimators in the presence of weak instruments can be poorly behaved, in particular, be quite biased in finite samples. In our application, finite sample approximations to the distributions of these estimators are obtained using Edgeworth and Saddlepoint expansions. Departures from normality of the distributions of these estimators are analyzed using higher order analytical corrections in these expansions. In a Monte-Carlo experiment, the performance of these expansions is compared to the first order approximation and other methods commonly used in finite samples such as the bootstrap.

Keywords: edgeworth expansions, higher order asymptotics, saddlepoint expansions, weak instruments

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Authors: A. Y. Mukhtar, J. B. Munyakazi, R. Ouifki

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Over the past few decades, the unprecedented increase in mobility has raised considerable concern about the relationship between mobility and vector-borne diseases and malaria in particular. Thus, one can claim that human mobility is one of the contributing factors to the resurgence of malaria. To assess human mobility on malaria burden among hosts, we formulate a movement-based model on a network of patches. We then extend human multi-group SEIAR deterministic epidemic models into a system of stochastic differential equations (SDEs). Our quantitative stochastic model which is expressed in terms of average rates of movement between compartments is fitted to time-series data (weekly malaria data of 2011 for each patch) using the maximum likelihood approach. Using the metapopulation (multi-group) model, we compute and analyze the basic reproduction number. The result shows that human movement is sufficient to preserve malaria disease firmness in the patches with the low transmission. With these results, we concluded that the sensitivity of malaria to the human mobility is turning to be greatly important over the implications of future malaria control in South Sudan.

Keywords: basic reproduction number, malaria, maximum likelihood, movement, stochastic model

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Authors: Showkat Ahmad Lone, Ahmadur Rahman, Ariful Islam

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The major assumption in accelerated life tests (ALT) is that the mathematical model relating the lifetime of a test unit and the stress are known or can be assumed. In some cases, such life–stress relationships are not known and cannot be assumed, i.e. ALT data cannot be extrapolated to use condition. So, in such cases, partially accelerated life test (PALT) is a more suitable test to be performed for which tested units are subjected to both normal and accelerated conditions. This study deals with estimating information about failure times of items under step-stress partially accelerated life tests using progressive failure-censored hybrid data with random removals. The life data of the units under test is considered to follow exponential life distribution. The removals from the test are assumed to have binomial distributions. The point and interval maximum likelihood estimations are obtained for unknown distribution parameters and tampering coefficient. An optimum test plan is developed using the D-optimality criterion. The performances of the resulting estimators of the developed model parameters are evaluated and investigated by using a simulation algorithm.

Keywords: binomial distribution, d-optimality, multiple censoring, optimal design, partially accelerated life testing, simulation study

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Authors: Mahmut Yildirim

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This paper proposed the bidirectional long short-term memory (Bi-LSTM) network-aided deep learning (DL)-based signal detection for Orthogonal frequency division multiplexing with all index modulation (OFDM-AIM), namely Bi-DeepAIM. OFDM-AIM is developed to increase the spectral efficiency of OFDM with index modulation (OFDM-IM), a promising multi-carrier technique for communication systems beyond 5G. In this paper, due to its strong classification ability, Bi-LSTM is considered an alternative to the maximum likelihood (ML) algorithm, which is used for signal detection in the classical OFDM-AIM scheme. The performance of the Bi-DeepAIM is compared with LSTM network-aided DL-based OFDM-AIM (DeepAIM) and classic OFDM-AIM that uses (ML)-based signal detection via BER performance and computational time criteria. Simulation results show that Bi-DeepAIM obtains better bit error rate (BER) performance than DeepAIM and lower computation time in signal detection than ML-AIM.

