This document provides an overview of logistic regression for categorical response variables. It begins with examples of binary, ordinal, and nominal categorical variables. It then demonstrates how logistic regression models the log-odds of an event rather than the mean, as linear regression does. The key aspects of binary logistic regression models are described, including the logit form and probability form of the model. Examples are provided using R to model gender based on height, the success of golf putts based on length, and the effectiveness of a medical treatment compared to placebo. Key outputs from logistic regression in R like coefficients, odds ratios, and model comparison are also summarized.
This document provides an overview of logistic regression for categorical response variables. It begins with examples of binary, ordinal, and nominal categorical response variables. It then demonstrates how ordinary linear regression is inappropriate for binary response data and introduces the logistic regression model as an alternative. The document explains the logistic regression model equation, illustrates model fitting in R, and interprets the results including odds ratios. It provides an example analysis of a dataset on golf putts.
Numerical integration is the approximate computation of an integral using numerical techniques. The numerical computation of an integral is sometimes called quadrature. ... A generalization of the trapezoidal rule is Romberg integration, which can yield accurate results for many fewer function evaluations.
The document describes a recursive process for assigning values to x variables indexed from 1 to m. For each even index k, xk is defined as a polynomial in δ with decreasing powers and alternating signs. For each odd index k, xk is defined as the same polynomial but with the signs flipped. It is shown that as m approaches infinity and δ approaches 1, the pair of values (x1, x2) approach the point (1/2, 1/2).
Calculus 10th edition anton solutions manualReece1334
Download at: https://goo.gl/e1svMM
People also search:
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Applied statistics and probability for engineers solution montgomery && rungerAnkit Katiyar
This document is the copyright page and preface for the book "Applied Statistics and Probability for Engineers" by Douglas C. Montgomery and George C. Runger. The copyright is held by John Wiley & Sons, Inc. in 2003. This book was edited, designed, and produced by various teams at John Wiley & Sons and printed by Donnelley/Willard. The preface states that the purpose of the included Student Solutions Manual is to provide additional help for students in understanding the problem-solving processes presented in the main text.
The document appears to discuss Bayesian statistical modeling and inference. It includes definitions of terms like the correlation coefficient (ρ), bivariate normal distributions, and binomial distributions. It shows the setup of a Bayesian hierarchical model with multivariate normal outcomes and estimates of the model parameters, including the correlations (ρA and ρB) between two groups of bivariate data.
This document provides two examples of analyzing the forces and critical angle required for impending motion of a pin on a surface. It considers the forces and reactions for motion to the left and right. The critical angle is determined by resolving the applied force into components related to mass and acceleration and friction. The pin will accelerate if the angle is less than critical and will not move if the angle is greater than critical. The role of pin diameter is also briefly mentioned.
- The document discusses random number generation and probability distributions. It presents methods for generating random numbers from Bernoulli, binomial, beta, and multinomial distributions using random bits generated from linear congruential generators.
- Graphical examples are shown comparing histograms of generated random samples to theoretical probability density functions. Code examples in R demonstrate how to simulate random number generation from various discrete distributions.
- The goal is to introduce different methods for random number generation from basic discrete distributions that are important for modeling random phenomena and Monte Carlo simulations.
This document provides an overview of logistic regression for categorical response variables. It begins with examples of binary, ordinal, and nominal categorical response variables. It then demonstrates how ordinary linear regression is inappropriate for binary response data and introduces the logistic regression model as an alternative. The document explains the logistic regression model equation, illustrates model fitting in R, and interprets the results including odds ratios. It provides an example analysis of a dataset on golf putts.
Numerical integration is the approximate computation of an integral using numerical techniques. The numerical computation of an integral is sometimes called quadrature. ... A generalization of the trapezoidal rule is Romberg integration, which can yield accurate results for many fewer function evaluations.
The document describes a recursive process for assigning values to x variables indexed from 1 to m. For each even index k, xk is defined as a polynomial in δ with decreasing powers and alternating signs. For each odd index k, xk is defined as the same polynomial but with the signs flipped. It is shown that as m approaches infinity and δ approaches 1, the pair of values (x1, x2) approach the point (1/2, 1/2).
Calculus 10th edition anton solutions manualReece1334
Download at: https://goo.gl/e1svMM
People also search:
calculus 10th edition pdf
anton calculus pdf
howard anton calculus 10th edition solution pdf
calculus late transcendentals combined with wiley plus set
calculus multivariable version
calculus by howard anton pdf free download
calculus anton bivens davis 10th edition solutions pdf
calculus anton pdf download
Applied statistics and probability for engineers solution montgomery && rungerAnkit Katiyar
This document is the copyright page and preface for the book "Applied Statistics and Probability for Engineers" by Douglas C. Montgomery and George C. Runger. The copyright is held by John Wiley & Sons, Inc. in 2003. This book was edited, designed, and produced by various teams at John Wiley & Sons and printed by Donnelley/Willard. The preface states that the purpose of the included Student Solutions Manual is to provide additional help for students in understanding the problem-solving processes presented in the main text.
The document appears to discuss Bayesian statistical modeling and inference. It includes definitions of terms like the correlation coefficient (ρ), bivariate normal distributions, and binomial distributions. It shows the setup of a Bayesian hierarchical model with multivariate normal outcomes and estimates of the model parameters, including the correlations (ρA and ρB) between two groups of bivariate data.
This document provides two examples of analyzing the forces and critical angle required for impending motion of a pin on a surface. It considers the forces and reactions for motion to the left and right. The critical angle is determined by resolving the applied force into components related to mass and acceleration and friction. The pin will accelerate if the angle is less than critical and will not move if the angle is greater than critical. The role of pin diameter is also briefly mentioned.
