Russo Vub Seminar
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The document discusses interpreting probability in causal modelling approaches in the social sciences. It argues that objective Bayesianism provides the best interpretation of probability for causal modelling by treating probabilities as frequency-driven epistemic probabilities that make use of empirical constraints. This allows probabilities to be applied to both generic and single-case causal claims and helps guide decisions through rational degrees of belief informed by evidence and experience.
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Russo Ihpst Seminar
1) The document discusses different interpretations of probability, as it relates to causal modeling in the social sciences, including both generic and single-case causal claims.
2) It argues that objective Bayesianism, which treats probabilities as degrees of rational belief that incorporate empirical constraints, provides the best interpretation for probabilistic causal modeling.
3) Under an objective Bayesian view, probabilities can be used to evaluate hypotheses in both generic and single cases, allowing for rational decision making in areas like hypothesis testing and policy decisions.
Judgment Under Uncertainty: Anchoring and Adjustment Bias
This paper sets out the general basis for the
concept of the anchoring and adjustment bias.
Need to focus on anchoring and adjustment in the process of using these audit tools.
(ironically this document is not likely to be used for my phd).
Hypothesis testing
Okay, let me try to analyze this step-by-step:
1) Null Hypothesis (H0): The advertisement had no effect on sales.
2) Alternative Hypothesis (H1): The advertisement increased sales.
3) We can test this using a paired t-test, since we have sales data from the same shops before and after.
4) Calculate the mean difference between before and after sales for each shop. Then take the average of those differences.
5) Use the t-statistic to determine if the average difference is significantly greater than 0, which would indicate the advertisement increased sales.
So in summary, a paired t-test can be used to determine if the advertisement
Final mayo's aps_talk
D. G. Mayo (Virginia Tech) "Error Statistical Control: Forfeit at your Peril" presented May 23 at the session on "The Philosophy of Statistics: Bayesianism, Frequentism and the Nature of Inference," 2015 APS Annual Convention in NYC.
Basics of Educational Statistics (Hypothesis and types)
This document discusses hypothesis in research. It defines a hypothesis as a tentative assumption made to be tested. There are two main types of hypotheses: directional hypotheses, which predict the direction of a relationship between variables, and non-directional hypotheses, used when findings are contradictory. Associative hypotheses propose relationships between variables, while causal hypotheses propose cause-and-effect interactions. The document also discusses the importance of hypotheses in research and the two types of errors in hypothesis testing: Type I errors, which reject a true null hypothesis, and Type II errors, which accept a false null hypothesis.
Test of hypotheses part i
This document discusses hypothesis testing, including:
1) The steps of hypothesis testing are stating the null and alternative hypotheses, calculating a test statistic and p-value, and drawing a conclusion about whether to reject the null hypothesis.
2) A hypothesis test is used to assess evidence against a claim, while a confidence interval estimates a population parameter.
3) The null hypothesis is the initial claim and the alternative hypothesis is what the test is assessing evidence for. A small p-value provides evidence against the null hypothesis.
4) The conclusion is to reject the null hypothesis if the p-value is below the significance level, otherwise fail to reject the null hypothesis due to insufficient evidence against it.
Hypothesis Testing
Hypothesis testing allows us to use sample data to test claims about population parameters, such as determining whether a population mean equals a specific value. The process involves making an initial assumption called the null hypothesis, collecting sample data as evidence, and determining whether the evidence makes the null hypothesis reasonable or not based on the probability of obtaining that evidence. If the evidence makes the null hypothesis unlikely, it is rejected in favor of the alternative hypothesis; otherwise, the null hypothesis is not rejected due to insufficient evidence against it. Important assumptions for valid hypothesis testing include that the sample is random and large enough for its distribution to be approximately normal.
HYPOTHESIS TESTING
Hypothesis tests are used to statistically determine the probability that a hypothesis is accepted at a given significance level. The purpose is to determine if there is enough statistical evidence to support a hypothesis. A hypothesis predicts the relationship between variables and can be tested, whereas a research question does not make a prediction. Good hypotheses are compatible with current knowledge, logically consistent, clearly stated, and testable. The null hypothesis asserts there is no difference or relationship, while the alternative or research hypothesis predicts a difference or relationship. Setting a significance level helps determine if results reject the null hypothesis.
Recommended
Russo Ihpst Seminar
1) The document discusses different interpretations of probability, as it relates to causal modeling in the social sciences, including both generic and single-case causal claims.
2) It argues that objective Bayesianism, which treats probabilities as degrees of rational belief that incorporate empirical constraints, provides the best interpretation for probabilistic causal modeling.
3) Under an objective Bayesian view, probabilities can be used to evaluate hypotheses in both generic and single cases, allowing for rational decision making in areas like hypothesis testing and policy decisions.
Judgment Under Uncertainty: Anchoring and Adjustment Bias
This paper sets out the general basis for the
concept of the anchoring and adjustment bias.
Need to focus on anchoring and adjustment in the process of using these audit tools.
(ironically this document is not likely to be used for my phd).
Hypothesis testing
Okay, let me try to analyze this step-by-step:
1) Null Hypothesis (H0): The advertisement had no effect on sales.
2) Alternative Hypothesis (H1): The advertisement increased sales.
3) We can test this using a paired t-test, since we have sales data from the same shops before and after.
4) Calculate the mean difference between before and after sales for each shop. Then take the average of those differences.
5) Use the t-statistic to determine if the average difference is significantly greater than 0, which would indicate the advertisement increased sales.
So in summary, a paired t-test can be used to determine if the advertisement
Final mayo's aps_talk
D. G. Mayo (Virginia Tech) "Error Statistical Control: Forfeit at your Peril" presented May 23 at the session on "The Philosophy of Statistics: Bayesianism, Frequentism and the Nature of Inference," 2015 APS Annual Convention in NYC.
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This document discusses hypothesis in research. It defines a hypothesis as a tentative assumption made to be tested. There are two main types of hypotheses: directional hypotheses, which predict the direction of a relationship between variables, and non-directional hypotheses, used when findings are contradictory. Associative hypotheses propose relationships between variables, while causal hypotheses propose cause-and-effect interactions. The document also discusses the importance of hypotheses in research and the two types of errors in hypothesis testing: Type I errors, which reject a true null hypothesis, and Type II errors, which accept a false null hypothesis.
Test of hypotheses part i
This document discusses hypothesis testing, including:
1) The steps of hypothesis testing are stating the null and alternative hypotheses, calculating a test statistic and p-value, and drawing a conclusion about whether to reject the null hypothesis.