Keywords: bidirectional long short-term memory, deep learning, maximum likelihood, OFDM with all index modulation, signal detection

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Authors: Ariful Islam, Showkat Ahmad Lone

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The Mukherjee-Islam Model is commonly used as a simple life time distribution to assess system reliability. The model exhibits a better fit for failure information and provides more appropriate information about hazard rate and other reliability measures as shown by various authors. It is possible to introduce a location parameter at a time (i.e., a time before which failure cannot occur) which makes it a more useful failure distribution than the existing ones. Even after shifting the location of the distribution, it represents a decreasing, constant and increasing failure rate. It has been shown to represent the appropriate lower tail of the distribution of random variables having fixed lower bound. This study presents the reliability computations and probability weighted moment estimation of three parameter model. A comparative analysis is carried out between three parameters finite range model and some existing bathtub shaped curve fitting models. Since probability weighted moment method is used, the results obtained can also be applied on small sample cases. Maximum likelihood estimation method is also applied in this study.

Keywords: comparative analysis, maximum likelihood estimation, Mukherjee-Islam failure model, probability weighted moment estimation, reliability

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Authors: Jayanta Pokharel, Gokarna Aryal, Netra Kanaal, Chris Tsokos

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Investment in stocks and shares aims to seek potential gains while weighing the risk of future needs, such as retirement, children's education etc. Analysis of the behavior of the stock market returns and making prediction is important for investors to mitigate risk on investment. Historically, the normal variance models have been used to describe the behavior of stock market returns. However, the returns of the financial assets are actually skewed with higher kurtosis, heavier tails, and a higher center than the normal distribution. The Laplace distribution and its family are natural candidates for modeling stock returns. The Variance-Gamma (VG) distribution is the most sought-after distributions for modeling asset returns and has been extensively discussed in financial literatures. In this paper, it explore the other Laplace family, such as Asymmetric Laplace, Skewed Laplace, Kumaraswamy Laplace (KS) together with Variance-Gamma to model the weekly returns of the S&P 500 Index and it's eleven business sector indices. The method of maximum likelihood is employed to estimate the parameters of the distributions and our empirical inquiry shows that the Kumaraswamy Laplace distribution performs much better for stock returns modeling among the choice of distributions used in this study and in practice, KS can be used as a strong alternative to VG distribution.

Keywords: stock returns, variance-gamma, kumaraswamy laplace, maximum likelihood

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Authors: Khandoker Akib Mohammad

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While analyzing time-to-event data, it is possible that a certain fraction of subjects will never experience the event of interest, and they are said to be cured. When this feature of survival models is taken into account, the models are commonly referred to as cure models. In the presence of covariates, the conditional survival function of the population can be modelled by using the cure model, which depends on the probability of being uncured (incidence) and the conditional survival function of the uncured subjects (latency), and a combination of logistic regression and Cox proportional hazards (PH) regression is used to model the incidence and latency respectively. In this paper, we have shown the asymptotic normality of the profile likelihood estimator via asymptotic expansion of the profile likelihood and obtain the explicit form of the variance estimator with an implicit function in the profile likelihood. We have also shown the efficient score function based on projection theory and the profile likelihood score function are equal. Our contribution in this paper is that we have expressed the efficient information matrix as the variance of the profile likelihood score function. A simulation study suggests that the estimated standard errors from bootstrap samples (SMCURE package) and the profile likelihood score function (our approach) are providing similar and comparable results. The numerical result of our proposed method is also shown by using the melanoma data from SMCURE R-package, and we compare the results with the output obtained from the SMCURE package.