- The document discusses random number generation and probability distributions. It presents methods for generating random numbers from Bernoulli, binomial, beta, and multinomial distributions using random bits generated from linear congruential generators.
- Graphical examples are shown comparing histograms of generated random samples to theoretical probability density functions. Code examples in R demonstrate how to simulate random number generation from various discrete distributions.
- The goal is to introduce different methods for random number generation from basic discrete distributions that are important for modeling random phenomena and Monte Carlo simulations.
Beta and gamma are the two most popular functions in mathematics. Gamma is a single variable function, whereas Beta is a two-variable function. The relation between beta and gamma function will help to solve many problems in physics and mathematics.
This document discusses probability density functions (pdfs) and how they relate to probability distribution functions. It provides examples of common pdfs like the uniform and Gaussian distributions. The Gaussian or normal distribution is described in more detail. The document also discusses how to determine the pdf of a random variable that is a function of another random variable, whether the function is monotonic or non-monotonic. Key aspects like changing of variables in integrals and combining probabilities for multiple values are addressed.
Hand book of Howard Anton calculus exercises 8th editionPriSim
The document contains the table of contents for a calculus textbook. It lists 17 chapters covering topics such as functions, limits, derivatives, integrals, vector calculus, and applications of calculus. It also includes 6 appendices reviewing concepts in real numbers, trigonometry, coordinate planes, and polynomial equations.
Design of an automotive differential with reduction ratio greater than 6eSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
This document discusses trigonometric substitutions that can be used to evaluate integrals containing expressions of the form √a2 - x2, √a2 + x2, and √x2 - a2. It provides the substitutions x = a*sin(θ), x = a*tan(θ), and x = a*sec(θ) respectively, and shows the resulting algebraic relationships. It also includes an example problem demonstrating the use of these substitutions.
B.tech ii unit-2 material beta gamma functionRai University
1. The document discusses the gamma and beta functions, which are defined in terms of improper definite integrals involving exponential and power functions.
2. Examples are provided to demonstrate properties and applications of the gamma function, including evaluating integrals involving the gamma function.
3. The beta function is defined in terms of an integral from 0 to 1, and its relationship to the gamma function is described.
This document presents an overview of optimization algorithms on Riemannian manifolds. It begins by introducing concepts such as vector transport and retraction mappings that are used to generalize algorithms from Euclidean spaces to manifolds. It then summarizes several classical optimization methods including gradient descent, conjugate gradient, and variants of quasi-Newton methods adapted to the Riemannian setting using these geometric concepts. The convergence of the Fletcher-Reeves method is analyzed under standard assumptions on the objective function. Overall, the document provides a conceptual and mathematical foundation for optimization on manifolds.
shooting method with Range kutta methodSetuThacker
how to solve the differential equation by using shooting method & range Kutta method.there is one problem statement, which is related to the temperature distribution problem over an iron rod. there is two graphs of the 2nd order and 4th order Range Kutta. there is one combine graph of the both the method which gives correct & closest answer.
Thank You...!!!
- Hiroaki Shiokawa's research interests include graph mining, network analysis, and efficient algorithms. He was previously employed at NTT from 2011 to 2015.
- His current research focuses on developing clustering algorithms for large-scale networks and evaluating their performance on real-world network datasets.
- He has published highly cited papers in top data mining and network science conferences such as KDD, CIKM, and WSDM.
The document demonstrates various operations that can be performed on vectors and data frames in R. It shows how to create, subset, reorder, and modify vectors and data frames. Key operations include subsetting vectors and data frames using indices or logical vectors, applying functions to entire vectors or selected elements, and reordering a data frame based on the values in one of its columns.
On Approach to Increase Integration Rate of Elements of an Operational Amplif...BRNSS Publication Hub
In this paper, we introduce an approach to optimize manufacturing of an operational amplifier circuit based on field-effect transistors. Main aims of the optimization are (i) decreasing dimensions of elements of the considered operational amplifier and (ii) increasing of performance and reliability of the considered field-effect transistors. Dimensions of considered field-effect transistors will be decreased due to manufacture of these transistors framework heterostructure with specific structure, doping of required areas of the heterostructure by diffusion or ion implantation, and optimization of annealing of dopant and/or radiation defects. Performance and reliability of the above field-effect transistors could be increased by optimization of annealing of dopant and/or radiation defects and using inhomogeneity of properties of heterostructure. Choosing of inhomogeneity of properties of heterostructure leads to increasing of compactness of distribution of concentration of dopant. At the same time, one can obtain increasing of homogeneity of the above concentration. In this paper, we also introduce an analytical approach for prognosis of technological process of manufacturing of the considered operational amplifier. The approach gives a possibility to take into account variation of parameters of processes in space and at the same time in space. At the same time, one can take into account nonlinearity of the considered processes.
Comparing Machine Learning Algorithms in Text MiningAndrea Gigli
In this project I compare different Machine Learning Algorithm on different Text Mining Tasks.
ML algorithms: Naive Bayes, Support Vector Machine, Decision Trees, Random Forest, Ordinal Regression as ML task
Tasks considered: Classifying Positive and Negative Reviews, Predicting Review Stars, Quantifying Sentiment Over Time, Detecting Fake Reviews
In the presence of relevant physical observations, one can usually calibrate a computer model, and even estimate systematic discrepancies of the model from reality. Estimating and quantifying the uncertainty in this model discrepancy can lead to reliable predictions - so long as the prediction "is similar to" the available physical observations. Exactly how to define "similar" has proven difficult in many applications. Clearly it depends on how well the computational model captures the relevant physics in the system, as well as how portable the model discrepancy is in going from the available physical data to the prediction. This talk will discuss these concepts using computational models ranging from simple to very complex.