2) A hypothesis test is used to assess evidence against a claim, while a confidence interval estimates a population parameter.
3) The null hypothesis is the initial claim and the alternative hypothesis is what the test is assessing evidence for. A small p-value provides evidence against the null hypothesis.
4) The conclusion is to reject the null hypothesis if the p-value is below the significance level, otherwise fail to reject the null hypothesis due to insufficient evidence against it.
Hypothesis Testing
Hypothesis testing allows us to use sample data to test claims about population parameters, such as determining whether a population mean equals a specific value. The process involves making an initial assumption called the null hypothesis, collecting sample data as evidence, and determining whether the evidence makes the null hypothesis reasonable or not based on the probability of obtaining that evidence. If the evidence makes the null hypothesis unlikely, it is rejected in favor of the alternative hypothesis; otherwise, the null hypothesis is not rejected due to insufficient evidence against it. Important assumptions for valid hypothesis testing include that the sample is random and large enough for its distribution to be approximately normal.
HYPOTHESIS TESTING
Hypothesis tests are used to statistically determine the probability that a hypothesis is accepted at a given significance level. The purpose is to determine if there is enough statistical evidence to support a hypothesis. A hypothesis predicts the relationship between variables and can be tested, whereas a research question does not make a prediction. Good hypotheses are compatible with current knowledge, logically consistent, clearly stated, and testable. The null hypothesis asserts there is no difference or relationship, while the alternative or research hypothesis predicts a difference or relationship. Setting a significance level helps determine if results reject the null hypothesis.
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Slides from Rutgers Seminar talk by Deborah G Mayo
December 3, 2014
Rutgers, Department of Statistics and Biostatistics
Abstract: Getting beyond today’s most pressing controversies revolving around statistical methods, I argue, requires scrutinizing their underlying statistical philosophies.Two main philosophies about the roles of probability in statistical inference are probabilism and performance (in the long-run). The first assumes that we need a method of assigning probabilities to hypotheses; the second assumes that the main function of statistical method is to control long-run performance. I offer a third goal: controlling and evaluating the probativeness of methods. An inductive inference, in this conception, takes the form of inferring hypotheses to the extent that they have been well or severely tested. A report of poorly tested claims must also be part of an adequate inference. I develop a statistical philosophy in which error probabilities of methods may be used to evaluate and control the stringency or severity of tests. I then show how the “severe testing” philosophy clarifies and avoids familiar criticisms and abuses of significance tests and cognate methods (e.g., confidence intervals). Severity may be threatened in three main ways: fallacies of statistical tests, unwarranted links between statistical and substantive claims, and violations of model assumptions.
Hypothesis testing
This document discusses hypotheses, including their characteristics, criteria for construction, testing approaches, and types of errors. It defines a hypothesis as a tentative explanation for behaviors or events that can be scientifically tested. Key points include:
- Hypotheses must be clear, precise, testable and specify the relationship between variables.
- The null hypothesis is what is being tested, while the alternative is what may be accepted if the null is rejected.
- Tests can be two-tailed, testing in both directions, or one-tailed, testing in one specified direction.
- Type I error occurs when a true null hypothesis is rejected, while Type II error is accepting a false null hypothesis.
Hypothesis
The document discusses hypothesis testing, which involves testing a hypothesis about a population using a sample of data. It explains that a hypothesis test has four main steps: 1) stating the null and alternative hypotheses, where the null hypothesis asserts there is no difference between the sample and population, 2) setting the significance level, 3) determining the test statistic and critical region for rejecting the null hypothesis, and 4) making a decision to reject or fail to reject the null hypothesis based on whether the test statistic falls in the critical region. Type I and type II errors are also defined. The document provides examples of null and alternative hypotheses using mathematical symbols and discusses how to determine if a p-value is statistically significant.
Hypothesis Testing
- Hypothesis testing involves testing assumptions about population parameters by analyzing sample data. The goal is to either accept or reject the null hypothesis based on the sample evidence.
- There are two hypotheses - the null hypothesis, which assumes no effect or relationship between variables, and the alternative hypothesis, which assumes an effect or relationship.
- The procedure involves setting the null hypothesis, collecting sample data, and using a statistical test to determine whether to reject or accept the null hypothesis based on the level of difference between the sample and null hypothesis. If the difference is significant, the null is rejected.
Hypothesis
A hypothesis is the translation of the information that we are keen on. Utilizing Hypothesis Testing, we attempt to decipher or reach inferences about the populace utilizing test information. A Hypothesis assesses two totally unrelated articulations about a populace to figure out which explanation is best upheld by the example information.
Hypothesis testing ppt final
This document provides an overview of hypothesis testing in inferential statistics. It defines a hypothesis as a statement or assumption about relationships between variables or tentative explanations for events. There are two main types of hypotheses: the null hypothesis (H0), which is the default position that is tested, and the alternative hypothesis (Ha or H1). Steps in hypothesis testing include establishing the null and alternative hypotheses, selecting a suitable test of significance or test statistic based on sample characteristics, formulating a decision rule to either accept or reject the null hypothesis based on where the test statistic value falls, and understanding the potential for errors. Key criteria for constructing hypotheses and selecting appropriate statistical tests are also outlined.
Hypothesis
This document defines key concepts related to hypothesis testing. It explains that a hypothesis is a temporary assumption made to conduct research. The two main types of hypotheses are the null hypothesis, which assumes no difference or relationship, and the alternative hypothesis, which assumes a significant difference or relationship. The document outlines the steps to test a hypothesis, which include setting the hypotheses, significance level, test statistic, critical region, calculating and comparing test statistics, and making a decision to accept or reject the null hypothesis. Common test statistics and significance levels are also defined.
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This document summarizes an honors thesis that examines how varying the scale of financial incentives in economic experiments affects measured risk preferences. The thesis conducted a study using Holt and Laury's lottery choice framework with three treatments that differed in payoff structures and probabilities to induce risk behavior. The study found that increasing the scale of payoffs resulted in significantly more risk-averse behavior. Contrary to other research, demographic factors like gender and risky behaviors from a follow-up survey did not predict risk preferences. Self-financing college did predict more risk-averse choices in two treatments, suggesting income should be controlled for. The results provide evidence that the scale of incentives used is important for eliciting realistic risk behavior in experiments.
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Hypothesis
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This document summarizes a discussion on Nancy Reid's paper "BFF Four–Are we Converging?". Reid identifies obstacles to the fusion of Bayesian, frequentist and fiducial statistics, including confusion over the nature and use of probability in statistical inference. The discussion explores different views of probability as describing physical variability, subjective degrees of belief, or the reliability of statistical methods. It also examines notions of calibration and how accounts of statistical inference should be evaluated based on their ability to avoid selection biases and enable statistical testing and falsification.