Keywords: Cox PH model, cure model, efficient score function, EM algorithm, implicit function, profile likelihood

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Authors: Wanhyun Cho, Soonja Kang, Sangkyoon Kim, Soonyoung Park

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In this paper, we propose a novel inference algorithm for the multi-class Gaussian process classification model that can be used in the field of human behavior recognition. This algorithm can drive simultaneously both a posterior distribution of a latent function and estimators of hyper-parameters in a Gaussian process classification model with multi-class. Our algorithm is based on the Laplace approximation (LA) technique and variational EM framework. This is performed in two steps: called expectation and maximization steps. First, in the expectation step, using the Bayesian formula and LA technique, we derive approximately the posterior distribution of the latent function indicating the possibility that each observation belongs to a certain class in the Gaussian process classification model. Second, in the maximization step, using a derived posterior distribution of latent function, we compute the maximum likelihood estimator for hyper-parameters of a covariance matrix necessary to define prior distribution for latent function. These two steps iteratively repeat until a convergence condition satisfies. Moreover, we apply the proposed algorithm with human action classification problem using a public database, namely, the KTH human action data set. Experimental results reveal that the proposed algorithm shows good performance on this data set.

Keywords: bayesian rule, gaussian process classification model with multiclass, gaussian process prior, human action classification, laplace approximation, variational EM algorithm

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Authors: Kajingulu Malandala, Ranganai Edmore

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The asymmetric Laplace distribution (ADL) is commonly used as the likelihood function of the Bayesian quantile regression, and it offers different families of likelihood method for quantile regression. Notwithstanding their popularity and practicality, ADL is not smooth and thus making it difficult to maximize its likelihood. Furthermore, Bayesian inference is time consuming and the selection of likelihood may mislead the inference, as the Bayes theorem does not automatically establish the posterior inference. Furthermore, ADL does not account for greater skewness and Kurtosis. This paper develops a new aspect of quantile regression approach for count data based on inverse of the cumulative density function of the Poisson, binomial and Delaporte distributions using the integrated nested Laplace Approximations. Our result validates the benefit of using the integrated nested Laplace Approximations and support the approach for count data.

Keywords: quantile regression, Delaporte distribution, count data, integrated nested Laplace approximation

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Authors: Khanh To Duc, Monica Chiogna, Gianfranco Adimari

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With three diagnostic categories, assessment of the performance of diagnostic tests is achieved by the analysis of the receiver operating characteristic (ROC) surface, which generalizes the ROC curve for binary diagnostic outcomes. The volume under the ROC surface (VUS) is a summary index usually employed for measuring the overall diagnostic accuracy. When the true disease status can be exactly assessed by means of a gold standard (GS) test, unbiased nonparametric estimators of the ROC surface and VUS are easily obtained. In practice, unfortunately, disease status verification via the GS test could be unavailable for all study subjects, due to the expensiveness or invasiveness of the GS test. Thus, often only a subset of patients undergoes disease verification. Statistical evaluations of diagnostic accuracy based only on data from subjects with verified disease status are typically biased. This bias is known as verification bias. Here, we consider the problem of correcting for verification bias when continuous diagnostic tests for three-class disease status are considered. We assume that selection for disease verification does not depend on disease status, given test results and other observed covariates, i.e., we assume that the true disease status, when missing, is missing at random. Under this assumption, we discuss several solutions for ROC surface analysis based on imputation and re-weighting methods. In particular, verification bias-corrected estimators of the ROC surface and of VUS are proposed, namely, full imputation, mean score imputation, inverse probability weighting and semiparametric efficient estimators. Consistency and asymptotic normality of the proposed estimators are established, and their finite sample behavior is investigated by means of Monte Carlo simulation studies. Two illustrations using real datasets are also given.

Keywords: imputation, missing at random, inverse probability weighting, ROC surface analysis

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Authors: Neda Orak, Mostafa Zarei