The document describes various variable selection methods applied to predict violent crime rates using socioeconomic data from US cities. It analyzes a dataset with 95 variables and 807 observations, using several variable selection techniques to determine the most predictive factors of violent crime. These include best random subset selection (BRSS), which approximates best subset selection by randomly selecting variable combinations. BRSS identified factors like immigration, ethnicity, family structure, and income as best predicting violent crime rates. Model performance was evaluated using metrics like R2, and BRSS had strong out-of-sample prediction, outperforming some other common techniques.
The document analyzes material selection for the shelf and front cover of a product. For the shelf, polyvinylchloride (PVC) is identified as the best option based on its mechanical properties, cost, and mass. Specifically, PVC rigid molding and extrusion is selected with a thickness of 5mm. For the front cover, injection molding is specified with a maximum thickness of 6mm and force range of 90-120N. The document establishes constraints on the material's modulus of elasticity, yield strength and deformation to meet the design requirements.
The document contains 14 example problems solving for various values in gear design equations. Problem 14-1 solves for pressure angle, velocity, load, and bending stress. Problem 14-2 similarly solves for a different gear set. Problem 14-3 converts units and solves for velocity, load, and bending stress in MPa.
1. The document discusses the gamma and beta functions, which are defined in terms of improper definite integrals and belong to the category of special transcendental functions.
2. Several properties and examples involving the gamma and beta functions are provided, including their relationship via the equation β(m,n)= Γ(m)Γ(n)/Γ(m+n).
3. Dirichlet's integral and its extension to calculating areas and volumes are covered. Four examples demonstrating the application of gamma and beta functions are worked out.
Data Science Training in Bangalore | Learnbay.in | Decision Tree | Machine Le...Learnbay Datascience
Decision Tree by Learnbay | Data Science Training in Bangalore | Machine Learning Courses. Learnbay offers classroom data science training courses in Bangalore with project and job assistance for working professionals.For more details visit https://www.learnbay.in/shop/courses/data-science-training-courses-bangalore/
This document provides an overview of logistic regression for categorical response variables. It begins with examples of binary, ordinal, and nominal categorical response variables. It then demonstrates how ordinary linear regression is inappropriate for binary response data and introduces the logistic regression model as an alternative. The document explains the logistic regression model equation, illustrates model fitting in R, and interprets the results including odds ratios. It provides an example analysis of data on transcranial magnetic stimulation for migraines. Finally, it compares different approaches to testing associations for binary response variables.
This document provides an overview of logistic regression for categorical response variables. It begins with examples of binary, ordinal, and nominal categorical response variables. It then demonstrates how ordinary linear regression is inappropriate for binary response data and introduces the logistic regression model as an alternative. The key aspects of logistic regression covered include the logit link function, interpreting odds ratios, and using the logistic model to predict probabilities rather than raw values. Examples are provided using R to model binary response golf putting and medical treatment data.
This document discusses logistic regression for categorical response variables. It provides examples of binary and ordinal categorical response variables like whether someone smokes (yes/no) or the success of a medical treatment (survives/dies). It then demonstrates how to perform binary logistic regression in R to predict a binary outcome like gender from height. Key aspects covered include interpreting the logistic regression coefficients, plotting the logistic curve, and calculating odds ratios to compare two groups.
Beta and gamma are the two most popular functions in mathematics. Gamma is a single variable function, whereas Beta is a two-variable function. The relation between beta and gamma function will help to solve many problems in physics and mathematics.
This document discusses probability density functions (pdfs) and how they relate to probability distribution functions. It provides examples of common pdfs like the uniform and Gaussian distributions. The Gaussian or normal distribution is described in more detail. The document also discusses how to determine the pdf of a random variable that is a function of another random variable, whether the function is monotonic or non-monotonic. Key aspects like changing of variables in integrals and combining probabilities for multiple values are addressed.
Hand book of Howard Anton calculus exercises 8th editionPriSim
The document contains the table of contents for a calculus textbook. It lists 17 chapters covering topics such as functions, limits, derivatives, integrals, vector calculus, and applications of calculus. It also includes 6 appendices reviewing concepts in real numbers, trigonometry, coordinate planes, and polynomial equations.
Design of an automotive differential with reduction ratio greater than 6eSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
This document discusses trigonometric substitutions that can be used to evaluate integrals containing expressions of the form √a2 - x2, √a2 + x2, and √x2 - a2. It provides the substitutions x = a*sin(θ), x = a*tan(θ), and x = a*sec(θ) respectively, and shows the resulting algebraic relationships. It also includes an example problem demonstrating the use of these substitutions.
B.tech ii unit-2 material beta gamma functionRai University
1. The document discusses the gamma and beta functions, which are defined in terms of improper definite integrals involving exponential and power functions.
2. Examples are provided to demonstrate properties and applications of the gamma function, including evaluating integrals involving the gamma function.
3. The beta function is defined in terms of an integral from 0 to 1, and its relationship to the gamma function is described.
This document presents an overview of optimization algorithms on Riemannian manifolds. It begins by introducing concepts such as vector transport and retraction mappings that are used to generalize algorithms from Euclidean spaces to manifolds. It then summarizes several classical optimization methods including gradient descent, conjugate gradient, and variants of quasi-Newton methods adapted to the Riemannian setting using these geometric concepts. The convergence of the Fletcher-Reeves method is analyzed under standard assumptions on the objective function. Overall, the document provides a conceptual and mathematical foundation for optimization on manifolds.
shooting method with Range kutta methodSetuThacker
how to solve the differential equation by using shooting method & range Kutta method.there is one problem statement, which is related to the temperature distribution problem over an iron rod. there is two graphs of the 2nd order and 4th order Range Kutta. there is one combine graph of the both the method which gives correct & closest answer.
