MIT RES.6-012 Introduction to Probability, Spring 2018 (English) (Part 4)

Thursday, December 12, 2024

Starting a new Lecture Notes Series on MIT RES.9-003 Brains, Minds and Machines Summer Course, Summer 2015

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MIT RES.9-003 Brains, Minds and Machines Summer Course, Summer 2015 By Lecture Notes together!

Lecture 136: L13.5 Forecast Revisions

Lecture 137: L13.6 The Conditional Variance

Lecture 138: L13.7 Derivation of the Law of Total Variance

Lecture 139: L13.8 A Simple Example

Lecture 140: L13.9 Section Means and Variances

Lecture 141: L13.10 Mean of the Sum of a Random Number of Random Variables

Lecture 142: L13.11 Variance of the Sum of a Random Number of Random Variables

Lecture 143: S13.1 Conditional Expectation Properties

Lecture 144: L14.1 Lecture Overview

Lecture 145: L14.2 Overview of Some Application Domains

Lecture 146: L14.3 Types of Inference Problems

Lecture 147: L14.4 The Bayesian Inference Framework

Lecture 148: L14.5 Discrete Parameter, Discrete Observation

Lecture 149: L14.6 Discrete Parameter, Continuous Observation

Lecture 150: L14.7 Continuous Parameter, Continuous Observation

Lecture 151: L14.8 Inferring the Unknown Bias of a Coin and the Beta Distribution

Lecture 152: L14.9 Inferring the Unknown Bias of a Coin - Point Estimates

Lecture 153: L14.10 Summary

Lecture 154: S14.1 The Beta Formula

Lecture 155: L15.1 Lecture Overview

Lecture 156: L15.2 Recognizing Normal PDFs

Lecture 157: L15.3 Estimating a Normal Random Variable in the Presence of Additive Noise

Lecture 158: L15.4 The Case of Multiple Observations

Lecture 159: L15.5 The Mean Squared Error

Lecture 160: L15.6 Multiple Parameters; Trajectory Estimation

Lecture 161: L15.7 Linear Normal Models

Lecture 162: L15.8 Trajectory Estimation Illustration

Lecture 163: L16.1 Lecture Overview

Lecture 164: L16.2 LMS Estimation in the Absence of Observations

Lecture 165: L16.3 LMS Estimation of One Random Variable Based on Another

Lecture 166: L16.4 LMS Performance Evaluation

Lecture 167: L16.5 Example: The LMS Estimate

Lecture 168: L16.6 Example Continued: LMS Performance Evaluation

Lecture 169: L16.7 LMS Estimation with Multiple Observations or Unknowns

Lecture 170: L16.8 Properties of the LMS Estimation Error

Lecture 171: L17.1 Lecture Overview

Lecture 172: L17.2 LLMS Formulation

Lecture 173: L17.3 Solution to the LLMS Problem

Lecture 174: L17.4 Remarks on the LLMS Solution and on the Error Variance

Lecture 175: L17.5 LLMS Example

Lecture 176: L17.6 LLMS for Inferring the Parameter of a Coin

Lecture 177: L17.7 LLMS with Multiple Observations

Lecture 178: L17.8 The Simplest LLMS Example with Multiple Observations

Lecture 179: L17.9 The Representation of the Data Matters in LLMS

Lecture 180: L18.1 Lecture Overview