Statistical Rethinking 2023 - Lecture 01

Course description and materials: https://github.com/rmcelreath/stat_rethinking_2023

Transcript

1. Statistical Rethinking
   1. The Golem of Prague
   2023
   

   View Slide

2. Texts in Statistical Science
   Richard McElreath
   McElreath
   Statistical Rethinking
   A Bayesian Course
   with Examples in R and Stan
   SECOND EDITION
   Second
   Edition
   Statistical Rethinking
   F ESBę
   'ĶĴłĿIJ ƊƉ *MMVTUSBUJPO PG .BSUJO #FIBJNT
   HMPCF TIPXJOH UIF TNBMM XPSME UIBU
   $PMPNCP BOUJDJQBUFE &VSPQF MJFT PO UIF SJHIU
   IBOE TJEF "TJB MJFT PO UIF MFę ćF CJH JTMBOE
   MBCFMFE i$JQBOHVw JT +BQBO
   XPSMET VTJOH UIF TUSFOHUIT PG RVBMJUBUJWF JOTJHIU UP DSJUJDJ[F TNBMM XPSME RVBOUJUBUJWF JOTJHIU
   ćF QSFDJTJPO BOE USBOTQBSFODZ PG UIF TNBMM XPSME JT QPXFSGVM BOE FTTFOUJBM #VU JU JT WFSZ
   EJďDVMU UP JODPSQPSBUF BMM PG PVS TDJFOUJĕD LOPXMFEHF BOE FYQFSUJTF JOUP UIF TNBMM XPSME 4P
   PęFO XF SFBMJ[F IPX CBE B NPEFM JT POMZ XIFO XF TFF IPX CBEMZ JU CFIBWFT JO UIF CSPBEFS
   TDJFOUJĕD DPOUFYU
   *O UIJT DIBQUFS ZPV XJMM CFHJO UP CVJME #BZFTJBO NPEFMT "MNPTU BMM PG UIF XPSL JO UIJT
   DIBQUFS UBLFT QMBDF JO UIF TNBMM XPSME 8FMM TUBSU XJUI B TJNQMF HPBM FTUJNBOE
   8IBU QSP
   QPSUJPO PG UIF &BSUIT TVSGBDF JT DPWFSFE CZ XBUFS ćJT JT B EFTDSJQUJWF FTUJNBOE CVU JU TUJMM
   SFRVJSFT DBVTBM BTTVNQUJPOT BCPVU IPX UIF TBNQMF BSJTFT 0ODF UIPTF BTTVNQUJPOT BSF JO
   QMBDF XFMM VTF #BZFTJBO JOGFSFODF UP QSPEVDF BO FTUJNBUF
   3FUIJOLJOH 'BTU BOE GSVHBM JO UIF MBSHF XPSME ćF OBUVSBM XPSME JT DPNQMFY BT USZJOH UP EP TDJFODF
   TFSWFT UP SFNJOE VT :FU FWFSZUIJOH GSPN UIF IVNCMF UJDL UP UIF JOEVTUSJPVT TRVJSSFM UP UIF JEMF TMPUI
   NBOBHFT UP GSFRVFOUMZ NBLF BEBQUJWF EFDJTJPOT #VU JUT B HPPE CFU UIBU NPTU BOJNBMT BSF OPU #BZFTJBO
   JG POMZ CFDBVTF CFJOH #BZFTJBO JT FYQFOTJWF BOE EFQFOET VQPO IBWJOH B HPPE NPEFM *OTUFBE BOJNBMT
   VTF WBSJPVT IFVSJTUJDT UIBU BSF ĕU UP UIFJS FOWJSPONFOUT QBTU PS QSFTFOU ćFTF IFVSJTUJDT UBLF BEBQUJWF
   TIPSUDVUT BOE TP NBZ PVUQFSGPSN B SJHPSPVT #BZFTJBO BOBMZTJT PODF DPTUT PG JOGPSNBUJPO HBUIFSJOH
   BOE QSPDFTTJOH BOE PWFSĕUUJOH $IBQUFS
   BSF UBLFO JOUP BDDPVOU 0ODF ZPV BMSFBEZ LOPX XIJDI
   JOGPSNBUJPO UP JHOPSF PS BUUFOE UP CFJOH GVMMZ #BZFTJBO JT B XBTUF *UT OFJUIFS OFDFTTBSZ OPS TVďDJFOU
   GPS NBLJOH HPPE EFDJTJPOT BT SFBM BOJNBMT EFNPOTUSBUF #VU GPS IVNBO BOJNBMT #BZFTJBO BOBMZTJT
   QSPWJEFT B HFOFSBM XBZ UP EJTDPWFS SFMFWBOU JOGPSNBUJPO BOE QSPDFTT JU MPHJDBMMZ
   ćF HBSEFO PG GPSLJOH EBUB
   0VS HPBM JO UIJT TFDUJPO JT UP CVJME #BZFTJBO JOGFSFODF VQ GSPN IVNCMF CFHJOOJOHT TP
   UIFSF JT OP TVQFSTUJUJPO BCPVU JU #BZFTJBO JOGFSFODF JT SFBMMZ KVTU DPVOUJOH BOE DPNQBSJOH PG
   QPTTJCJMJUJFT 8F NBLF DBVTBM BTTVNQUJPOT XF FOVNFSBUF UIF JNQMJDBUJPOT PG UIPTF BTTVNQ
   THIRD
   