Thank You...!!!
- Hiroaki Shiokawa's research interests include graph mining, network analysis, and efficient algorithms. He was previously employed at NTT from 2011 to 2015.
- His current research focuses on developing clustering algorithms for large-scale networks and evaluating their performance on real-world network datasets.
- He has published highly cited papers in top data mining and network science conferences such as KDD, CIKM, and WSDM.
The document demonstrates various operations that can be performed on vectors and data frames in R. It shows how to create, subset, reorder, and modify vectors and data frames. Key operations include subsetting vectors and data frames using indices or logical vectors, applying functions to entire vectors or selected elements, and reordering a data frame based on the values in one of its columns.
On Approach to Increase Integration Rate of Elements of an Operational Amplif...BRNSS Publication Hub
In this paper, we introduce an approach to optimize manufacturing of an operational amplifier circuit based on field-effect transistors. Main aims of the optimization are (i) decreasing dimensions of elements of the considered operational amplifier and (ii) increasing of performance and reliability of the considered field-effect transistors. Dimensions of considered field-effect transistors will be decreased due to manufacture of these transistors framework heterostructure with specific structure, doping of required areas of the heterostructure by diffusion or ion implantation, and optimization of annealing of dopant and/or radiation defects. Performance and reliability of the above field-effect transistors could be increased by optimization of annealing of dopant and/or radiation defects and using inhomogeneity of properties of heterostructure. Choosing of inhomogeneity of properties of heterostructure leads to increasing of compactness of distribution of concentration of dopant. At the same time, one can obtain increasing of homogeneity of the above concentration. In this paper, we also introduce an analytical approach for prognosis of technological process of manufacturing of the considered operational amplifier. The approach gives a possibility to take into account variation of parameters of processes in space and at the same time in space. At the same time, one can take into account nonlinearity of the considered processes.
Comparing Machine Learning Algorithms in Text MiningAndrea Gigli
In this project I compare different Machine Learning Algorithm on different Text Mining Tasks.
ML algorithms: Naive Bayes, Support Vector Machine, Decision Trees, Random Forest, Ordinal Regression as ML task
Tasks considered: Classifying Positive and Negative Reviews, Predicting Review Stars, Quantifying Sentiment Over Time, Detecting Fake Reviews
In the presence of relevant physical observations, one can usually calibrate a computer model, and even estimate systematic discrepancies of the model from reality. Estimating and quantifying the uncertainty in this model discrepancy can lead to reliable predictions - so long as the prediction "is similar to" the available physical observations. Exactly how to define "similar" has proven difficult in many applications. Clearly it depends on how well the computational model captures the relevant physics in the system, as well as how portable the model discrepancy is in going from the available physical data to the prediction. This talk will discuss these concepts using computational models ranging from simple to very complex.
The document describes various variable selection methods applied to predict violent crime rates using socioeconomic data from US cities. It analyzes a dataset with 95 variables and 807 observations, using several variable selection techniques to determine the most predictive factors of violent crime. These include best random subset selection (BRSS), which approximates best subset selection by randomly selecting variable combinations. BRSS identified factors like immigration, ethnicity, family structure, and income as best predicting violent crime rates. Model performance was evaluated using metrics like R2, and BRSS had strong out-of-sample prediction, outperforming some other common techniques.
The document analyzes material selection for the shelf and front cover of a product. For the shelf, polyvinylchloride (PVC) is identified as the best option based on its mechanical properties, cost, and mass. Specifically, PVC rigid molding and extrusion is selected with a thickness of 5mm. For the front cover, injection molding is specified with a maximum thickness of 6mm and force range of 90-120N. The document establishes constraints on the material's modulus of elasticity, yield strength and deformation to meet the design requirements.
The document contains 14 example problems solving for various values in gear design equations. Problem 14-1 solves for pressure angle, velocity, load, and bending stress. Problem 14-2 similarly solves for a different gear set. Problem 14-3 converts units and solves for velocity, load, and bending stress in MPa.
1. The document discusses the gamma and beta functions, which are defined in terms of improper definite integrals and belong to the category of special transcendental functions.
2. Several properties and examples involving the gamma and beta functions are provided, including their relationship via the equation β(m,n)= Γ(m)Γ(n)/Γ(m+n).
3. Dirichlet's integral and its extension to calculating areas and volumes are covered. Four examples demonstrating the application of gamma and beta functions are worked out.
Data Science Training in Bangalore | Learnbay.in | Decision Tree | Machine Le...Learnbay Datascience
Decision Tree by Learnbay | Data Science Training in Bangalore | Machine Learning Courses. Learnbay offers classroom data science training courses in Bangalore with project and job assistance for working professionals.For more details visit https://www.learnbay.in/shop/courses/data-science-training-courses-bangalore/
This document provides an overview of logistic regression for categorical response variables. It begins with examples of binary, ordinal, and nominal categorical response variables. It then demonstrates how ordinary linear regression is inappropriate for binary response data and introduces the logistic regression model as an alternative. The document explains the logistic regression model equation, illustrates model fitting in R, and interprets the results including odds ratios. It provides an example analysis of data on transcranial magnetic stimulation for migraines. Finally, it compares different approaches to testing associations for binary response variables.
This document provides an overview of logistic regression for categorical response variables. It begins with examples of binary, ordinal, and nominal categorical response variables. It then demonstrates how ordinary linear regression is inappropriate for binary response data and introduces the logistic regression model as an alternative. The key aspects of logistic regression covered include the logit link function, interpreting odds ratios, and using the logistic model to predict probabilities rather than raw values. Examples are provided using R to model binary response golf putting and medical treatment data.
