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State Space Model Notebook Club

Ravin Kumar

@canyon289

Kickoff

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Chapter 6

State Space Models

A very general model that subsumes a whole class of special cases of interest in much the same way that linear regression does is the state-space model or the dynamic linear model, which was introduced in Kalman (1960) and Kalman and Bucy (1961). The model arose in the space tracking setting, where the state equation defines the motion equations for the position or state of a spacecraft with location xt and the data yt reflect information that can be observed from a tracking device such as velocity and azimuth. Although introduced as a method primarily for use in aerospace-related research, the model has been applied to modeling data from economics (Harrison and Stevens,1976; Harvey and Pierse, 1984; Harvey and Todd, 1983; Kitagawa and Gersch 1984, Shumway and Stoffer, 1982), medicine (Jones, 1984) and the soil sciences (Shumway, 1988, §3.4.5). An excellent treatment of time series analysis based on the state space model is the text by Durbin and Koopman (2001).

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- Shumway and Stoffer

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Welcome

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- Ravin

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Agenda

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  1. Why a book club
  2. About me
  3. About you
  4. About us
  5. Why a book club
  6. Community Tour
  7. Q&A
  8. Optional Environment Install

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Why a book club

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About this book club

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A casual place to learn

  • Learn fundamental statistical concepts
  • Apply statistics in real world scenarios
  • Code and run these models
    • Supporting technologies such as JAX
  • Meet new people
    • Interact with motivated folks

Why

  • For fun
  • For work, jobs, interviews
  • To give back
  • Whatever else you want

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Causal Inference Book club was fantastic

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About me

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Not a statistician by training

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Open Source Contributor

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This is not affiliated with Google. I’m not representing Google. All opinions are my own

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About you

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About you

New Math

Code Libraries

Application

Philosophies and ideas

Share ideas

Meet other people

Help each other move forward

Informing decisions at work

Making estimations under real world uncertainty

Building models on a timeline

Like to learn

Enjoy Community

Applied Statistician

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By end we should be able to

  • Intuitively explain state space models
  • Be able to talk through state space model applications
  • Write State Space Models in Code
  • Contribute code to Dynamax
  • Have a bigger network
    • Be part of robust support community
  • Have access to a library of references

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About the book club

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Heavy focus on Application and Code

  • Learning by coding is how I learn best
  • In all my work I get paid to inform decisions and deploy production systems
  • Dynamax is an awesome library

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Reusing a successful format

Async First Book Club

2 - 4 weeks of reading and community interactions over discourse

  • Read through the book
  • Chat on Discourse

Synchronous Session

Usually a 1 hour livestream on Sundays. It could be

  • Me chatting about the previous week’s topic
  • A group discussion
  • Bringing on a guest

Anything else you want

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What each of us can bring

Things I’ll do

  • Set the pacing and chunking of material
    • Schedule
    • Topics
  • Run live discussions every couple weeks or so
    • Youtube livestream
  • Walk through code and application
    • Backed by the math of course
  • Share my personal experience

Things you can do

  • Follow along
  • Share with the community
    • Questions
    • Case Studies
    • Other resources
  • Make open source contributions to DynaMax
  • Lead sessions
    • Mathematics
    • Theory
    • Deeper dives into particular topics

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You’re already making it happen

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Rough Session Outline

This is our rough schedule

  • Session 1: Notation and theory
  • Session 2: HMMs
  • Session X1 X2 X3: Linear Gaussian SSMs
  • Session Y1 Y2 Y3: Non Linear Gaussian SSMs
  • Session Z: Generalized Gaussian SSMs

All of this will be posted on Discourse

  • We’ll take extra time and split up sessions as needed
  • At least one session a month
  • May add additional sessions if we want to dive further into particular topics
  • Update shared through Discourse and email

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Community Tour

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Things you can do

  1. Write down what your goals are.
    1. Objective functions make finding for what you want easier than random searches
  2. Join the communities
  3. Setup code environments
    • Local install is best
    • Colab works too
  4. Share with others
    • Post your goals on Discourse
    • Spread the word about the book club itself!

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Open Discussion

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Setting up a code environment