Statistical Rethinking 2022 Lecture 01

by Richard McElreath

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Statistical Rethinking (1) The Golem of Prague 2022

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Texts in Statistical Science Richard McElreath McElreath Statistical Rethinking A Bayesian Course with Examples in R and Stan SECOND EDITION Second Edition Statistical Rethinking Rethinking the role of statistical analysis in research 20 lectures

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GOLEMS DAGS OWLS

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Prague 16th century

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Art from: “Breath of Bones: A Tale of the Golem” (2014)

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

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

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Figure 1.1

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

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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

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Null Models Rarely Unique Null phylogeny? Null ecological community? Null social network?

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Hypotheses and Models Research requires more than than tiny null robots Also requires: Precise process model(s) Statistical model (procedure, golem) justified by implications of process model(s) and question (estimand)

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OWLS

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1. Draw some circles HOW TO DRAW AN OWL

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

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

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ESB 3FNFNCFS UIF QPTUFSJPS IFSF NFBOT UIF QSPCBCJMJUZ PG Q DPOEJUJPOBM 3 DPEF +Ǿ"-$ ʚǶ . ,ǿ !-*(ʙǍ Ǣ /*ʙǎ Ǣ ' )"/#ǡ*0/ʙǎǍǍǍ Ȁ +-*Ǿ+ ʚǶ - +ǿ ǎ Ǣ ǎǍǍǍ Ȁ +-*Ǿ/ ʚǶ $)*(ǿ Ǔ Ǣ .$5 ʙǖ Ǣ +-*ʙ+Ǿ"-$ Ȁ +*./ -$*- ʚǶ +-*Ǿ/ ȉ +-*Ǿ+ +*./ -$*- ʚǶ +*./ -$*- ȅ .0(ǿ+*./ -$*-Ȁ /PX XF XJTI UP ESBX TBNQMFT GSPN UIJT QPTUFSJPS *NBHJOF UI GVMM PG QBSBNFUFS WBMVFT OVNCFST TVDI BT FUD 8JUIJO FYJTUT JO QSPQPSUJPO UP JUT QPTUFSJPS QSPCBCJMJUZ TVDI UIBU WBMVFT OFBS UI DPNNPO UIBO UIPTF JO UIF UBJMT 8FSF HPJOH UP TDPPQ PVU W 1SPWJEFE UIF CVDLFU JT XFMM NJYFE UIF SFTVMUJOH TBNQMFT XJMM IBWF UI UIF FYBDU QPTUFSJPS EFOTJUZ ćFSFGPSF UIF JOEJWJEVBM WBMVFT PG Q XJMM JO QSPQPSUJPO UP UIF QPTUFSJPS QMBVTJCJMJUZ PG FBDI WBMVF )FSFT IPX ZPV DBO EP UIJT JO 3 XJUI POF MJOF PG DPEF 3 DPEF .(+' . ʚǶ .(+' ǿ +Ǿ"-$ Ǣ +-*ʙ+*./ -$*- Ǣ .$5 ʙǎ Ǒ Ǣ - + ćF XPSLIPSTF IFSF JT .(+' XIJDI SBOEPNMZ QVMMT WBMVFT GSPN B UIJT DBTF JT +Ǿ"-$ UIF HSJE PG QBSBNFUFS WBMVFT ćF QSPCBCJMJUZ PG +*./ -$*- XIJDI ZPV DPNQVUFE KVTU BCPWF ćF SFTVMUJOH TBNQMFT BSF EJTQMBZFE JO 'ĶĴłĿĲ ƋƉ 0O UIF MFę BM TBNQMFT BSF TIPXO TFRVFOUJBMMZ 3 DPEF +'*/ǿ .(+' . Ȁ *O UIJT QMPU JUT BT JG ZPV BSF ĘZJOH PWFS UIF QPTUFSJPS EJTUSJCVUJPO MPP 0 200 600 1000 0.0 0.4 0.8 Index p 0 200 600 1000 0.6 0.8 1.0 1.2 1.4 Index prior 0 200 600 1000 0.00 0.10 0.20 Index likelihood 0 200 600 1000 0.0000 0.0015 Index posterior

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Drawing the Bayesian Owl Three modes: Understand what you are doing Document your work, reduce error Respectable scientific workflow

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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

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Saturn, Galileo 1610

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Drawing the Bayesian Owl Bayesian approach is permissive, flexible Express uncertainty at all levels Direct solutions for measurement error, missing data Focus on scientific modeling

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DAGS

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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.

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Causal Inference Description Design

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

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

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Causal Prediction Knowing a cause means being able to predict the consequences of an intervention.   What if I do this?

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Causal Imputation Knowing a cause means being able to construct unobserved counterfactual outcomes.   What if I had done something else?

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DAGs Directed Acyclic Graphs Heuristic causal models Clarify scientific thinking Analyze to deduce appropriate statistical models Much more as the course develops s * " u