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Environmental assessment is an important session in environment management. Since various methods and techniques have been produces and implemented. Remote sensing (RS) is widely used in many scientific and research fields such as geology, cartography, geography, agriculture, forestry, land use planning, environment, etc. It can show earth surface objects cyclical changes. Also, it can show earth phenomena limits on basis of electromagnetic reflectance changes and deviations records. The research has been done on mangrove forests assessment by RS techniques. Mangrove forests quantitative analysis in Basatin and Bidkhoon estuaries was the aim of this research. It has been done by Landsat satellite images from 1975- 2013 and match to ground control points. This part of mangroves are the last distribution in northern hemisphere. It can provide a good background to improve better management on this important ecosystem. Landsat has provided valuable images to earth changes detection to researchers. This research has used MSS, TM, +ETM, OLI sensors from 1975, 1990, 2000, 2003-2013. Changes had been studied after essential corrections such as fix errors, bands combination, georeferencing on 2012 images as basic image, by maximum likelihood and IPVI Index. It was done by supervised classification. 2004 google earth image and ground points by GPS (2010-2012) was used to compare satellite images obtained changes. Results showed mangrove area in bidkhoon was 1119072 m2 by GPS and 1231200 m2 by maximum likelihood supervised classification and 1317600 m2 by IPVI in 2012. Basatin areas is respectively: 466644 m2, 88200 m2, 63000 m2. Final results show forests have been declined naturally. It is due to human activities in Basatin. The defect was offset by planting in many years. Although the trend has been declining in recent years again. So, it mentioned satellite images have high ability to estimation all environmental processes. This research showed high correlation between images and indexes such as IPVI and NDVI with ground control points.

Keywords: IPVI index, Landsat sensor, maximum likelihood supervised classification, Nayband National Park

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Authors: Mohamed Ali Ben Halima, Malik Koubi, Joseph Lanfranchi, Yohan Wloczysiak

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This article assesses the consequences on the frequency and duration of ordinary sick leave of the January 2012 and 2018 reforms modifying the scope of sick leave reimbursement in the French civil service. These reforms introduce a one-day waiting period which removes the compensation for the first day of ordinary sick leave. In order to evaluate these reforms, we use an administrative database from the National Pension Fund for local public employees (FPT). The first important result of our data analysis is that the one-day waiting period was not introduced at the same time in the French Local Public Service establishments, or even never in some. This peculiarity allows for an identification strategy using a difference-in-differences method based on the definition at each date of groups of employees treated and not treated by the reform, since establishments that apply the one-day waiting period coexist with establishments that do not apply it. Two types of estimators are used for this evaluation: individual and time fixed effects estimators and DIDM estimators which correct for the biases of the Two Way Fixed Effects one. The results confirm that the change in the sick pay system decreases the probability of having at least one ordinary sick leave as well as the number and duration of these episodes. On the other hand, the estimates show that longer leave episodes are not less affected than shorter ones. Finally, the validity tests of the estimators support the results obtained for the second period of 2018-2019, but suggest estimation biases for the period 2012-2013. The extent to which the endogeneity of the choices of implementation of the reform at the local level impact these estimates needs to be further tested.

Keywords: sick leave, one-day waiting period, territorial civil service, public policy evaluation

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Authors: Isha Saxena, Behzad Kazemtabrizi, Matthias C. M. Troffaes, Christopher Crabtree

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The calculations done at the beginning of the life of a wind farm are rarely reliable, which makes it important to conduct research and study the failure and repair rates of the wind turbines under various conditions. This miscalculation happens because the current models make a simplifying assumption that the failure/repair rate remains constant over time. This means that the reliability function is exponential in nature. This research aims to create a more accurate model using sensory data and a data-driven approach. The data cleaning and data processing is done by comparing the Power Curve data of the wind turbines with SCADA data. This is then converted to times to repair and times to failure timeseries data. Several different mathematical functions are fitted to the times to failure and times to repair data of the wind turbine components using Maximum Likelihood Estimation and the Posterior expectation method for Bayesian Parameter Estimation. Initial results indicate that two parameter Weibull function and exponential function produce almost identical results. Further analysis is being done using the complex system analysis considering the failures of each electrical and mechanical component of the wind turbine. The aim of this project is to perform a more accurate reliability analysis that can be helpful for the engineers to schedule maintenance and repairs to decrease the downtime of the turbine.