This document discusses logistic regression for categorical response variables. It provides examples of binary and ordinal categorical response variables like whether someone smokes (yes/no) or the success of a medical treatment (survives/dies). It then demonstrates how to perform binary logistic regression in R to predict a binary outcome like gender from height. Key aspects covered include interpreting the logistic regression coefficients, plotting the logistic curve, and calculating odds ratios to compare two groups.
This document discusses numerical integration techniques including the trapezoidal rule, Simpson's 1/3 rule, and Gaussian quadrature. It provides examples of calculating definite integrals using each method. The trapezoidal rule approximates the integral by dividing the region into trapezoids. Simpson's 1/3 rule is more accurate and divides the region into Simpson panels. Gaussian quadrature uses specific abscissas and weights to accurately estimate integrals, such as using one, two, or three points. Examples are provided to demonstrate calculating area under a curve and definite integrals using these numerical integration methods.
This document discusses algorithms for predictive modeling, including logistic regression. It presents a medical dataset containing measurements of heart patients and whether they survived. Logistic regression is applied to predict survival using maximum likelihood estimation. Numerical optimization techniques like BFGS and Fisher's algorithm are discussed for maximum likelihood estimation of logistic regression. Iteratively reweighted least squares is also presented as an alternative approach.
Explicit upper bound for the function of sum of divisorsAlexander Decker
1) The document discusses improving the explicit upper bound for the sum of divisors function σ(n) proved by Aleksander Ivic.
2) It proves a new upper bound of σ(n) < 2.509038354n log log n for n ≥ 82, improving on Ivic's result which was for n ≥ 7.
3) This is done by improving three lemmas used by Ivic regarding bounds on the prime factors of n and their sums and products.
The document provides information about normal probability distributions and how to solve problems using normal distributions. It defines the normal distribution and standard normal distribution. It gives the equation for a normal distribution and how to standardize a normal variable. Examples are provided on finding probabilities and areas under the normal curve. The document also discusses using normal approximations to the binomial and Poisson distributions and provides continuity correction rules for such approximations.
The document discusses various methods for modeling input distributions in simulation models, including trace-driven simulation, empirical distributions, and fitting theoretical distributions to real data. It provides examples of several continuous and discrete probability distributions commonly used in simulation, including the exponential, normal, gamma, Weibull, binomial, and Poisson distributions. Key parameters and properties of each distribution are defined. Methods for selecting an appropriate input distribution based on summary statistics of real data are also presented.
The work deals finite frequency H∞ control design for continuous time nonlinear systems, we provide sufficient conditions, ensuring that the closed-loop model is stable. Simulations will be gifted to show level of attenuation that a H∞ lower can be by our method obtained developed where further comparison.
This document summarizes the results of a study on classifying tables in HTML documents as genuine or non-genuine tables. It describes the dataset, features considered for the classification including layout, content type and word group features. It discusses various machine learning models tested - SVM, Decision Tree, Random Forest, Adaboost and Neural Networks. It provides the optimal parameters determined for each model and compares their performance on the table classification task based on accuracy, F1 score and confusion matrices.
In this work, we study H∞ control wind turbine fuzzy model for finite frequency(FF) interval. Less conservative results are obtained by using Finsler’s lemma technique, generalized Kalman Yakubovich Popov (gKYP), linear matrix inequality (LMI) approach and added several separate parameters, these conditions are given in terms of LMI which can be efficiently solved numerically for the problem that such fuzzy systems are admissible with H∞ disturbance attenuation level. The FF H∞ performance approach allows the state feedback command in a specific interval, the simulation example is given to validate our results.
The document provides an example of using R to compute maximum likelihood estimates (MLE) for common probability distributions. It demonstrates computing the MLE for the normal distribution using the nlm and optim functions in R. The MLE is estimated to be 1.714284 for the mean and 11.346933 for the variance. Some checks are shown to validate the MLE estimates. The document also provides examples of computing likelihood ratio tests and confidence intervals for the normal distribution parameters, and demonstrates a t-test and likelihood ratio test for the mean.
2014 spring crunch seminar (SDE/levy/fractional/spectral method)Zheng Mengdi
This document summarizes numerical methods for simulating stochastic partial differential equations (SPDEs) with tempered alpha-stable (TαS) processes. It discusses two main methods:
1) The compound Poisson (CP) approximation method, which simulates large jumps as a CP process and replaces small jumps with their expected drift term.
2) The series representation method, which represents the TαS process as an infinite series involving i.i.d. random variables.
It also provides algorithms for implementing these two methods and applies them to simulate specific examples like reaction-diffusion equations with TαS noise. Numerical results demonstrate that both methods can accurately capture the statistics of the underlying TαS
Response Surface in Tensor Train format for Uncertainty QuantificationAlexander Litvinenko
We apply low-rank Tensor Train format to solve PDEs with uncertain coefficients. First, we approximate uncertain permeability coefficient in TT format, then the operator and then apply iterations to solve stochastic Galerkin system.
A successful maximum likelihood parameter estimation in skewed distributions ...Hideo Hirose
A successful maximum likelihood parameter estimation scheme using
the continuation method (homotopy method) is introduced. This
algorithm is particularly useful for the three-parameter skewed
distributions including thresholds. Such three-parameter
distributions are, for example, Weibull, log-normal, gamma and
inverse Gaussian distributions. As the proposed algorithm can almost
always obtain the local maximum likelihood estimates automatically,
it is of considerable practical value. The Monte Carlo simulation
study shows the effectiveness of the proposed method.