BBA 020
This document discusses hypothesis testing, including:
- A hypothesis test is a method for making decisions using data to test an unproven statement about a factor or phenomenon.
- The null hypothesis states there is no difference between what is observed and what is expected. The alternative hypothesis specifies an alternative statement.
- Steps in hypothesis testing include formulating the hypotheses, selecting a statistical test, collecting data, determining critical values and probabilities, and deciding whether to reject or fail to reject the null hypothesis.
- Parametric tests assume a known distribution while nonparametric tests make no assumptions. Common tests mentioned include t-tests, z-tests, F-tests, chi-square tests, and rank correlation tests.
Hypothesis testing
This document discusses hypothesis testing. It defines a hypothesis as a predictive statement that relates independent and dependent variables and can be scientifically tested. The purpose of a hypothesis is to define relationships between variables. Characteristics of a good hypothesis are outlined. Null and alternative hypotheses are defined, with the null being what is currently assumed to be true. Type I and Type II errors in hypothesis testing are explained. Common statistical tests used to test hypotheses are described briefly, including t-tests, z-tests, F-tests, and chi-square tests. Key concepts like significance levels, confidence intervals, and contingency tables are also summarized.
Hypothesis Testing Lesson 1
The document provides an introduction to hypothesis testing, including its real-life applications, key definitions, and structure. It defines hypothesis testing as the process of testing the validity of a statistical hypothesis based on a random sample from a population. The document outlines the common steps in hypothesis testing: 1) stating the null and alternative hypotheses, 2) choosing a significance level, 3) determining the test statistic and decision criteria, 4) rejecting or failing to reject the null hypothesis, and 5) drawing a conclusion. It also defines important terminology like population mean, null and alternative hypotheses, test statistic, significance level, critical region, and p-value. Real-life examples from pharmaceutical testing and legal cases are provided to illustrate the motivation for hypothesis
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Hypothesis testing
Hypothesis testing and estimation are used to reach conclusions about a population by examining a sample of that population.
Hypothesis testing is widely used in medicine, dentistry, health care, biology and other fields as a means to draw conclusions about the nature of populations
Hypothesis testing
This document defines key concepts in statistical hypothesis testing. It explains that a statistical hypothesis is a conjecture about a population parameter. The null hypothesis (H0) states that there is no difference between a parameter and a particular value, while the alternative hypothesis (H1) states there is a difference. Tests can be one-tailed if H1 is > or <, or two-tailed if H1 is ≠. Type I and II errors occur if the wrong decision is made regarding H0. The level of significance and critical value help determine whether to reject or fail to reject H0.
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The document discusses hypothesis testing and t-tests, explaining that a hypothesis is a suggested explanation for a phenomenon that can be tested scientifically, and a t-test determines if the means of two groups are statistically different. It provides details on null and alternative hypotheses, how to perform a t-test, and how the t-statistic, degrees of freedom, and p-value are used to evaluate whether to reject the null hypothesis.
"The Statistical Replication Crisis: Paradoxes and Scapegoats”
D. G. Mayo LSE Popper talk, May 10, 2016.
Abstract: Mounting failures of replication in the social and biological sciences give a practical spin to statistical foundations in the form of the question: How can we attain reliability when Big Data methods make illicit cherry-picking and significance seeking so easy? Researchers, professional societies, and journals are increasingly getting serious about methodological reforms to restore scientific integrity – some are quite welcome (e.g., preregistration), while others are quite radical. Recently, the American Statistical Association convened members from differing tribes of frequentists, Bayesians, and likelihoodists to codify misuses of P-values. Largely overlooked are the philosophical presuppositions of both criticisms and proposed reforms. Paradoxically, alternative replacement methods may enable rather than reveal illicit inferences due to cherry-picking, multiple testing, and other biasing selection effects. Popular appeals to “diagnostic testing” that aim to improve replication rates may (unintentionally) permit the howlers and cookbook statistics we are at pains to root out. Without a better understanding of the philosophical issues, we can expect the latest reforms to fail.
Rm 3 Hypothesis
Hypothesis testing is an important tool in research. A hypothesis is a statement or proposition that can be tested through scientific investigation. The null hypothesis represents the default position that there is no relationship between variables or no difference among groups. The alternative hypothesis is what the researcher aims to prove. Through hypothesis testing, researchers aim to reject the null hypothesis by collecting data and calculating the probability of the results if the null hypothesis were true. This probability is then compared to the pre-determined significance level, often 5%, to determine whether to reject or fail to reject the null hypothesis. Proper hypothesis testing involves clearly stating the hypotheses, selecting a random sample, determining the appropriate statistical test based on the data, and interpreting the results.
On Severity, the Weight of Evidence, and the Relationship Between the Two
Margherita Harris
Visiting fellow in the Department of Philosophy, Logic and Scientific Method at the London
School of Economics and Political Science.
ABSTRACT: According to the severe tester, one is justified in declaring to have evidence in support of a
hypothesis just in case the hypothesis in question has passed a severe test, one that it would be very
unlikely to pass so well if the hypothesis were false. Deborah Mayo (2018) calls this the strong
severity principle. The Bayesian, however, can declare to have evidence for a hypothesis despite not
having done anything to test it severely. The core reason for this has to do with the
(infamous) likelihood principle, whose violation is not an option for anyone who subscribes to the
Bayesian paradigm. Although the Bayesian is largely unmoved by the incompatibility between
the strong severity principle and the likelihood principle, I will argue that the Bayesian’s never-ending
quest to account for yet an other notion, one that is often attributed to Keynes (1921) and that is
usually referred to as the weight of evidence, betrays the Bayesian’s confidence in the likelihood
principle after all. Indeed, I will argue that the weight of evidence and severity may be thought of as
two (very different) sides of the same coin: they are two unrelated notions, but what brings them
together is the fact that they both make trouble for the likelihood principle, a principle at the core of
Bayesian inference. I will relate this conclusion to current debates on how to best conceptualise
uncertainty by the IPCC in particular. I will argue that failure to fully grasp the limitations of an
epistemology that envisions the role of probability to be that of quantifying the degree of belief to
assign to a hypothesis given the available evidence can be (and has been) detrimental to an
adequate communication of uncertainty.