Keywords: reliability, bayesian parameter inference, maximum likelihood estimation, weibull function, SCADA data

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Authors: S. Suman, G. N. Singh

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The present manuscript addresses the estimation procedure of population parameter using Poisson probability distribution when characteristic under study possesses a rare sensitive attribute. The generalized form of unrelated randomized response model is suggested in order to acquire the truthful responses from respondents. The resultant estimators have been proposed for two situations when the information on an unrelated rare non-sensitive characteristic is known as well as unknown. The properties of the proposed estimators are derived, and the measure of confidentiality of respondent is also suggested for respondents. Empirical studies are carried out in the support of discussed theory.

Keywords: Poisson distribution, randomized response model, rare sensitive attribute, non-sensitive attribute

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Authors: Y. Sunecher, N. Mamode Khan, V. Jowaheer

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This paper considers the modelling of a non-stationary bivariate integer-valued autoregressive moving average of order one (BINARMA(1,1)) with correlated Poisson innovations. The BINARMA(1,1) model is specified using the binomial thinning operator and by assuming that the cross-correlation between the two series is induced by the innovation terms only. Based on these assumptions, the non-stationary marginal and joint moments of the BINARMA(1,1) are derived iteratively by using some initial stationary moments. As regards to the estimation of parameters of the proposed model, the conditional maximum likelihood (CML) estimation method is derived based on thinning and convolution properties. The forecasting equations of the BINARMA(1,1) model are also derived. A simulation study is also proposed where BINARMA(1,1) count data are generated using a multivariate Poisson R code for the innovation terms. The performance of the BINARMA(1,1) model is then assessed through a simulation experiment and the mean estimates of the model parameters obtained are all efficient, based on their standard errors. The proposed model is then used to analyse a real-life accident data on the motorway in Mauritius, based on some covariates: policemen, daily patrol, speed cameras, traffic lights and roundabouts. The BINARMA(1,1) model is applied on the accident data and the CML estimates clearly indicate a significant impact of the covariates on the number of accidents on the motorway in Mauritius. The forecasting equations also provide reliable one-step ahead forecasts.

Keywords: non-stationary, BINARMA(1, 1) model, Poisson innovations, conditional maximum likelihood, CML

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Authors: Lauren M. McKinnon, Justin B. Miller, Michael F. Whiting, John S. K. Kauwe, Perry G. Ridge

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Background: Ramp sequences increase translational speed and accuracy when rare, slowly-translated codons are found at the beginnings of genes. Here, the results of the first analysis of ramp sequences in a phylogenetic construct are presented. Methods: Ramp sequences were compared from 211 vertebrates (110 Mammalian and 101 non-mammalian). The presence and absence of ramp sequences were analyzed as a binary character in a parsimony and maximum likelihood framework. Additionally, ramp sequences were mapped to the Open Tree of Life taxonomy to determine the number of parallelisms and reversals that occurred, and these results were compared to what would be expected due to random chance. Lastly, aligned nucleotides in ramp sequences were compared to the rest of the sequence in order to examine possible differences in phylogenetic signal between these regions of the gene. Results: Parsimony and maximum likelihood analyses of the presence/absence of ramp sequences recovered phylogenies that are highly congruent with established phylogenies. Additionally, the retention index of ramp sequences is significantly higher than would be expected due to random chance (p-value = 0). A chi-square analysis of completely orthologous ramp sequences resulted in a p-value of approximately zero as compared to random chance. Discussion: Ramp sequences recover comparable phylogenies as other phylogenomic methods. Although not all ramp sequences appear to have a phylogenetic signal, more ramp sequences track speciation than expected by random chance. Therefore, ramp sequences may be used in conjunction with other phylogenomic approaches.

