Publications by Laboratory Exercise No. 5
Stat 142 Lab Exercise 1 Guide
1 Required packages First, let us load the necessary packages for this lab session. library(tidyverse) library(forecast) library(timetk) 2 Data sets Monthly inflation rate Annual inflation rate Quarterly HH consumption expenditure Global CO2 concentration 3 Examples of time series data 3.1 Monthly Inflation Rate for Eastern Visayas: 201...
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Stat 136 Lesson 2.1 (Bayesian inference for a proportion using discrete prior)
1 Three general steps of Bayesian inference: Express an opinion about the location of the proportion \(p\) before sampling (prior). Take the sample and record the observed proportion (data/likelihood). Use Bayes’ rule to sharpen or update the previous opinion about \(p\) given the information in the sample (posterior). 2 An example Suppose...
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Stat 136 Lesson 1.4 (Elements of Bayesian Models)
Elements of a Bayesian model Bayes’ formula extends naturally to statistical models. A Bayesian model is a parametric model in the classical (or frequentist) sense, but with the addition of a prior probability distribution for the model parameter, which is treated as a random variable rather than an unknown constant. The basic elements of a B...
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Stat 136- Lesson 1.3 (Odds and Bayes Factor)
1 Odds Another way of dealing with uncertain events that we are modeling as random is to form the odds of the event. The odds for an event C equals the probability of the event occurring divided by the probability of the event not occurring: \[ odds(C) = \frac{P(C)}{P(\overline{C})} \] Since the probability of the event not occurring equals on...
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Stat 122- Problem Set No. 1
Problem No. 1 Suppose a random variable \(Y\) has the following density function \[ f_Y(y) = \begin{cases} \frac{3}{2} y^2 + y, \; \text{if} \; 0\leq y \leq 1 \\ 0, \; \text{elsewhere} \end{cases} \] Find the probability density function of \(U = 5 - \frac{Y}{2}\). [10 pts.] Problem No. 2 The amount of flour used per day by a bakery is a r...
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Econ 115s Lesson 1.1 (Introduction to econometrics)
1 What is econometrics? Econometrics is based upon the development of statistical methods for estimating economic relationships, testing economic theories, and evaluating and implementing government and business policy. A common application of econometrics is the forecasting of such important macroeconomic variables as interest rates, inflatio...
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Stat 142 Lesson 1.2 (Components of a time series)
1 Introduction Patterns in time series data are the backbone of the analysis of it. As with other fields of statistics and, in particular, the field of machine learning, one of the primary goals of time series analysis is to identify patterns in data. Those patterns can then be utilized to provide meaningful insights about both past and future ...
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Stat 136 Lesson 1.1 (Main Approaches to Statistics)
The Scientific Method: A Process for Learning In the Middle Ages, science was deduced from principles set down many centuries earlier by authorities such as Aristotle. The idea that scientific theories should be tested against real world data revolutionized thinking. This way of thinking known as the scientific method sparked the Renaissance. T...
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Stat 136 Lesson 1.2 (The Bayes Theorem)
Conditional Probability and Law of Total Probability Recall that by definition, the conditional probability of A given B, is \[ P(A|B) = \frac{P(A \cap B)}{P(B)}, \text{provided} \; P(B)>0. \tag{1} \] Similarly, we have \[ P(B|A) = \frac{P(A \cap B)}{P(A)}, \text{provided} \; P(A)>0. \tag{2} \] By multiplication, we obtain from (2), \[ P(A \c...
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Stat 221- Correlation Analysis
Learning Objectives Identify the most appropriate measure of correlation/association, Compute measures of correlation/association using JASP,and Interpret results of correlation analyses Basic ideas Correlation analysis is a statistical technique used to determine the degree of linear relationship between two or more variables It is a meth...
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