Category: Inference
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Misconceptions About P Values and The History of Hypothesis Testing
1. Introduction The misconceptions surrounding p values are an example where knowing the history of the field and the mathematical and philosophical principles behind it can greatly help in understanding. The classical statistical testing of today is a hybrid of the approaches taken by R. A. Fisher on the one hand and Jerzy Neyman and…
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Confidence Interval Interpretation
In frequentist statistics (which is one the used by journals and academia), is a fixed quantity, not a random variable. Hence, a confidence interval is not a probability statement about . A 95 percent confidence interval does not mean that the interval would capture the true value 95 percent of the time. This statement would…
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Hypothesis Testing and p-values
1. Introduction Hypothesis testing is a method of inference. Definition 1 A hypothesis is a statement about a population parameter. Definition 2 Null and Alternate Hypothesis: We partition the parameter space into two disjoint sets and and we wish to test: We call the null hypothesis and the alternate hypothesis. Definition 3 Rejection Region: Let…
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Parametric Inference
There are two methods of estimating . 1. Method of Moments It is a method of generating parametric estimators. These estimators are not optimal but they are easy to compute. They are also used to generate starting values for other numerical parametric estimation methods. Definition 1 Moments and Sample Moments: Suppose that the parameter has…
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Introduction to Statistical Inference
1. Introduction We assume that the data we are looking at comes from a probability distribution with some unknown parameters that control the exact shape of the distribution. Definition 1 Statistical Inference: It is the process of using given data to infer the properties of the distribution (for example the values of the parameters) which…
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Frequentists and Bayesians
1. Interpretations of Probability 1.1. Bayesians and Frequentists There are two possible ways to interpret the meaning of probability. 1.2. Maps and Territories Here ‘territory’ refers to the world as it exists or the reality as it is. The map refers to our model of the world or the way we see and interpret it.…