   View Slide

3. F ESBę
   4."-- 803-%4 "/% -"3(& 803-%4
   'ĶĴłĿIJ ƊƉ *MMVTUSBUJPO PG .BSUJO #FIBJNT
   HMPCF TIPXJOH UIF TNBMM XPSME UIBU
   $PMPNCP BOUJDJQBUFE &VSPQF MJFT PO UIF SJHIU
   IBOE TJEF "TJB MJFT PO UIF MFę ćF CJH JTMBOE
   MBCFMFE i$JQBOHVw JT +BQBO
   XPSMET VTJOH UIF TUSFOHUIT PG RVBMJUBUJWF JOTJHIU UP DSJUJDJ[F TNBMM XPSME RVBOUJUBUJWF JOTJHIU
   ćF QSFDJTJPO BOE USBOTQBSFODZ PG UIF TNBMM XPSME JT QPXFSGVM BOE FTTFOUJBM #VU JU JT WFSZ
   EJďDVMU UP JODPSQPSBUF BMM PG PVS TDJFOUJĕD LOPXMFEHF BOE FYQFSUJTF JOUP UIF TNBMM XPSME 4P
   PęFO XF SFBMJ[F IPX CBE B NPEFM JT POMZ XIFO XF TFF IPX CBEMZ JU CFIBWFT JO UIF CSPBEFS
   TDJFOUJĕD DPOUFYU
   *O UIJT DIBQUFS ZPV XJMM CFHJO UP CVJME #BZFTJBO NPEFMT "MNPTU BMM PG UIF XPSL JO UIJT
   DIBQUFS UBLFT QMBDF JO UIF TNBMM XPSME 8FMM TUBSU XJUI B TJNQMF HPBM FTUJNBOE
   8IBU QSP
   QPSUJPO PG UIF &BSUIT TVSGBDF JT DPWFSFE CZ XBUFS ćJT JT B EFTDSJQUJWF FTUJNBOE CVU JU TUJMM
   SFRVJSFT DBVTBM BTTVNQUJPOT BCPVU IPX UIF TBNQMF BSJTFT 0ODF UIPTF BTTVNQUJPOT BSF JO
   QMBDF XFMM VTF #BZFTJBO JOGFSFODF UP QSPEVDF BO FTUJNBUF
   3FUIJOLJOH 'BTU BOE GSVHBM JO UIF MBSHF XPSME ćF OBUVSBM XPSME JT DPNQMFY BT USZJOH UP EP TDJFODF
   TFSWFT UP SFNJOE VT :FU FWFSZUIJOH GSPN UIF IVNCMF UJDL UP UIF JOEVTUSJPVT TRVJSSFM UP UIF JEMF TMPUI
   NBOBHFT UP GSFRVFOUMZ NBLF BEBQUJWF EFDJTJPOT #VU JUT B HPPE CFU UIBU NPTU BOJNBMT BSF OPU #BZFTJBO
   JG POMZ CFDBVTF CFJOH #BZFTJBO JT FYQFOTJWF BOE EFQFOET VQPO IBWJOH B HPPE NPEFM *OTUFBE BOJNBMT
   VTF WBSJPVT IFVSJTUJDT UIBU BSF ĕU UP UIFJS FOWJSPONFOUT QBTU PS QSFTFOU ćFTF IFVSJTUJDT UBLF BEBQUJWF
   TIPSUDVUT BOE TP NBZ PVUQFSGPSN B SJHPSPVT #BZFTJBO BOBMZTJT PODF DPTUT PG JOGPSNBUJPO HBUIFSJOH
   BOE QSPDFTTJOH BOE PWFSĕUUJOH $IBQUFS
   BSF UBLFO JOUP BDDPVOU 0ODF ZPV BMSFBEZ LOPX XIJDI
   JOGPSNBUJPO UP JHOPSF PS BUUFOE UP CFJOH GVMMZ #BZFTJBO JT B XBTUF *UT OFJUIFS OFDFTTBSZ OPS TVďDJFOU
   GPS NBLJOH HPPE EFDJTJPOT BT SFBM BOJNBMT EFNPOTUSBUF #VU GPS IVNBO BOJNBMT #BZFTJBO BOBMZTJT
   QSPWJEFT B HFOFSBM XBZ UP EJTDPWFS SFMFWBOU JOGPSNBUJPO BOE QSPDFTT JU MPHJDBMMZ
   Changes and updates
   Fewer examples, more depth
   Detailed workflow, testing
   Interventions, post-stratification
   Foreground measurement, missing
   Sensitivity analysis
   