Keywords: codon usage bias, phylogenetics, phylogenomics, ramp sequence

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Authors: Guinevere Servis

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This paper hypothesizes that withdrawal from positive self-awareness, and the increase of counterfactual-thinking and self-handicapping can help provide ample justification for an individual before, during and/or after committing a crime. The understanding of who someone is, one’s perspective on the world, and why they think the way they do is key to therapy in preventing recidivism. Developing habits to escape self-awareness, by using self-handicapping and counterfactual ideologies, may provide the necessary thinking patterns to decide disobeying the law is a worthy act to pursue. An increase in self-awareness is hypothesized to decrease the likelihood of recidivism, and ways of thinking that withdraw from self awareness can increase the likelihood of it. Especially for those who have been disadvantaged in life and disobeyed the law, self-handicapping and counterfactual thinking can also help to justify one's wrongdoing. The understanding of how a criminal views their disadvantages in the world, and one’s thinking patterns are hypothesized to help one better understand the entire scope on why a crime was committed and thus reduce the likelihood of recidivism. Utilizing therapy for prisoners to increase self-awareness of both thought and action can lead to a healthy, happier life and reduce the likelihood of reoffending. By discussing the terms associated with self-awareness theory and other psychological topics such as self-handicapping, counterfactual thinking, this paper argues the actions towards increasing positive self-awareness can help decrease likelihood of recidivism. Adversely, hypothesizing that increasing the ways of thinking that withdraw one from self-awareness, through counterfactual thinking and self-handicapping, can inherently increase the likelihood of recidivism. Evaluating these findings to further understand the needed changes in correctional institutions is fundamental to reducing crime, benefiting the criminal, the victim(s) and their family, and the state.

Keywords: crime, self-awareness theory, correctional institutions, self-regulate, counterfactual thinking, recidivism

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Authors: Desta Brhanu Gebrehiwot

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The study aims to investigate the impact of land tenure arrangements on fertilizer use per hectare in Northern Ethiopia. Household and Plot level data are used for analysis. Land tenure contracts such as sharecropping and fixed rent arrangements have endogeneity. Different unobservable characteristics may affect renting-out decisions. Thus, the appropriate method of analysis was the instrumental variable estimation technic. Therefore, the family of instrumental variable estimation methods two-stage least-squares regression (2SLS, the generalized method of moments (GMM), Limited information maximum likelihood (LIML), and instrumental variable Tobit (IV-Tobit) was used. Besides, a method to handle a binary endogenous variable is applied, which uses a two-step estimation. In the first step probit model includes instruments, and in the second step, maximum likelihood estimation (MLE) (“etregress” command in Stata 14) was used. There was lower fertilizer use per hectare on sharecropped and fixed rented plots relative to owner-operated. The result supports the Marshallian inefficiency principle in sharecropping. The difference in fertilizer use per hectare could be explained by a lack of incentivized detailed contract forms, such as giving more proportion of the output to the tenant under sharecropping contracts, which motivates to use of more fertilizer in rented plots to maximize the production because most sharecropping arrangements share output equally between tenants and landlords.

Keywords: tenure-contracts, endogeneity, plot-level data, Ethiopia, fertilizer

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Authors: Tal Remez, Or Litany, Alex Bronstein

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The pursuit of smaller pixel sizes at ever increasing resolution in digital image sensors is mainly driven by the stringent price and form-factor requirements of sensors and optics in the cellular phone market. Recently, Eric Fossum proposed a novel concept of an image sensor with dense sub-diffraction limit one-bit pixels (jots), which can be considered a digital emulation of silver halide photographic film. This idea has been recently embodied as the EPFL Gigavision camera. A major bottleneck in the design of such sensors is the image reconstruction process, producing a continuous high dynamic range image from oversampled binary measurements. The extreme quantization of the Poisson statistics is incompatible with the assumptions of most standard image processing and enhancement frameworks. The recently proposed maximum-likelihood (ML) approach addresses this difficulty, but suffers from image artifacts and has impractically high computational complexity. In this work, we study a variant of a sensor with binary threshold pixels and propose a reconstruction algorithm combining an ML data fitting term with a sparse synthesis prior. We also show an efficient hardware-friendly real-time approximation of this inverse operator. Promising results are shown on synthetic data as well as on HDR data emulated using multiple exposures of a regular CMOS sensor.

