Week 3: Learning from Random Samples Brandon Stewart1 Princeton September 26/28, 2016 1These slides are heavily influenced by Matt Blackwell, Adam Glynn, Justin Grimmer and Jens Hainmueller. Some illustrations by Shay O'Brien. Stewart (Princeton) Week 3: Learning From Random Samples September 26/28, 2016 1 / 141 I random variables I joint distributions This Week I Monday: Point Estimation F sampling and sampling distributions F point estimates F properties (bias, variance, consistency) I Wednesday: Interval Estimation F confidence intervals F comparing two groups Next Week I hypothesis testing I what is regression? Long Run I probability ! inference ! regression Questions? Where We've Been and Where We're Going... Last Week Stewart (Princeton) Week 3: Learning From Random Samples September 26/28, 2016 2 / 141 I joint distributions This Week I Monday: Point Estimation F sampling and sampling distributions F point estimates F properties (bias, variance, consistency) I Wednesday: Interval Estimation F confidence intervals F comparing two groups Next Week I hypothesis testing I what is regression? Long Run I probability ! inference ! regression Questions? Where We've Been and Where We're Going... Last Week I random variables Stewart (Princeton) Week 3: Learning From Random Samples September 26/28, 2016 2 / 141 This Week I Monday: Point Estimation F sampling and sampling distributions F point estimates F properties (bias, variance, consistency) I Wednesday: Interval Estimation F confidence intervals F comparing two groups Next Week I hypothesis testing I what is regression? Long Run I probability ! inference ! regression Questions? Where We've Been and Where We're Going... Last Week I random variables I joint distributions Stewart (Princeton) Week 3: Learning From Random Samples September 26/28, 2016 2 / 141 I Monday: Point Estimation F sampling and sampling distributions F point estimates F properties (bias, variance, consistency) I Wednesday: Interval Estimation F confidence intervals F comparing two groups Next Week I hypothesis testing I what is regression? Long Run I probability ! inference ! regression Questions? Where We've Been and Where We're Going... Last Week I random variables I joint distributions This Week Stewart (Princeton) Week 3: Learning From Random Samples September 26/28, 2016 2 / 141 F point estimates F properties (bias, variance, consistency) I Wednesday: Interval Estimation F confidence intervals F comparing two groups Next Week I hypothesis testing I what is regression? Long Run I probability ! inference ! regression Questions? Where We've Been and Where We're Going... Last Week I random variables I joint distributions This Week I Monday: Point Estimation F sampling and sampling distributions Stewart (Princeton) Week 3: Learning From Random Samples September 26/28, 2016 2 / 141 F properties (bias, variance, consistency) I Wednesday: Interval Estimation F confidence intervals F comparing two groups Next Week I hypothesis testing I what is regression? Long Run I probability ! inference ! regression Questions? Where We've Been and Where We're Going... Last Week I random variables I joint distributions This Week I Monday: Point Estimation F sampling and sampling distributions F point estimates Stewart (Princeton) Week 3: Learning From Random Samples September 26/28, 2016 2 / 141 I Wednesday: Interval Estimation F confidence intervals F comparing two groups Next Week I hypothesis testing I what is regression? Long Run I probability ! inference ! regression Questions? Where We've Been and Where We're Going... Last Week I random variables I joint distributions This Week I Monday: Point Estimation F sampling and sampling distributions F point estimates F properties (bias, variance, consistency) Stewart (Princeton) Week 3: Learning From Random Samples September 26/28, 2016 2 / 141 F comparing two groups Next Week I hypothesis testing I what is regression? Long Run I probability ! inference ! regression Questions? Where We've Been and Where We're Going... Last Week I random variables I joint distributions This Week I Monday: Point Estimation F sampling and sampling distributions F point estimates F properties (bias, variance, consistency) I Wednesday: Interval Estimation F confidence intervals Stewart (Princeton) Week 3: Learning From Random Samples September 26/28, 2016 2 / 141 Next Week I hypothesis testing I what is regression? Long Run I probability ! inference ! regression Questions? Where We've Been and Where We're Going... Last Week I random variables I joint distributions This Week I Monday: Point Estimation F sampling and sampling distributions F point estimates F properties (bias, variance, consistency) I Wednesday: Interval Estimation F confidence intervals F comparing two groups Stewart (Princeton) Week 3: Learning From Random Samples September 26/28, 2016 2 / 141 I hypothesis testing I what is regression? Long Run I probability ! inference ! regression Questions? Where We've Been and Where We're Going... Last Week I random variables I joint