   View Slide

4. DAGS
   

   View Slide

5. GOLEMS
   DAGS
   

   View Slide

6. OWLS
   DAGS
   GOLEMS
   

   View Slide

7. DAGS
   OWLS
   GOLEMS
   

   View Slide

8. View Slide

9. View Slide

10. Science Before Statistics
    For statistical models to produce scientific insight, they
    require additional scientific (causal) models
    The reasons for a statistical analysis are not found in the data
    themselves, but rather in the causes of the data
    The causes of the data cannot be extracted from the data
    alone. No causes in; no causes out.
    

    View Slide

11. What is Causal Inference?
    More than association between
    variables
    Causal inference is prediction of
    intervention
    Causal inference is imputation of
    missing observations
    

    View Slide

12. Causal Prediction
    Knowing a cause means being able to predict
    the consequences of an intervention. 

    What if I do this?
    

    View Slide

13. Causal Imputation
    Knowing a cause means being able to construct
    unobserved counterfactual outcomes. 

    What if I had done something else?
    

    View Slide

14. Causal Inference
    Description
    Design
    

    View Slide

15. Causes Are Not Optional
    Even when goal is descriptive, need
    causal model
    The sample differs from the population;
    describing the population requires
    causal thinking about why
    

    View Slide

16. DAGs
    Directed Acyclic Graphs
    Heuristic causal models
    Clarify scientific thinking
    Analyze to deduce appropriate statistical models
    “What can we decide, without additional assumptions?”
    Gateway to scientific modeling
    s
    * "
    u
    

    View Slide

17. DAGs
    H 2i HX kyReVV rQmH/ K2bm`2 i?2 +
    s
    * "
    u
    

    View Slide

18. DAGs
    H 2i HX kyReVV rQmH/ K2bm`2 i?2 +
    s
    * "
    u
    

    View Slide

19. DAGs
    H 2i HX kyReVV rQmH/ K2bm`2 i?2 +
    s
    * "
    u
    

    View Slide

20. DAGs
    H 2i HX kyReVV rQmH/ K2bm`2 i?2 +
    s
    * "
    u
    

    View Slide

21. DAGs
    H 2i HX kyReVV rQmH/ K2bm`2 i?2 +
    s
    * "
    u
    

    View Slide

22. DAGs
    H 2i HX kyReVV rQmH/ K2bm`2 i?2 +
    s
    * "
    u
    

    View Slide

23. s
    * "
    u
    DAGs
    Different queries, different models
    Which control variables?
    Absolute not safe to add everything — bad controls
    How to test/refine the causal model?
    DAGs are intuition pumps: get head out of data, into science
    

    View Slide

24. GOLEMS
    DAGS
    

    View Slide

25. Prague 16th century
    

    View Slide

26. Rabbi Löw (1512–1609)
    

    View Slide

27. Golems
    Clay robots
    Powerful
    No wisdom or foresight
    Dangerous
    “Breath of Bones: A Tale of the Golem” (2014)
    

    View Slide

28. Statistical Models
    5)& (0-&. 0' 13"(6&
    Clay robots
    Powerful
    No wisdom or foresight
    Dangerous
    

    View Slide

29. Figure 1.1
    

    View Slide

30. Statistical Models
    Incredibly limiting
    Focus on rejecting null
    hypotheses
    Relationship between research
    and test not clear
    Industrial framework
    5)& (0-&. 0' 13"(6&
    