0hypothesis testing.pdf
The document discusses hypotheses, including defining a hypothesis, the characteristics of a good hypothesis, and the steps involved in hypothesis testing. It notes that a hypothesis is a tentative explanation that can be tested, and outlines criteria for constructing strong hypotheses, such as being clear, precise, and testable. The document also covers the sources of hypotheses, approaches to testing hypotheses like classical and Bayesian statistics, and the types of errors that can occur in hypothesis testing like type 1 and type 2 errors.
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Slides from Rutgers Seminar talk by Deborah G Mayo
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Abstract: Getting beyond today’s most pressing controversies revolving around statistical methods, I argue, requires scrutinizing their underlying statistical philosophies.Two main philosophies about the roles of probability in statistical inference are probabilism and performance (in the long-run). The first assumes that we need a method of assigning probabilities to hypotheses; the second assumes that the main function of statistical method is to control long-run performance. I offer a third goal: controlling and evaluating the probativeness of methods. An inductive inference, in this conception, takes the form of inferring hypotheses to the extent that they have been well or severely tested. A report of poorly tested claims must also be part of an adequate inference. I develop a statistical philosophy in which error probabilities of methods may be used to evaluate and control the stringency or severity of tests. I then show how the “severe testing” philosophy clarifies and avoids familiar criticisms and abuses of significance tests and cognate methods (e.g., confidence intervals). Severity may be threatened in three main ways: fallacies of statistical tests, unwarranted links between statistical and substantive claims, and violations of model assumptions.
Hypothesis testing
This document discusses hypotheses, including their characteristics, criteria for construction, testing approaches, and types of errors. It defines a hypothesis as a tentative explanation for behaviors or events that can be scientifically tested. Key points include:
- Hypotheses must be clear, precise, testable and specify the relationship between variables.
- The null hypothesis is what is being tested, while the alternative is what may be accepted if the null is rejected.
- Tests can be two-tailed, testing in both directions, or one-tailed, testing in one specified direction.
- Type I error occurs when a true null hypothesis is rejected, while Type II error is accepting a false null hypothesis.
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The document discusses hypothesis testing, which involves testing a hypothesis about a population using a sample of data. It explains that a hypothesis test has four main steps: 1) stating the null and alternative hypotheses, where the null hypothesis asserts there is no difference between the sample and population, 2) setting the significance level, 3) determining the test statistic and critical region for rejecting the null hypothesis, and 4) making a decision to reject or fail to reject the null hypothesis based on whether the test statistic falls in the critical region. Type I and type II errors are also defined. The document provides examples of null and alternative hypotheses using mathematical symbols and discusses how to determine if a p-value is statistically significant.
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- Hypothesis testing involves testing assumptions about population parameters by analyzing sample data. The goal is to either accept or reject the null hypothesis based on the sample evidence.
- There are two hypotheses - the null hypothesis, which assumes no effect or relationship between variables, and the alternative hypothesis, which assumes an effect or relationship.
- The procedure involves setting the null hypothesis, collecting sample data, and using a statistical test to determine whether to reject or accept the null hypothesis based on the level of difference between the sample and null hypothesis. If the difference is significant, the null is rejected.
Hypothesis
A hypothesis is the translation of the information that we are keen on. Utilizing Hypothesis Testing, we attempt to decipher or reach inferences about the populace utilizing test information. A Hypothesis assesses two totally unrelated articulations about a populace to figure out which explanation is best upheld by the example information.
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This document provides an overview of hypothesis testing in inferential statistics. It defines a hypothesis as a statement or assumption about relationships between variables or tentative explanations for events. There are two main types of hypotheses: the null hypothesis (H0), which is the default position that is tested, and the alternative hypothesis (Ha or H1). Steps in hypothesis testing include establishing the null and alternative hypotheses, selecting a suitable test of significance or test statistic based on sample characteristics, formulating a decision rule to either accept or reject the null hypothesis based on where the test statistic value falls, and understanding the potential for errors. Key criteria for constructing hypotheses and selecting appropriate statistical tests are also outlined.
Hypothesis
This document defines key concepts related to hypothesis testing. It explains that a hypothesis is a temporary assumption made to conduct research. The two main types of hypotheses are the null hypothesis, which assumes no difference or relationship, and the alternative hypothesis, which assumes a significant difference or relationship. The document outlines the steps to test a hypothesis, which include setting the hypotheses, significance level, test statistic, critical region, calculating and comparing test statistics, and making a decision to accept or reject the null hypothesis. Common test statistics and significance levels are also defined.
Payoffs Probabilities and Preferences
This document summarizes an honors thesis that examines how varying the scale of financial incentives in economic experiments affects measured risk preferences. The thesis conducted a study using Holt and Laury's lottery choice framework with three treatments that differed in payoff structures and probabilities to induce risk behavior. The study found that increasing the scale of payoffs resulted in significantly more risk-averse behavior. Contrary to other research, demographic factors like gender and risky behaviors from a follow-up survey did not predict risk preferences. Self-financing college did predict more risk-averse choices in two treatments, suggesting income should be controlled for. The results provide evidence that the scale of incentives used is important for eliciting realistic risk behavior in experiments.
Feb21 mayobostonpaper
Deborah G. Mayo: Is the Philosophy of Probabilism an Obstacle to Statistical Fraud Busting?
Presentation slides for: Revisiting the Foundations of Statistics in the Era of Big Data: Scaling Up to Meet the Challenge[*] at the Boston Colloquium for Philosophy of Science (Feb 21, 2014).
Hypothesis
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Fusion Confusion? Comments on Nancy Reid: "BFF Four-Are we Converging?"
This document summarizes a discussion on Nancy Reid's paper "BFF Four–Are we Converging?". Reid identifies obstacles to the fusion of Bayesian, frequentist and fiducial statistics, including confusion over the nature and use of probability in statistical inference. The discussion explores different views of probability as describing physical variability, subjective degrees of belief, or the reliability of statistical methods. It also examines notions of calibration and how accounts of statistical inference should be evaluated based on their ability to avoid selection biases and enable statistical testing and falsification.
BBA 020
This document discusses hypothesis testing, including:
- A hypothesis test is a method for making decisions using data to test an unproven statement about a factor or phenomenon.
- The null hypothesis states there is no difference between what is observed and what is expected. The alternative hypothesis specifies an alternative statement.
- Steps in hypothesis testing include formulating the hypotheses, selecting a statistical test, collecting data, determining critical values and probabilities, and deciding whether to reject or fail to reject the null hypothesis.
- Parametric tests assume a known distribution while nonparametric tests make no assumptions. Common tests mentioned include t-tests, z-tests, F-tests, chi-square tests, and rank correlation tests.
