Week4 Lectures: Overview

Greetings from Dr. Sanchez. Welcome to Week 4. Video will appear 10/18/2021

In lecture 12, we will witness how a statistician fits the log normal model to radon data set using a very popular method used by statistician to estimate parameters of the models that we study. The radon data is an example of a random sample of households from which we obtained radon measurements. Model fitting is done constantly by statisticians, who unlike us play with data and infer from the data what was the probability model that generated the data. In Lecture 14 we will learn another model, the Poisson, for discrete random variables. Several supplementary materials help us see how the Poisson has been judged to fit data sets. The guest lecture by Dr. Gao helps us see how probability models are used in unsupervised and supervised machine learning. Then this week we have some theoretical derivations that are extremely important in probability theory and applications. LOTUS, the Law of the Unconcious Statistician featured in lectures 13 A, B, C, D,E allows us to find expectations and variances of functions of random variables. Sometimes practitioners need expectations of functions of a random variable to make decisions. The results presented in Lesson 13 are essential elements of your skill set.

Textbook Readings and Supplementary Materials

Chapter 5 in the textbook, Sections 5.4, 5.14, 5.15, 5.17
Chapter 7 in the textbook, Sections 7.3, 7.10, 7.16
Chapter 10 in the textbook, Section 10.2,10.5
Guest lecture: Dr. Ruiqi Gao's video.

Lecture 12: Fitting a lognormal model to data

Lecture 13: A-Learning Glass-Introduction to LOTUS

Lecture 13 B-LearningGlass-More LOTUS results

Lecture 13 C- LearningGlass LOTUS applied

Lecture 13 D Learning Glass LOTUS and families

Lecture 14 Poisson and Poisson model fitting

Goodness of fit test-Fitting the Poisson to birth data To be used in the review assignment this week (use the app in this url https://homepage.divms.uiowa.edu/~mbognar/applets/chisq.html to calculate the Probability that the chi square random variable is larger than the value you calculate).

Poisson probability calculator

Death by horse-kick

Modern-media replication of historical applications

Guest Lecturer video

Dr. Gao produced this video to illustrate to students in computational statistics classes that the computational methods they used in their classes, if applied in artificial intelligence would require the use of probability models. Although she did not produce the video specifically for Stat 100A, the video is much more relevant to us because it helps us see how important probability models are in all the methods that are guiding surgeries, cars, employment decisions, climate interventions, security and many more.

Modern Probabilistic Models in Artificial Intelligence, by Dr. Ruiqi Gao, Google.

Ph.D. UCLA Department of Statistics, 2021