    View Slide

31. View Slide

32. Null Models Rarely Unique
    Null population dynamics?
    Null phylogeny?
    Null ecological community?
    Null social network?
    Problem: Many processes
    produce similar distributions
    

    View Slide

33. View Slide

34. H0
    H1
    “Evolution
    is neutral”
    “Selection

    matters”
    P0A
    Neutral,
    non-equilibrium
    P0B
    Neutral,
    equilibrium
    P1B
    Fluctuating
    selection
    P1A
    Constant
    selection
    MI
    MII
    MIII
    Hypotheses Process models Statistical models
    Figure 1.2
    

    View Slide

35. H0
    “Evolution
    is neutral”
    P0A
    Neutral,
    equilibrium
    MII
    Hypotheses Process models Statistical models
    Figure 1.2
    

    View Slide

36. H0
    “Evolution
    is neutral”
    P0A
    Neutral,
    non-equilibrium
    P0B
    Neutral,
    equilibrium MI
    MII
    Hypotheses Process models Statistical models
    Figure 1.2
    

    View Slide

37. H0
    H1
    “Evolution
    is neutral”
    “Selection

    matters”
    P0A
    Neutral,
    non-equilibrium
    P0B
    Neutral,
    equilibrium
    P1B
    Fluctuating
    selection
    P1A
    Constant
    selection
    MI
    MII
    MIII
    Hypotheses Process models Statistical models
    Figure 1.2
    

    View Slide

38. View Slide

39. SPECIES
    a
    b
    species
    per
    island
    ISLANDS
    A B C
    1 0 1
    0 1 0
    1 1 i 1
    islands
    per
    D species
    0 2
    i 2
    Fig. 3. Example of a simple presence/absence matrix with a checker-
    board distribution: four islands and two species
    islands and are absent from species-rich islands (see Fig. 2 right,
    which has a supertramp as species e but has the same row
    sums and grand total as Fig. 2 left).
    Now compare the rearrangeability of the two matrices of
    Fig. 2. Recall that the rearrangement algorithm by which Connor
    and Simberloff generate simulated matrices seeks 2 by 2 subma-
    trices (not necessarily in adjacent rows or columns) of the form
    10)
    1)o (0,
    (?0
    and changes them to the opposite form. This manipulation alters
    neither row nor column sums and hence maintains the con-
    Islands
    00101011110100001110
    Ii010100001011110001
    00101111001001001110
    11010000110110110001
    10110000000011111011
    01001111111100000100
    10011101011001001100
    01100010100110110011
    00101011100100110110
    Species ii010100011011001001
    11010111100001011000
    00101000011110100111
    i0000111100011001110
    01111000011100110001
    11001100100111000110
    00110011011000111001
    00010101101011101010
    11101010010100010101
    01101101010001010101
    10010010101110101010
    Conor & Simberloff 1979, Diamond & Gilpin 1982
    Species
    Locations
    No null ecology
    

    View Slide

40. Null networks & fantastical beasts
    Figure 1: Dependence structure between data points must not change under permutations. In node-
    .
    CC-BY-NC-ND 4.0 International license
    available under a
    was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made
    The copyright holder for this preprint (which
    this version posted June 7, 2021.
    ;
    https://doi.org/10.1101/2021.06.04.447124
    doi:
    bioRxiv preprint
    Hart et al 2021
    Network permutation methods: low power, high false positives
    

    View Slide

41. Sankararaman et al 2012
    Neandertal-Human interbreeding
    

    View Slide

42. Sankararaman et al 2015
    Neandertal-Human interbreeding
    Ancient population sub-structure
    

    View Slide

43. Hypotheses and Models
    Research requires more than null robots
    Also requires:
    Generative causal models
    Statistical models justified by generative
    models & questions (estimands)
    An effective way to produce estimates
    

    View Slide

44. Justifying “controls”
    H 2i HX kyReVV rQmH/ K2bm`2 i?2 +
    s
    * "
    u
    

    View Slide

45. Justifying “controls”
    bBQM US2`H 2i HX kyReVV rQmH/ K2bm`2 i?
    s
    * "
    u
    Y ~ X
    Y ~ X + A
    Y ~ X + A + B
    Y ~ X + C
    Y ~ X + A + C
    Y ~ X + B + C
    