Hypothesis testing
This document discusses hypothesis testing. It defines a hypothesis as a predictive statement that relates independent and dependent variables and can be scientifically tested. The purpose of a hypothesis is to define relationships between variables. Characteristics of a good hypothesis are outlined. Null and alternative hypotheses are defined, with the null being what is currently assumed to be true. Type I and Type II errors in hypothesis testing are explained. Common statistical tests used to test hypotheses are described briefly, including t-tests, z-tests, F-tests, and chi-square tests. Key concepts like significance levels, confidence intervals, and contingency tables are also summarized.
Hypothesis Testing Lesson 1
The document provides an introduction to hypothesis testing, including its real-life applications, key definitions, and structure. It defines hypothesis testing as the process of testing the validity of a statistical hypothesis based on a random sample from a population. The document outlines the common steps in hypothesis testing: 1) stating the null and alternative hypotheses, 2) choosing a significance level, 3) determining the test statistic and decision criteria, 4) rejecting or failing to reject the null hypothesis, and 5) drawing a conclusion. It also defines important terminology like population mean, null and alternative hypotheses, test statistic, significance level, critical region, and p-value. Real-life examples from pharmaceutical testing and legal cases are provided to illustrate the motivation for hypothesis
Senn repligate
Stephen Senn slides:"‘Repligate’: reproducibility in statistical studies. What does it mean and in what sense does it matter?" presented May 23 at the session on "The Philosophy of Statistics: Bayesianism, Frequentism and the Nature of Inference"," at the 2015 APS Annual Convention in NYC
Hypothesis testing
Hypothesis testing and estimation are used to reach conclusions about a population by examining a sample of that population.
Hypothesis testing is widely used in medicine, dentistry, health care, biology and other fields as a means to draw conclusions about the nature of populations
Hypothesis testing
This document defines key concepts in statistical hypothesis testing. It explains that a statistical hypothesis is a conjecture about a population parameter. The null hypothesis (H0) states that there is no difference between a parameter and a particular value, while the alternative hypothesis (H1) states there is a difference. Tests can be one-tailed if H1 is > or <, or two-tailed if H1 is ≠. Type I and II errors occur if the wrong decision is made regarding H0. The level of significance and critical value help determine whether to reject or fail to reject H0.
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The document discusses hypothesis testing and t-tests, explaining that a hypothesis is a suggested explanation for a phenomenon that can be tested scientifically, and a t-test determines if the means of two groups are statistically different. It provides details on null and alternative hypotheses, how to perform a t-test, and how the t-statistic, degrees of freedom, and p-value are used to evaluate whether to reject the null hypothesis.
"The Statistical Replication Crisis: Paradoxes and Scapegoats”
D. G. Mayo LSE Popper talk, May 10, 2016.
Abstract: Mounting failures of replication in the social and biological sciences give a practical spin to statistical foundations in the form of the question: How can we attain reliability when Big Data methods make illicit cherry-picking and significance seeking so easy? Researchers, professional societies, and journals are increasingly getting serious about methodological reforms to restore scientific integrity – some are quite welcome (e.g., preregistration), while others are quite radical. Recently, the American Statistical Association convened members from differing tribes of frequentists, Bayesians, and likelihoodists to codify misuses of P-values. Largely overlooked are the philosophical presuppositions of both criticisms and proposed reforms. Paradoxically, alternative replacement methods may enable rather than reveal illicit inferences due to cherry-picking, multiple testing, and other biasing selection effects. Popular appeals to “diagnostic testing” that aim to improve replication rates may (unintentionally) permit the howlers and cookbook statistics we are at pains to root out. Without a better understanding of the philosophical issues, we can expect the latest reforms to fail.
Rm 3 Hypothesis
Hypothesis testing is an important tool in research. A hypothesis is a statement or proposition that can be tested through scientific investigation. The null hypothesis represents the default position that there is no relationship between variables or no difference among groups. The alternative hypothesis is what the researcher aims to prove. Through hypothesis testing, researchers aim to reject the null hypothesis by collecting data and calculating the probability of the results if the null hypothesis were true. This probability is then compared to the pre-determined significance level, often 5%, to determine whether to reject or fail to reject the null hypothesis. Proper hypothesis testing involves clearly stating the hypotheses, selecting a random sample, determining the appropriate statistical test based on the data, and interpreting the results.
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Similar to Russo Vub Seminar
On Severity, the Weight of Evidence, and the Relationship Between the Two
Margherita Harris
Visiting fellow in the Department of Philosophy, Logic and Scientific Method at the London
School of Economics and Political Science.
ABSTRACT: According to the severe tester, one is justified in declaring to have evidence in support of a
hypothesis just in case the hypothesis in question has passed a severe test, one that it would be very
unlikely to pass so well if the hypothesis were false. Deborah Mayo (2018) calls this the strong
severity principle. The Bayesian, however, can declare to have evidence for a hypothesis despite not
having done anything to test it severely. The core reason for this has to do with the
(infamous) likelihood principle, whose violation is not an option for anyone who subscribes to the
Bayesian paradigm. Although the Bayesian is largely unmoved by the incompatibility between
the strong severity principle and the likelihood principle, I will argue that the Bayesian’s never-ending
quest to account for yet an other notion, one that is often attributed to Keynes (1921) and that is
usually referred to as the weight of evidence, betrays the Bayesian’s confidence in the likelihood
principle after all. Indeed, I will argue that the weight of evidence and severity may be thought of as
two (very different) sides of the same coin: they are two unrelated notions, but what brings them
together is the fact that they both make trouble for the likelihood principle, a principle at the core of
Bayesian inference. I will relate this conclusion to current debates on how to best conceptualise
uncertainty by the IPCC in particular. I will argue that failure to fully grasp the limitations of an
epistemology that envisions the role of probability to be that of quantifying the degree of belief to
assign to a hypothesis given the available evidence can be (and has been) detrimental to an
adequate communication of uncertainty.
0hypothesis testing.pdf
The document discusses hypotheses, including defining a hypothesis, the characteristics of a good hypothesis, and the steps involved in hypothesis testing. It notes that a hypothesis is a tentative explanation that can be tested, and outlines criteria for constructing strong hypotheses, such as being clear, precise, and testable. The document also covers the sources of hypotheses, approaches to testing hypotheses like classical and Bayesian statistics, and the types of errors that can occur in hypothesis testing like type 1 and type 2 errors.