Keywords: binary pixels, maximum likelihood, neural networks, sparse coding

Procedia PDF Downloads 172

Authors: Fazlul Hoque, Tahmina Akter Joya, Asma Akter, Supawat Rungsuriyawiboon

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Rice is the staple food in Bangladesh, and therefore, self-sufficiency in rice production remains a major concern. However, Bangladesh is experiencing insufficiency in rice production due to high production cost and low national average productivity of 2.848 ton/ha in comparison to other rice-growing countries in the world. This study aims to find out the profit efficiency and determinants of profit efficiency in Boro rice cultivation in Manikganj and Dhaka districts of Bangladesh. It also focuses on technology adoption and effect of technology adoption on profit efficiency of Boro rice cultivation in Bangladesh. The data were collected from 300 households growing Boro rice through face to face interviews by one set structured questionnaire; Frontier Version 4.1 and STATA 15 software were employed to analyze the data according to the purpose of the study. Maximum likelihood estimates of the specified profit model showed that profit efficiency of the farmer varied between 23% and 97% with a mean of 76% which implied as 24% of the profit is lost due to a combination of technical and allocative inefficiencies in Boro rice cultivation in the study area. The inefficiency model revealed that the education level of the farmer, farm size, variety of seed, and training and extension service influence the profit inefficiency significantly. The study also explained that the level of technology adoption index affects profit efficiency. The technology adoption in Boro rice cultivation is influenced by the education level of the farmer, farm size and farm capital.

Keywords: farmer, maximum likelihood estimation, profit efficiency, rice

Procedia PDF Downloads 110

Authors: Nadarajah I. Ramesh

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Much of the research on stochastic point process models for rainfall has focused on Poisson cluster models constructed from either the Neyman-Scott or Bartlett-Lewis processes. The doubly stochastic Poisson process provides a rich class of point process models, especially for fine-scale rainfall modelling. This paper provides an account of recent development on this topic and presents the results based on some of the fine-scale rainfall models constructed from this class of stochastic point processes. Amongst the literature on stochastic models for rainfall, greater emphasis has been placed on modelling rainfall data recorded at hourly or daily aggregation levels. Stochastic models for sub-hourly rainfall are equally important, as there is a need to reproduce rainfall time series at fine temporal resolutions in some hydrological applications. For example, the study of climate change impacts on hydrology and water management initiatives requires the availability of data at fine temporal resolutions. One approach to generating such rainfall data relies on the combination of an hourly stochastic rainfall simulator, together with a disaggregator making use of downscaling techniques. Recent work on this topic adopted a different approach by developing specialist stochastic point process models for fine-scale rainfall aimed at generating synthetic precipitation time series directly from the proposed stochastic model. One strand of this approach focused on developing a class of doubly stochastic Poisson process (DSPP) models for fine-scale rainfall to analyse data collected in the form of rainfall bucket tip time series. In this context, the arrival pattern of rain gauge bucket tip times N(t) is viewed as a DSPP whose rate of occurrence varies according to an unobserved finite state irreducible Markov process X(t). Since the likelihood function of this process can be obtained, by conditioning on the underlying Markov process X(t), the models were fitted with maximum likelihood methods. The proposed models were applied directly to the raw data collected by tipping-bucket rain gauges, thus avoiding the need to convert tip-times to rainfall depths prior to fitting the models. One advantage of this approach was that the use of maximum likelihood methods enables a more straightforward estimation of parameter uncertainty and comparison of sub-models of interest. Another strand of this approach employed the DSPP model for the arrivals of rain cells and attached a pulse or a cluster of pulses to each rain cell. Different mechanisms for the pattern of the pulse process were used to construct variants of this model. We present the results of these models when they were fitted to hourly and sub-hourly rainfall data. The results of our analysis suggest that the proposed class of stochastic models is capable of reproducing the fine-scale structure of the rainfall process, and hence provides a useful tool in hydrological modelling.