Minimum edit distance is used to determine the similarity between two strings by calculating the minimum number of edit operations (insertions, deletions, substitutions) needed to transform one string into the other. Dynamic programming is commonly used to efficiently compute the minimum edit distance through building an edit distance table and backtracking to find the optimal alignment between the strings. This technique has applications in areas like computational biology, machine translation, and information extraction.
This document discusses multicollinearity, beginning with definitions and the case of perfect multicollinearity. It then examines the case of near or imperfect multicollinearity using data on the demand for widgets. There is high multicollinearity between the price and income variables, resulting in unstable coefficient estimates with large standard errors and insignificant t-statistics. The document outlines methods to detect multicollinearity such as high R-squared but insignificant variables, high pairwise correlations, auxiliary regressions, and variance inflation factors. It provides an example using data on chicken demand.
This document summarizes key concepts about linear time-invariant (LTI) systems including:
1. LTI systems exhibit superposition and the output is the summation of individual impulse responses.
2. Inputs can be represented as a linear combination of shifted unit impulses. The output is the convolution sum of the input and impulse response.
3. Convolution represents the output of an LTI system and can be computed using a summation or integral. Common properties like commutativity and distributivity apply.
This document provides an introduction to fuzzy logic and fuzzy systems. It discusses classical set theory versus fuzzy set theory and membership functions. Types of fuzzy membership functions like triangular, trapezoidal, and Gaussian are shown. The key components of a fuzzy logic controller including fuzzification, fuzzy inference system, and defuzzification are described. Several defuzzification methods such as mean of maxima, centroid, and approximate centroid are explained. Examples of fuzzy applications in areas like washing machines and autonomous vehicles are presented. The document also discusses building fuzzy systems using MATLAB/Simulink and at the command line. Finally, it briefly introduces PID fuzzy controllers.
Introduction to AI for Nonprofits with Tapp NetworkTechSoup
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...PECB
Denis is a dynamic and results-driven Chief Information Officer (CIO) with a distinguished career spanning information systems analysis and technical project management. With a proven track record of spearheading the design and delivery of cutting-edge Information Management solutions, he has consistently elevated business operations, streamlined reporting functions, and maximized process efficiency.
Certified as an ISO/IEC 27001: Information Security Management Systems (ISMS) Lead Implementer, Data Protection Officer, and Cyber Risks Analyst, Denis brings a heightened focus on data security, privacy, and cyber resilience to every endeavor.
His expertise extends across a diverse spectrum of reporting, database, and web development applications, underpinned by an exceptional grasp of data storage and virtualization technologies. His proficiency in application testing, database administration, and data cleansing ensures seamless execution of complex projects.
What sets Denis apart is his comprehensive understanding of Business and Systems Analysis technologies, honed through involvement in all phases of the Software Development Lifecycle (SDLC). From meticulous requirements gathering to precise analysis, innovative design, rigorous development, thorough testing, and successful implementation, he has consistently delivered exceptional results.
Throughout his career, he has taken on multifaceted roles, from leading technical project management teams to owning solutions that drive operational excellence. His conscientious and proactive approach is unwavering, whether he is working independently or collaboratively within a team. His ability to connect with colleagues on a personal level underscores his commitment to fostering a harmonious and productive workplace environment.
Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
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Macroeconomics- Movie Location
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A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...Dr. Vinod Kumar Kanvaria
Exploiting Artificial Intelligence for Empowering Researchers and Faculty,
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How to Manage Your Lost Opportunities in Odoo 17 CRMCeline George
Odoo 17 CRM allows us to track why we lose sales opportunities with "Lost Reasons." This helps analyze our sales process and identify areas for improvement. Here's how to configure lost reasons in Odoo 17 CRM
2. Categorical Response Variables
Examples:
Whether or not a person
smokes
Smoker
smokerNon
Y
Success of a medical
treatment
Dies
Survives
Y
Opinion poll responses
Disagree
Neutral
Agree
Y
Binary Response
Ordinal Response
3. Example: Height predicts Gender
Y = Gender (0=Male 1=Female)
X = Height (inches)
Try an ordinary linear regression
> regmodel=lm(Gender~Hgt,data=Pulse)
> summary(regmodel)
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 7.343647 0.397563 18.47 <2e-16 ***
Hgt -0.100658 0.005817 -17.30 <2e-16 ***
5. Ordinary linear regression is used a lot, and is
taught in every intro stat class. Logistic regression
is rarely taught or even mentioned in intro stats,
but mostly because of inertia.
We now have the computing power and
software to implement logistic regression.
6. π = Proportion of “Success”
In ordinary regression the model predicts the
mean Y for any combination of predictors.
What’s the “mean” of a 0/1 indicator variable?
success""ofProportion
trialsof#
'1of#
s
n
y
y i
Goal of logistic regression: Predict the “true”
proportion of success, π, at any value of the
predictor.
7. Binary Logistic Regression Model
Y = Binary response X = Quantitative predictor
π = proportion of 1’s (yes,success) at any X
p =
e
b0 +b1 X
1+ e
b0 +b1 X
Equivalent forms of the logistic regression model:
What does this look like?
X10
1
log
Logit form Probability form
N.B.: This is natural log (aka “ln”)
13. Example: Golf Putts
Length 3 4 5 6 7
Made 84 88 61 61 44
Missed 17 31 47 64 90
Total 101 119 108 125 134
Build a model to predict the proportion of
putts made (success) based on length (in feet).