Many decisions are based on beliefs concerning the likelihoo.docx
Many decisions are based on beliefs
concerning the likelihood of uncertain
events such as the outcome of an elec-
tion, the guilt of a defendant, or the
future value of the dollar. These beliefs
are usually expressed in statements such
as "I think that . .. ," "chances are
. . .," "it is unlikely that . .. ," and
so forth. Occasionally, beliefs concern-
ing uncertain events are expressed in
numerical form as odds or subjective
probabilities. What determines such be-
liefs? How do people assess the prob-
ability of an uncertain event or the
value of an uncertain quantity? This
article shows that people rely on a
limited number of heuristic principles
which reduce the complex tasks of as-
sessing probabilities and predicting val-
ues to simpler judgmental operations.
In general, these heuristics are quite
useful, but sometimes they lead to severe
and systematic errors.
The subjective assessment of proba-
bility resembles the subjective assess-
ment of physical quantities such as
distance or size. These judgments are
all based on data of limited validity,
which are processed according to heu-
ristic rules. For example, the apparent
distance of an object is determined in
part by its clarity. The more sharply the
object is seen, the closer it appears to
be. This rule has some validity, because
in any given scene the more distant
objects are seen less sharply than nearer
objects. However, the reliance on this
rule leads to systematic errors in the
estimation of distance. Specifically, dis-
tances are often overestimated when
visibility is poor because the contours
of objects are blurred. On the other
hand, distances are often underesti-
mated when visibility is good because
the objects are seen sharply. Thus, the
reliance on clarity as an indication of
distance leads to common biases. Such
biases are also found in the intuitive
judgment of probability. This article
describes three heuristics that are em-
ployed to assess probabilities and to
predict values. Biases to which these
heuristics lead are enumerated, and the
applied and theoretical implications of
these observations are discussed.
Representativeness
Many of the probabilistic questions
with which people are concerned belong
to one of the following types: What is
the probability that object A belongs to
class B? What is the probability that
event A originates from process B?
What is the probability that process B
will generate event A? In answering
such questions, people typically rely on
the representativeness heuristic, in
which probabilities are evaluated by the
degree to which A is representative of
B, that is, by the degree to which A
resembles B. For example, when A is
highly representative of B, the proba-
bility that A originates from B is judged
to be high. On the other hand, if A is
not similar to B, the probability that A
originates from B is judged to be low.
For an illustration of judgment b.
Capits Presentation
This document summarizes a paper about interpreting probability in causal models for cancer epidemiology. It discusses different interpretations of probability, including classical, logical, physical, subjective and objective Bayesian interpretations. It argues that a frequency-cum-objective Bayesian interpretation is best for generic causal claims, while an objective Bayesian interpretation works for single-case causal claims. Risks, odds and probabilities are discussed as ways to express the likelihood of outcomes occurring. The paper examines issues in cancer epidemiology to explore questions of causation and probability interpretation.
Hypothesis testing
This document discusses hypothesis testing and interpretation of data. It provides an example of two lecturers, Sandy and Mandy, who want to test whether providing seminar classes in addition to lectures improves student performance compared to lectures alone. The document outlines the steps in hypothesis testing: 1) Identify the research problem and variables, 2) Specify the null and alternative hypotheses, 3) Choose a significance level, 4) Identify the test statistic, 5) Determine the rejection region, and 6) Select the appropriate statistical test. It defines type 1 and type 2 errors and explains key concepts like the null hypothesis, alternative hypothesis, and significance level.
Spanos lecture 7: An Introduction to Bayesian Inference
This document provides an introduction to Bayesian inference through lecture notes on probability and statistics. It discusses three interpretations of probability: classical, degrees of belief, and frequency. The classical interpretation relies on an explicit chance mechanism with equally likely outcomes, which is too restrictive for empirical modeling. The degrees of belief interpretation considers probability as subjective beliefs, while the frequency interpretation views probability as the limit of relative frequencies in repeated experiments, as justified by the Strong Law of Large Numbers.
Russo urbino presentazione
This document provides an overview of Federica Russo's work on probability and causality in the social sciences. It discusses her perspectives on the syntax and semantics of probability, and how she views probability from an epistemic interpretation. It also briefly summarizes some of her previous arguments including how she sees probability as being Janus-faced between frequency-driven and credence-driven views. The document suggests some new ideas Russo is developing around dispersion, variation, and distinguishing between statistical individuals and populations versus observed individuals. It concludes by emphasizing the useful interactions between probability theory, population science, and philosophy in constructing knowledge.
ch 2 hypothesis
This document discusses hypothesis, its definition, characteristics, and the steps of hypothesis testing. A hypothesis is an educated guess or claim about a population that is tentatively accepted to guide further investigation. Important characteristics of a hypothesis include being clear, testable, limited in scope, consistent with known facts, and able to be tested within a reasonable time. The steps of hypothesis testing are specifying the null hypothesis, significance level, computing the p-value, and comparing it to the significance level to determine whether to reject the null hypothesis. Limitations of hypothesis testing include only providing evidence for or against the null hypothesis and the ability to detect even small differences as sample sizes increase.
The role of background assumptions in severity appraisal (
In the past decade discussions around the reproducibility of scientific findings have led to a re-appreciation of the importance of guaranteeing claims are severely tested. The inflation of Type 1 error rates due to flexibility in the data analysis is widely considered
one of the underlying causes of low replicability rates. Solutions, such as study preregistration, are becoming increasingly popular to combat this problem. Preregistration only allows researchers to evaluate the severity of a test, but not all
preregistered studies provide a severe test of a claim. The appraisal of the severity of a
test depends on background information, such as assumptions about the data generating process, and auxiliary hypotheses that influence the final choice for the
design of the test. In this article, I will discuss the difference between subjective and
inter-subjectively testable assumptions underlying scientific claims, and the importance
of separating the two. I will stress the role of justifications in statistical inferences, the
conditional nature of scientific conclusions following these justifications, and highlight
how severe tests could lead to inter-subjective agreement, based on a philosophical approach grounded in methodological falsificationism. Appreciating the role of background assumptions in the appraisal of severity should shed light on current discussions about the role of preregistration, interpreting the results of replication studies, and proposals to reform statistical inferences.
Types of hypothesis
This document discusses different types of hypotheses used in research. It defines a hypothesis as a proposed explanation for a phenomenon that can be tested. The main types discussed are simple vs complex hypotheses, logical vs empirical hypotheses, directional vs non-directional hypotheses, associative vs causal hypotheses, and the null hypothesis vs the alternative hypothesis. It also discusses types of errors that can occur when testing hypotheses and concludes by emphasizing that hypotheses are provisional explanations that must be tested and can be replaced if not supported.