Keywords: fine-scale rainfall, maximum likelihood, point process, stochastic model

Procedia PDF Downloads 251

Authors: I. V. Pinto, M. R. Sooriyarachchi

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It can be frequently observed that the data arising in our environment have a hierarchical or a nested structure attached with the data. Multilevel modelling is a modern approach to handle this kind of data. When multilevel modelling is combined with a binary response, the estimation methods get complex in nature and the usual techniques are derived from quasi-likelihood method. The estimation methods which are compared in this study are, marginal quasi-likelihood (order 1 & order 2) (MQL1, MQL2) and penalized quasi-likelihood (order 1 & order 2) (PQL1, PQL2). A statistical model is of no use if it does not reflect the given dataset. Therefore, checking the adequacy of the fitted model through a goodness-of-fit (GOF) test is an essential stage in any modelling procedure. However, prior to usage, it is also equally important to confirm that the GOF test performs well and is suitable for the given model. This study assesses the suitability of the GOF test developed for binary response multilevel models with respect to the method used in model estimation. An extensive set of simulations was conducted using MLwiN (v 2.19) with varying number of clusters, cluster sizes and intra cluster correlations. The test maintained the desirable Type-I error for models estimated using PQL2 and it failed for almost all the combinations of MQL. Power of the test was adequate for most of the combinations in all estimation methods except MQL1. Moreover, models were fitted using the four methods to a real-life dataset and performance of the test was compared for each model.

Keywords: goodness-of-fit test, marginal quasi-likelihood, multilevel modelling, penalized quasi-likelihood, power, quasi-likelihood, type-I error

Procedia PDF Downloads 117

Authors: Sizar Abed Mohammed, Zahraa Ghazi Sadeeq

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The use of the classic method, least squares (OLS) to estimate the linear regression parameters, when they are available assumptions, and capabilities that have good characteristics, such as impartiality, minimum variance, consistency, and so on. The development of alternative statistical techniques to estimate the parameters, when the data are contaminated with outliers. These are powerful methods (or resistance). In this paper, three of robust methods are studied, which are: Maximum likelihood type estimate M-estimator, Modified Maximum likelihood type estimate MM-estimator and Least Trimmed Squares LTS-estimator, and their results are compared with OLS method. These methods applied to real data taken from Duhok company for manufacturing furniture, the obtained results compared by using the criteria: Mean Squared Error (MSE), Mean Absolute Percentage Error (MAPE) and Mean Sum of Absolute Error (MSAE). Important conclusions that this study came up with are: a number of typical values detected by using four methods in the furniture line and very close to the data. This refers to the fact that close to the normal distribution of standard errors, but typical values in the doors line data, using OLS less than that detected by the powerful ways. This means that the standard errors of the distribution are far from normal departure. Another important conclusion is that the estimated values of the parameters by using the lifeline is very far from the estimated values using powerful methods for line doors, gave LTS- destined better results using standard MSE, and gave the M- estimator better results using standard MAPE. Moreover, we noticed that using standard MSAE, and MM- estimator is better. The programs S-plus (version 8.0, professional 2007), Minitab (version 13.2) and SPSS (version 17) are used to analyze the data.

Keywords: Robest, LTS, M estimate, MSE

Procedia PDF Downloads 207

Authors: Alvaro Callejas-Ramos, Lorena Alvarez-Perez, Alexander Benitez-Buenache, Anibal R. Figueiras-Vidal

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This contribution presents a promising formulation which allows to extend the principled binary rebalancing procedures, also known as neutral re-balancing mechanisms in the sense that they do not alter the likelihood ratio

Keywords: Bregman divergences, imbalanced multiclass classifi-cation, informed re-balancing, invariant likelihood ratio

Procedia PDF Downloads 178