    View Slide

46. Justifying “controls”
    bBQM US2`H 2i HX kyReVV rQmH/ K2bm`2 i?
    s
    * "
    u
    Y ~ X
    Y ~ X + A
    Y ~ X + A + B
    Y ~ X + C
    Y ~ X + A + C
    Y ~ X + B + C
    “Adjustment set”
    

    View Slide

47. Finite data, infinite problems
    DAG is not enough
    Need generative model to design/
    debug inference
    Need a strategy to derive estimate
    and uncertainty
    Easiest approach: Bayesian data
    analysis
    F
    /PUJDF UIBU FWFO UIPVHI UIF UISFF XIJUF TJEFT MPPL UIF TBNF GSPN
    KVTU SFDPSE UIF DPMPS PG UIF TJEFT BęFS BMM‰UIFZ BSF SFBMMZ EJČFSFOU F
    CFDBVTF JU NFBOT UIBU UIFSF BSF UISFF NPSF XBZT UP TFF UIBO UP TFF
    /PX DPOTJEFS UIF HBSEFO BT XF HFU BOPUIFS UPTT PG UIF HMPCF *U
    POF MBZFS
    /PX UIFSF BSF QPTTJCMF QBUIT UISPVHI UIF HBSEFO POF GPS FBDI
    TFDPOE ESBX GSPN UIF CBH FBDI PG UIF QBUIT BCPWF BHBJO GPSLT JOUP GP
    #FDBVTF XF CFMJFWF UIBU FBDI UPTT PG UIF HMPCF HJWFT FBDI TJEF B GBJS
    SFHBSEMFTT PG XIJDI TJEFT XBT TBNQMFE QSFWJPVTMZ ćF UIJSE MBZFS J
    

    View Slide

48. Bayes is practical, not philosophical
    Simple analyses: little difference,
    adds mess
    Realistic analyses: huge difference
    Measurement error, missing data,
    latent variables, regularization
    Bayesian models are generative
    

    View Slide

49. Statistics wars are over
    Bayes no longer controversial or
    marginalized
    Bayesian methods routine
    Waiting for teaching to catch up
    The action is in machine learning,
    which has different battles
    

    View Slide

50. OWLS
    DAGS
    GOLEMS
    

    View Slide

51. 1. Draw some circles
    HOW TO DRAW AN OWL
    

    View Slide

52. 1. Draw some circles 2. Draw the rest of the owl
    HOW TO DRAW AN OWL
    

    View Slide

53. 1. Draw some circles 2. Draw the rest of the owl
    HOW TO DRAW AN OWL
    

    View Slide

54. 
    3 DPEF
    
    # function to toss a globe covered p by water N times
    sim_globe <- function( p=0.7 , N=9 ) {
    sample(c("W","L"),size=N,prob=c(p,1-p),replace=TRUE)
    }
    /PUIJOH IBQQFOT VOUJM XF DBMM UIF GVODUJPO CZ JUT OBNF
    3 DPEF
    
    sim_globe()
    [1] "L" "W" "W" "W" "L" "L" "L" "W" "L"
    3FQFBU DBMMJOH UIF GVODUJPO UP TFF UIBU JU TJNVMBUFT B EJČFSFOU TBNQMF FBDI UJNF "OE CZ
    OBNJOH UIF QSPQPSUJPO PG XBUFS p BOE OVNCFS PG UPTTFT N JO UIF GVODUJPO EFĕOJUJPO XF DBO
    FBTJMZ DIBOHF UIFTF WBMVFT XIFO XF DBMM UIF GVODUJPO
    Bę
    26"-*5: "4463"/$&
    # function to compute posterior distribution
    compute_posterior <- function( the_sample , poss=c(0,0.25,0.5,0.75,1) ) {
    W <- sum(the_sample=="W") # number of W observed
    L <- sum(the_sample=="L") # number of L observed
    ways <- sapply( poss , function(q) (q*4)^W * ((1-q)*4)^L )
    post <- ways/sum(ways)
    bars <- sapply( post, function(q) make_bar(q) )
    data.frame( poss , ways , post=round(post,3) , bars )
    }
    5P VTF UIJT GVODUJPO ZPV OFFE UP HJWF JU B TBNQMF "OE XF DBO KVTU FNCFE UIF QSFWJPVT
    TJNVMBUJPO GVODUJPO JOTJEF JU
    3 DPEF
    