Testing of Hypothesis.pptx
This document discusses hypothesis testing procedures. It begins by introducing hypothesis testing and defining key terms like the null hypothesis and alternative hypothesis. It then outlines the typical steps in hypothesis testing: 1) formulating the hypotheses, 2) setting the significance level, 3) choosing a test criterion, 4) performing computations, and 5) making a decision. It also discusses concepts like type I and type II errors, and one-tailed vs two-tailed tests. Tail tests refer to whether the rejection region is in one tail or both tails of the sampling distribution. The document provides examples and explanations of these statistical hypothesis testing concepts.
STSTISTICS AND PROBABILITY THEORY .pptx
The document discusses key concepts in probability theory including probability, random experiments, sample spaces, events, random variables, probability distributions, and Bayes' theorem. It covers the binomial, Poisson, and normal distributions and their characteristics and applications. Decision theory is introduced as analyzing choices under uncertainty involving defining problems, identifying outcomes, assessing criteria, and evaluating alternatives to make optimal decisions.
hypothesis testing overview
Hypothesis testing involves stating a null hypothesis (H0) and an alternative hypothesis (H1). H0 assumes there is no effect or relationship in the population. H1 states there is an effect. A study is conducted and statistics are used to determine if the data supports rejecting H0 in favor of H1. The p-value indicates the probability of obtaining results as extreme as the observed data or more extreme if H0 is true. If p ≤ the predetermined significance level (α = 0.05), H0 is rejected in favor of H1. Otherwise, H0 is retained but not proven true. Type I and II errors can occur when the true hypothesis is incorrectly rejected or retained.
Cog5 lecppt chapter11
This chapter discusses judgment and reasoning. It covers several topics:
- Judgment heuristics people use like availability and representativeness that can lead to biases.
- Detecting covariation between variables and neglecting base rates which impacts accuracy.
- Assessing evidence that confirms versus disconfirms one's beliefs and persevering in false beliefs.
- Different types of logical reasoning like syllogisms, conditionals, and Wason's selection task. People don't always use formal logic and make predictable errors.
- How decision making aims for utility maximization but is impacted by framing and risk preferences.
Philosophy of Probability
This document summarizes three philosophical interpretations of probability: classical probability, frequency probability, and subjective/inductive probability. Classical probability defines probability as the ratio of favorable to possible outcomes assuming equal possibility. Frequency probability defines probability as the limit of relative frequencies of outcomes from repeated trials. Subjective probability defines probability as a person's degree of belief based on reason and experience, but it is difficult to justify inductive inferences.
Dubrovnik Pres
This document discusses the relationship between empiricism and the interpretation of probability. It argues that the interpretation of probability is relevant for empiricism because (1) empiricists use statistical inferences to make knowledge claims from empirical data, and (2) statistical inferences involve probability statements. The document then examines different interpretations of probability and proposes considering probability as a polysemic concept that can represent both subjective degrees of belief and objective tendencies displayed by chance devices.
Topic Learning TeamNumber of Pages 2 (Double Spaced)Num.docx
Topic: Learning Team
Number of Pages: 2 (Double Spaced)
Number of sources: 1
Writing Style: APA
Type of document: Essay
Academic Level:Master
Category: Psychology
VIP Support: N/A
Language Style: English (U.S.)
Order Instructions:
I will attach the instruction. On this paper please follow the instructions carefully. Thank you
Correlation
PSYCH/610 Version 2
1
University of Phoenix Material
Correlation
A researcher is interested in investigating the relationship between viewing time (in seconds) and ratings of aesthetic appreciation. Participants are asked to view a painting for as long as they like. Time (in seconds) is measured. After the viewing time, the researcher asks the participants to provide a ‘preference rating’ for the painting on a scale ranging from 1-10. Create a scatter plot depicting the following data:
Viewing Time in Seconds
Preference Rating
10
3
12
4
24
7
5
3
16
6
3
4
11
4
5
2
21
8
23
9
9
5
3
3
17
5
14
6
What does the scatter plot suggest about the relationship between viewing time and aesthetic preference? Is it accurate to state that longer viewing times are the result of greater preference for paintings? Explain. Submit your scatter plot and your answers to the questions to your instructor.
LEARNING OBJECTIVES
· Explain how researchers use inferential statistics to evaluate sample data.
· Distinguish between the null hypothesis and the research hypothesis.
· Discuss probability in statistical inference, including the meaning of statistical significance.
· Describe the t test and explain the difference between one-tailed and two-tailed tests.
· Describe the F test, including systematic variance and error variance.
· Describe what a confidence interval tells you about your data.
· Distinguish between Type I and Type II errors.
· Discuss the factors that influence the probability of a Type II error.
· Discuss the reasons a researcher may obtain nonsignificant results.
· Define power of a statistical test.
· Describe the criteria for selecting an appropriate statistical test.
Page 267IN THE PREVIOUS CHAPTER, WE EXAMINED WAYS OF DESCRIBING THE RESULTS OF A STUDY USING DESCRIPTIVE STATISTICS AND A VARIETY OF GRAPHING TECHNIQUES.In addition to descriptive statistics, researchers use inferential statistics to draw more general conclusions about their data. In short, inferential statistics allow researchers to (a) assess just how confident they are that their results reflect what is true in the larger population and (b) assess the likelihood that their findings would still occur if their study was repeated over and over. In this chapter, we examine methods for doing so.
SAMPLES AND POPULATIONS
Inferential statistics are necessary because the results of a given study are based only on data obtained from a single sample of research participants. Researchers rarely, if ever, study entire populations; their findings are based on sample data. In addition to describing the sample data, we want to make statements ab.
THEOREM OF TOTAL AND COMPOUND PROBABILITY.pptx
This document discusses different types of probability and theorems related to probability calculations. It defines probability, theoretical probability, experimental probability, and subjective probability. It then explains the theorem of total probability, which calculates the total probability of an event by considering mutually exclusive events related to that event. Next, it introduces Bayes' theorem, which provides a mathematical rule for revising estimates based on new information or observations. Finally, it defines the theorem of compound probability, which is the probability of two events occurring simultaneously, and provides formulas for calculating compound probability for independent and dependent events.
HUMAN RESOURCE INFORMATION SYSTEM
This document discusses types of probability and human resource information systems (HRIS). It begins with an introduction to probability theory and its applications in statistics. It then defines key probability concepts like random experiments, sample spaces, events, outcomes, and approaches to measuring probability through classical, frequency, and axiomatic methods. The document also discusses uses of HRIS in functions like payroll, training, recruitment and its benefits in providing accurate data, analysis and decision making. However, it notes some HRIS challenges like costs and limited understanding. In conclusion, the document argues that while machines are created to serve humans, we are increasingly dependent on them for thought and action.