14. Logistic Regression for Putting
Call:
glm(formula = Made ~ Length, family = binomial, data =
Putts1)
Deviance Residuals:
Min 1Q Median 3Q Max
-1.8705 -1.1186 0.6181 1.0026 1.4882
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 3.25684 0.36893 8.828 <2e-16 ***
Length -0.56614 0.06747 -8.391 <2e-16 ***
---
15. 3 4 5 6 7
-0.50.00.51.01.5
PuttLength
logitPropMade
Linear part of
logistic fit
log
ˆp
1- ˆp
æ
è
ç
ö
ø
÷ vs. Length
16. Probability Form of Putting Model
2 4 6 8 10 12
0.00.20.40.60.81.0
PuttLength
ProbabilityMade Length
Length
e
e
566.0257.3
566.0257.3
1
ˆ
19. -3 -2 -1 0 1 2 3
0.00.20.40.60.81.0
x
Prob
p =
e0+1*x
1+ e0+1*x
x increases
by 1
x increases
by 1
π increases by .072
π increases
by .231
the odds increase by
a factor of 2.718
20. Odds
The logistic model assumes a linear
relationship between the predictors
and log(odds).
log
p
1- p
æ
èç
ö
ø÷ = b0
+ b1
X
⇒
Logit form of the model:
odds =
p
1- p
= e
b0 +b1 X
21. Odds Ratio
A common way to compare two groups
is to look at the ratio of their odds
2
1
Odds
Odds
ORRatioOdds
Note: Odds ratio (OR) is similar to relative risk (RR).
RR =
p1
p2
OR = RR*
1- p2
1- p1
So when p is small, OR ≈ RR.
22. X is replaced by X + 1:
odds = eb0+b1X
is replaced by
odds = eb0+b1( X+1)
So the ratio is
eb0+b1( X+1)
e
b0+b1X
= eb0+b1( X+1)-(b0+b1X )
= eb1
23. Example: TMS for Migraines
Transcranial Magnetic Stimulation vs. Placebo
Pain Free? TMS Placebo
YES 39 22
NO 61 78
Total 100 100
22.0ˆ Placebo
oddsTMS
=
39 /100
61/100
=
39
61
= 0.639
282.0
78
22
Placeboodds
Odds ratio =
0.639
0.282
= 2.27 Odds are 2.27 times higher of getting
relief using TMS than placebo
ˆpTMS = 0.39 ˆp =
0.639
1+0.639
= 0.39
24. Logistic Regression for TMS data
> lmod=glm(cbind(Yes,No)~Group,family=binomial,data=TMS)
> summary(lmod)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -1.2657 0.2414 -5.243 1.58e-07 ***
GroupTMS 0.8184 0.3167 2.584 0.00977 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 6.8854 on 1 degrees of freedom
Residual deviance: 0.0000 on 0 degrees of freedom
AIC: 13.701
Note: e0.8184 = 2.27 = odds ratio
26. Response variable: Y = Success/Failure
Predictor variable: X = Group #1 / Group #2
• Method #1: Binary logistic regression
• Method #2: Z- test, compare two proportions
• Method #3: Chi-square test for 2-way table
All three “tests” are essentially equivalent, but the
logistic regression approach allows us to mix other
categorical and quantitative predictors in the model.
A Single Binary Predictor for a Binary Response
27. Putting Data
Odds using data from 6 feet = 0.953
Odds using data from 5 feet = 1.298
Odds ratio (6 ft to 5 ft) = 0.953/1.298 = 0.73
The odds of making a putt from 6 feet are
73% of the odds of making from 5 feet.
30. Interpreting “Slope” using Odds Ratio
X10
1
log
When we increase X by 1, the ratio of the
new odds to the old odds is .1
e
X
eodds 10
⇒
i.e. odds are multiplied by .1
e
31. Odds Ratios for Putts
4 to 3 feet 5 to 4 feet 6 to 5 feet 7 to 6 feet
0.575 0.457 0.734 0.513
From samples at each distance:
4 to 3 feet 5 to 4 feet 6 to 5 feet 7 to 6 feet
0.568 0.568 0.568 0.568
From fitted logistic:
In a logistic model, the odds ratio is constant when
changing the predictor by one.
32. Example: 2012 vs 2014 congressional elections
How does %vote won by Obama relate to a
Democrat winning a House seat?
See the script elections 12, 14.R
33. Example: 2012 vs 2014 congressional elections
How does %vote won by Obama relate to a
Democrat winning a House seat?
In 2012 a Democrat had a decent chance even
if Obama got only 50% of the vote in the
district. In 2014 that was less true.
34. In 2012 a Democrat had a decent chance even if Obama
got only 50% of the vote in the district. In 2014 that was
less true.
35. There is an easy way to graph logistic curves in R.
> library(TeachingDemos)
> with(elect, plot(Obama12,jitter(Dem12,amount=.05)))
> logitmod14=glm(Dem14~Obama12,family=binomial,data=elect)
> Predict.Plot(logitmod14, pred.var="Obama12”,add=TRUE,
plot.args = list(lwd=3,col="black"))
36. > summary(PuttModel)
Call:
glm(formula = Made ~ Length, family = binomial)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 3.25684 0.36893 8.828 <2e-16 ***
Length -0.56614 0.06747 -8.391 <2e-16 ***
---
Null deviance: 800.21 on 586 degrees of freedom
Residual deviance: 719.89 on 585 degrees of freedom
> PuttModel=glm(Made~Length, family=binomial,data=Putts1)
> anova(PuttModel)
Analysis of Deviance Table
Df Deviance Resid. Df Resid. Dev
NULL 586 800.21
Length 1 80.317 585 719.89
R Logistic Output
37. Two forms of logistic data
1. Response variable Y = Success/Failure or 1/0: “long
form” in which each case is a row in a spreadsheet
(e.g., Putts1 has 587 cases). This is often called
“binary response” or “Bernoulli” logistic regression.
2. Response variable Y = Number of Successes for a
group of data with a common X value: “short form”
(e.g., Putts2 has 5 cases – putts of 3 ft, 4 ft, … 7 ft).