    compute_posterior( sim_globe() )
    poss ways post bars
    1 0.00 0 0.000
    2 0.25 243 0.291 ######
    3 0.50 512 0.612 ############
    4 0.75 81 0.097 ##
    5 1.00 0 0.000
    SBę
    26"-*5: "4463"/$&
    # function to compute posterior distribution
    compute_posterior <- function( the_sample , poss=c(0,0.25,0.5,0.75,1) ) {
    W <- sum(the_sample=="W") # number of W observed
    L <- sum(the_sample=="L") # number of L observed
    ways <- sapply( poss , function(q) (q*4)^W * ((1-q)*4)^L )
    post <- ways/sum(ways)
    bars <- sapply( post, function(q) make_bar(q) )
    data.frame( poss , ways , post=round(post,3) , bars )
    }
    5P VTF UIJT GVODUJPO ZPV OFFE UP HJWF JU B TBNQMF "OE XF DBO KVTU FNCFE UIF QSFWJPVT
    TJNVMBUJPO GVODUJPO JOTJEF JU
    3
    
    compute_posterior( sim_globe() )
    poss ways post bars
    1 0.00 0 0.000
    2 0.25 243 0.291 ######
    3 0.50 512 0.612 ############
    4 0.75 81 0.097 ##
    5 1.00 0 0.000
    3FQFBU UIJT GVODUJPO DBMM B GFX UJNFT UP TIPX UIBU BT UIF TBNQMF WBSJFT TP UPP EPFT UIF QPTUF
    SJPS EJTUSJCVUJPO
    ę
    4."-- 803-%
    0 0.2 0.4 0.6 0.8 1
    proportion water
    posterior probability
    0.00 0.05 0.10 0.15 0.20 0.25 0.30
    11 possibilities
    1
    2
    3
    4
    

    View Slide

55. Drawing the Bayesian Owl
    Scientific data analyses: 

    Amateur software engineering
    Three modes:
    Understand what you are doing
    Document your work, reduce error
    Respectable scientific workflow
    

    View Slide

56. Drawing the Bayesian Owl
    1. Theoretical estimand
    2. Scientific (causal) model(s)
    3. Use 1 & 2 to build statistical model(s)
    4. Simulate from 2 to validate 3 yields 1
    5. Analyze real data
    

    View Slide

57. Drawing the Bayesian Owl
    1. Theoretical estimand
    2. Scientific (causal) model(s)
    3. Use 1 & 2 to build statistical model(s)
    4. Simulate from 2 to validate 3 yields 1
    5. Analyze real data
    

    View Slide

58. Drawing the Bayesian Owl
    1. Theoretical estimand
    2. Scientific (causal) model(s)
    3. Use 1 & 2 to build statistical model(s)
    4. Simulate from 2 to validate 3 yields 1
    5. Analyze real data
    

    View Slide

59. Drawing the Bayesian Owl
    1. Theoretical estimand
    2. Scientific (causal) model(s)
    3. Use 1 & 2 to build statistical model(s)
    4. Simulate from 2 to validate 3 yields 1
    5. Analyze real data
    

    View Slide

60. Drawing the Bayesian Owl
    1. Theoretical estimand
    2. Scientific (causal) model(s)
    3. Use 1 & 2 to build statistical model(s)
    4. Simulate from 2 to validate 3 yields 1
    5. Analyze real data
    

    View Slide

61. DAGs, Golems & Owls
    DAGs: Transparent scientific assumptions to 

    justify scientific effort

    expose it to useful critique

    connect theories to golems
    Golems: Brainless, powerful statistical models
    Owls: Documented procedures, quality assurance
    

    View Slide

62. Model
    Theory
    Evidence
    

    View Slide

63. Course Schedule
    Week 1 Bayesian inference Chapters 1, 2, 3
    Week 2 Linear models & Causal Inference Chapter 4
    Week 3 Causes, Confounds & Colliders Chapters 5 & 6
    Week 4 Overfitting / Interactions Chapters 7 & 8
    Week 5 MCMC & Generalized Linear Models Chapters 9, 10, 11
    Week 6 Integers & Other Monsters Chapters 11 & 12
    Week 7 Multilevel models I Chapter 13
    Week 8 Multilevel models II Chapter 14
    Week 9 Measurement & Missingness Chapter 15
    Week 10 Generalized Linear Madness Chapter 16
    https://github.com/rmcelreath/stat_rethinking_2023
    

    View Slide