D. Mayo: Philosophy of Statistics & the Replication Crisis in Science
D. Mayo discusses various disputes-notably the replication crisis in science-in the context of her just released book: Statistical Inference as Severe Testing: How to Get Beyond the Statistics Wars.
Similar to Russo Vub Seminar (20)
On Severity, the Weight of Evidence, and the Relationship Between the Two
On Severity, the Weight of Evidence, and the Relationship Between the Two
Many decisions are based on beliefs concerning the likelihoo.docx
Many decisions are based on beliefs concerning the likelihoo.docx
Spanos lecture 7: An Introduction to Bayesian Inference
Spanos lecture 7: An Introduction to Bayesian Inference
The role of background assumptions in severity appraisal (
The role of background assumptions in severity appraisal (
Topic Learning TeamNumber of Pages 2 (Double Spaced)Num.docx
Topic Learning TeamNumber of Pages 2 (Double Spaced)Num.docx
D. Mayo: Philosophy of Statistics & the Replication Crisis in Science
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For the full video of this presentation, please visit: https://www.edge-ai-vision.com/2024/06/how-axelera-ai-uses-digital-compute-in-memory-to-deliver-fast-and-energy-efficient-computer-vision-a-presentation-from-axelera-ai/
Bram Verhoef, Head of Machine Learning at Axelera AI, presents the “How Axelera AI Uses Digital Compute-in-memory to Deliver Fast and Energy-efficient Computer Vision” tutorial at the May 2024 Embedded Vision Summit.
As artificial intelligence inference transitions from cloud environments to edge locations, computer vision applications achieve heightened responsiveness, reliability and privacy. This migration, however, introduces the challenge of operating within the stringent confines of resource constraints typical at the edge, including small form factors, low energy budgets and diminished memory and computational capacities. Axelera AI addresses these challenges through an innovative approach of performing digital computations within memory itself. This technique facilitates the realization of high-performance, energy-efficient and cost-effective computer vision capabilities at the thin and thick edge, extending the frontier of what is achievable with current technologies.
In this presentation, Verhoef unveils his company’s pioneering chip technology and demonstrates its capacity to deliver exceptional frames-per-second performance across a range of standard computer vision networks typical of applications in security, surveillance and the industrial sector. This shows that advanced computer vision can be accessible and efficient, even at the very edge of our technological ecosystem.Principle of conventional tomography-Bibash Shahi ppt..pptx
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Read Taking AI to the Next Level in Manufacturing to gain insights on AI adoption in the manufacturing industry, such as:
1. How quickly AI is being implemented in manufacturing.
2. Which barriers stand in the way of AI adoption.
3. How data quality and governance form the backbone of AI.
4. Organizational processes and structures that may inhibit effective AI adoption.
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June Patch Tuesday
Ivanti’s Patch Tuesday breakdown goes beyond patching your applications and brings you the intelligence and guidance needed to prioritize where to focus your attention first. Catch early analysis on our Ivanti blog, then join industry expert Chris Goettl for the Patch Tuesday Webinar Event. There we’ll do a deep dive into each of the bulletins and give guidance on the risks associated with the newly-identified vulnerabilities.
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In the realm of cybersecurity, offensive security practices act as a critical shield. By simulating real-world attacks in a controlled environment, these techniques expose vulnerabilities before malicious actors can exploit them. This proactive approach allows manufacturers to identify and fix weaknesses, significantly enhancing system security.
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DLAU und die Lizenzen nach dem CCB- und CCX-Modell sind für viele in der HCL-Community seit letztem Jahr ein heißes Thema. Als Notes- oder Domino-Kunde haben Sie vielleicht mit unerwartet hohen Benutzerzahlen und Lizenzgebühren zu kämpfen. Sie fragen sich vielleicht, wie diese neue Art der Lizenzierung funktioniert und welchen Nutzen sie Ihnen bringt. Vor allem wollen Sie sicherlich Ihr Budget einhalten und Kosten sparen, wo immer möglich. Das verstehen wir und wir möchten Ihnen dabei helfen!
Wir erklären Ihnen, wie Sie häufige Konfigurationsprobleme lösen können, die dazu führen können, dass mehr Benutzer gezählt werden als nötig, und wie Sie überflüssige oder ungenutzte Konten identifizieren und entfernen können, um Geld zu sparen. Es gibt auch einige Ansätze, die zu unnötigen Ausgaben führen können, z. B. wenn ein Personendokument anstelle eines Mail-Ins für geteilte Mailboxen verwendet wird. Wir zeigen Ihnen solche Fälle und deren Lösungen. Und natürlich erklären wir Ihnen das neue Lizenzmodell.
Nehmen Sie an diesem Webinar teil, bei dem HCL-Ambassador Marc Thomas und Gastredner Franz Walder Ihnen diese neue Welt näherbringen. Es vermittelt Ihnen die Tools und das Know-how, um den Überblick zu bewahren. Sie werden in der Lage sein, Ihre Kosten durch eine optimierte Domino-Konfiguration zu reduzieren und auch in Zukunft gering zu halten.
Diese Themen werden behandelt
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- Wie funktionieren CCB- und CCX-Lizenzen wirklich?
- Verstehen des DLAU-Tools und wie man es am besten nutzt
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Manage and optimize your license adoption and consumption with SAM4U, an SAP free customer software asset management tool.
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Editor's Notes
- For instance, if A is the proposition that a coin tossed at time t will fall heads, X is the proposition that the chance of A at time t is x , and E is the available evidence that does not contradict X ; the Principal Principle then says that x equals the actual degree of belief that the coin falls heads, conditionally on the proposition that its chance of falling heads is x . In other words, the chance of A equals the degree to which an agent believes in A .
- In fully personalistic approaches coherence is nec and suff for assignments of prior proba. So, the objection: aren’t frequencies just a pedagogical need? Carnap gives an interesting answer (Philosophical Foundations of Probability, §50-51, 41C). 1. we can do without frequencies if inductive logic is accepted. Reason 1: prob1 (subj) can be explicated as estimate of proba2 (obj). So, if proba2 is know, then proba1 just equals this value. Reason 2: even if proba2 is unknown, we can still compute proba1 as estimate of the unknown proba2 from *frequencies* in the sample But the subjectivist can still play a last card: the exchangeability argument. Briefly and informally, De Finetti shows that different agents may start with different prior probabilities, but, as evidence accumulates, their posterior proba will tend to converge, thus giving the illusory impression that objective probability exists.