This is often called “Binomial counts” logistic
regression.
38. > str(Putts1)
'data.frame': 587 obs. of 2 variables:
$ Length: int 3 3 3 3 3 3 3 3 3 3 ...
$ Made : int 1 1 1 1 1 1 1 1 1 1 ...
> longmodel=glm(Made~Length,family=binomial,data=Putts1)
> summary(longmodel)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 3.25684 0.36893 8.828 <2e-16 ***
Length -0.56614 0.06747 -8.391 <2e-16 ***
---
Null deviance: 800.21 on 586 degrees of freedom
Residual deviance: 719.89 on 585 degrees of freedom
39. > str(Putts2)
'data.frame': 5 obs. of 4 variables:
$ Length: int 3 4 5 6 7
$ Made : int 84 88 61 61 44
$ Missed: int 17 31 47 64 90
$ Trials: int 101 119 108 125 134
>
shortmodel=glm(cbind(Made,Missed)~Length,family=binomial,data=Putts2)
> summary(shortmodel)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 3.25684 0.36893 8.828 <2e-16 ***
Lengths -0.56614 0.06747 -8.391 <2e-16 ***
---
Null deviance: 81.3865 on 4 degrees of freedom
Residual deviance: 1.0692 on 3 degrees of freedom
40. Binary Logistic Regression Model
Y = Binary
response
X = Single predictor
π = proportion of 1’s (yes, success) at any x
X
X
o
o
e
e
1
1
1
Equivalent forms of the logistic regression model:
X10
1
log
Logit form
Probability form
41. Y = Binary
response
X = Single predictor
X
X
o
o
e
e
1
1
1
X10
1
log
Logit form
Probability form
X1,X2,…,Xk = Multiple
predictorsπ = proportion of 1’s (yes, success) at any xπ = proportion of 1’s at any x1, x2, …, xk
kk XXX
22110
1
log
kko
kko
XXX
XXX
e
e
2211
2211
1
Binary Logistic Regression Model
Equivalent forms of the logistic regression model:
42. Interactions in logistic regression
Consider Survival in an ICU as a function of
SysBP -- BP for short – and Sex
> intermodel=glm(Survive~BP*Sex, family=binomial, data=ICU)
> summary(intermodel)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -1.439304 1.021042 -1.410 0.15865
BP 0.022994 0.008325 2.762 0.00575 **
Sex 1.455166 1.525558 0.954 0.34016
BP:Sex -0.013020 0.011965 -1.088 0.27653
Null deviance: 200.16 on 199 degrees of freedom
Residual deviance: 189.99 on 196 degrees of freedom
43. Rep = red,
Dem = blue
Lines are
very close
to parallel;
not a
significant
interaction
0.00.20.40.60.81.0
Auto industry contributions (lifetime)
ProbofvotingYes
0 1 10 100 1,000 10,000 1,000,000
44. Generalized Linear Model
(1) What is the link between Y and b0 + b1X?
(2) What is the distribution of Y given X?
(a) Regular reg: indentity
(b) Logistic reg: logit
(c) Poisson reg: log
(a) Regular reg: Normal (Gaussian)
(b) Logistic reg: Binomial
(c) Poisson reg: Poisson
45. C-index, a measure of concordance
Med school acceptance: predicted by MCAT
and GPA?
Med school acceptance: predicted by coin toss??
47. Now consider that there were 30 successes and
25 failures. There are 30*25=750 possible pairs.
We hope that the predicted Pr(success) is greater
for the success than for the failure in a pair! If yes
then the pair is “concordant”.
> with(MedGPA, table(Acceptance,Accept.hat))
Accept.hat
Acceptance FALSE TRUE
0 18 7
1 7 23
C-index = % concordant pairs
48. > #C-index work using the MedGPA data
> library(rms) #after installing the rms package
> m3=lrm(Acceptance~MCAT+GPA10, data=MedGPA)
> m3
lrm(formula = Acceptance~ MCAT + GPA10)
Model Likelihood Discrimination Rank Discrim.
Ratio Test Indexes Indexes
Obs 55 LR chi2 21.78 R2 0.437 C 0.834
0 25 d.f. 2 g 2.081 Dxy 0.668
1 30 Pr(> chi2) <0.0001 gr 8.015 gamma 0.669
max |deriv| 2e-07 gp 0.342 tau-a 0.337
Brier 0. 167
Coef S.E. Wald Z Pr(>|Z|)
Intercept -22.373 6.454 -3.47 0.0005
MCAT 0.1645 0.1032 1.59 0.1108
GPA10 0.4678 0.1642 2.85 0.0044
The R package rms has a command, lrm, that
does logistic regression and gives the C-index.
49. > newAccept=sample(MedGPA$Acceptance) #scramble the acceptances
> m1new=lrm(newAccept~MCAT+GPA10,data=MedGPA)
> m1new
lrm(formula = newAccept ~ MCAT + GPA10)
Model Likelihood Discrimination Rank Discrim.
Ratio Test Indexes Indexes
Obs 55 LR chi2 0.24 R2 0.006 C 0.520
0 25 d.f. 2 g 0.150 Dxy 0.040
1 30 Pr(> chi2) 0.8876 gr 1.162 gamma 0.041
max |deriv| 1e-13 gp 0.037 tau-a 0.020
Brier 0.247
Coef S.E. Wald Z Pr(>|Z|)
Intercept -1.4763 3.4196 -0.43 0.6659
MCAT 0.0007 0.0677 0.01 0.9912
GPA10 0.0459 0.1137 0.40 0.6862
Suppose we scramble the cases..
Then the C-index should be ½, like coin tossing