distributions This Week I Monday: Point Estimation F sampling and sampling distributions F point estimates F properties (bias, variance, consistency) I Wednesday: Interval Estimation F confidence intervals F comparing two groups Next Week Stewart (Princeton) Week 3: Learning From Random Samples September 26/28, 2016 2 / 141 I what is regression? Long Run I probability ! inference ! regression Questions? Where We've Been and Where We're Going... Last Week I random variables I joint distributions This Week I Monday: Point Estimation F sampling and sampling distributions F point estimates F properties (bias, variance, consistency) I Wednesday: Interval Estimation F confidence intervals F comparing two groups Next Week I hypothesis testing Stewart (Princeton) Week 3: Learning From Random Samples September 26/28, 2016 2 / 141 Long Run I probability ! inference ! regression Questions? Where We've Been and Where We're Going... Last Week I random variables I joint distributions This Week I Monday: Point Estimation F sampling and sampling distributions F point estimates F properties (bias, variance, consistency) I Wednesday: Interval Estimation F confidence intervals F comparing two groups Next Week I hypothesis testing I what is regression? Stewart (Princeton) Week 3: Learning From Random Samples September 26/28, 2016 2 / 141 I probability ! inference ! regression Questions? Where We've Been and Where We're Going... Last Week I random variables I joint distributions This Week I Monday: Point Estimation F sampling and sampling distributions F point estimates F properties (bias, variance, consistency) I Wednesday: Interval Estimation F confidence intervals F comparing two groups Next Week I hypothesis testing I what is regression? Long Run Stewart (Princeton) Week 3: Learning From Random Samples September 26/28, 2016 2 / 141 Questions? Where We've Been and Where We're Going... Last Week I random variables I joint distributions This Week I Monday: Point Estimation F sampling and sampling distributions F point estimates F properties (bias, variance, consistency) I Wednesday: Interval Estimation F confidence intervals F comparing two groups Next Week I hypothesis testing I what is regression? Long Run I probability ! inference ! regression Stewart (Princeton) Week 3: Learning From Random Samples September 26/28, 2016 2 / 141 Where We've Been and Where We're Going... Last Week I random variables I joint distributions This Week I Monday: Point Estimation F sampling and sampling distributions F point estimates F properties (bias, variance, consistency) I Wednesday: Interval Estimation F confidence intervals F comparing two groups Next Week I hypothesis testing I what is regression? Long Run I probability ! inference ! regression Questions? Stewart (Princeton) Week 3: Learning From Random Samples September 26/28, 2016 2 / 141 For the last few classes we have talked about probability|that is, if we knew how the world worked, we are describing what kind of data we should expect. Now we want to move the other way. If we have a set of data, can we estimate the various parts of the probability distributions that we have talked about. Can we estimate the mean, the variance, the covariance, etc? Moving forward this is going to be very important. Why? Because we are going to want to estimate the population conditional expectation in regression. Inference: given that we observe something in the data, what is our best guess of what it will be in other samples? Where We've Been and Where We're Going... Stewart (Princeton) Week 3: Learning From Random Samples September 26/28, 2016 3 / 141 For the last few classes we have talked about probability|that is, if we knew how the world worked, we are describing what kind of data we should expect. Now we want to move the other way. If we have a set of data, can we estimate the various parts of the probability distributions that we have talked about. Can we estimate the mean, the variance, the covariance, etc? Moving forward this is going to be very important. Why? Because we are going to want to estimate the population conditional expectation in regression. Where We've Been and Where We're Going... Inference: given that we observe something in the data, what is our best guess of what it will be in other samples? Stewart (Princeton) Week 3: Learning From Random Samples September 26/28, 2016 3 / 141 Now we want to move the other way. If we have a set of data, can we estimate the various parts of the probability distributions that we have talked about. Can we estimate the mean, the variance, the covariance, etc? Moving forward this is going to be very important. Why? Because we are going to want to estimate the population conditional expectation in regression. Where We've Been and Where We're Going... Inference: given that we observe something in the data, what is our best guess of what it will be in other samples? For the last few classes we have talked about probability|that is, if we knew how the world worked, we are describing what kind of data we should expect.