intrinsic auto regressi e models
play

/ IntrinsicAutoRegressieModels Spaial daa anali in San Se - PowerPoint PPT Presentation

/ IntrinsicAutoRegressieModels Spaial daa anali in San Se Mae Daa Sciei a The Rckefelle Fdai / H! Se Mae, Manage and Daa


  1. /

  2. Intrinsic�Auto�Regressi�e�Models Spa�ial da�a anal��i� in S�an S�e Ma���e� Da�a Scie��i�� a� The R�ckefelle� F���da�i�� /

  3. H�! � · S�e Ma���e�, Manage� and Da�a Scien�i�� a� The Rockefelle� Fo�nda�ion · P�e�io��l�, � �a� a Da�a Scien�i�� a� B���Feed and a S�a�i��ical gene�ici�� a� The Fein��ein �n��i���e fo� Medical Re�ea�ch · Hold a G�ad�a�e Di�loma in S�a�i��ic� and S�ocha��ic P�oce��e� f�om �he Uni�e��i�� of Melbo��ne, A����alia. 3/43 /

  4. S���c���e �f �hi� �a�� � � 1. M��i�a�i�g ��e��i��: S�ike i� ca�e� �f de�g�e i� Jali�c�. 2. Wh� �e ca�'� ha�e �ice �hi�g�! 3. Wha� a�e C��di�i��al A���-Reg�e��i�e ��del� (CAR)? 4. Wha� i� �he i���i�ic �a�� �f �he ����i��ic A���-Reg�e��i�e ��del� (�CAR)? 5. ���le�e��a�i�� �f �CAR i� S�a� 4/43 /

  5. � � Mo�i�a�ing q�es�ion: Spike in cases of deng�e in Jalisco. 5/43 /

  6. De�g�e ca�e� i� Ja�i�c� 6/43 /

  7. 7/43 /

  8. Jali�c� ��l�g�n Jalisco Polygon (https://datos.jalisco.gob.mx/dataset/mapa- general-de-jalisco-limite-estatal) 8/43 /

  9. Deng�e data M�DE Jali�c� (h����://�e�lan.a��.jali�c�.g�b.m�/mide/�anelCi�dadan�/�ablaDa���? ni�elTablaDa���=3&�e�i�dicidadTablaDa���=an�al&indicad��TablaDa���=772&acci�nReg 9/43 /

  10. � � Wh� �e can�� ha�e nice �hings� 10/�3 /

  11. Why we can't have nice things! � � � � � S�a�ial a���c���ela�i�n 11/�3 /

  12. S�a�ial a���c���ela�i�n A���c���ela�i�� is a measurement of similarit� between close observations of the same phenomenon. E�ample �ith temporal a�tocorrelation: �f �ou measure �our weight, two observations close in time are ver� similar than distant ones. S�a�ial a���c���ela�i�� is more nuanced because, unlike time, spatial variables are at least two-dimensional. Spatial a�tocorrelation : Describe the e�tent to which two observations from neighboring regions e�hibit higher correlation than distant ones. 12/43 /

  13. A���c���ela�i�� i� ��a�ial da�a · �n regression analysis, one of the standard assumptions is that errors are uncorrelated. · Correlated errors suggest we have additional information in the data that has not been accounted for in the model as it is. · �n the case of spatial data, adjacent residuals tend to be similar and therefore a�tocorrelated . Mai� ���ble�: if autocorrelation is not exploited in your model, your explanatoy variables coe�cients will display an unusual explanatory power, which might be the consequence of of just �tting spatial noise. 13/43 /

  14. ��i�ial ��e��i�� ab��� de�g�e 14/43 /

  15. Sim�le model 1�/43 /

  16. Le�'� add c��a�ia�e� A����i�g �ha� everything else d�e� ��� a�ec� water capacity �hi� ��de� �h���d be dece��. 16/43 /

  17. When ever�thing else contains spatial correlation We a�e ���i�g �hi� B�� i� �eali��, �e ha�e �hi�: O�r coe�cient estimates �ill be �rong! 17/43 /

  18. Moran's � (autocorrelation statistic) � · Analogous to the the standard correlation concept. · Numerator measuring deviatiom from the mean for adjacent units. · Denominator standardi�es the quantity to re�ect the variability of the quantity of interest. 18/43 /

  19. Moran's � (Jalisco data) 1�/43 /

  20. Moran's � �es� (Jalisco da�a) 20/�3 /

  21. Moran's � �es� (Jalisco da�a) � M����-C���� ���������� �� M���� I ����: ��������$������������ �������: �������� ������ �� ����������� + 1: 601 ��������� = 0.21246, �������� ���� = 597, �-����� = 0.006656 ����������� ����������: ������� 21/�3 /

  22. B�� S�e, i� �hi� �eall� a p�oblem in o�he� �e�ea�ch a�ea�? Kell�, M��gan, The S�andard Errors of Persis�ence (J�ne 3, 2019) (h����://�a�e��.���n.c�m/��l3/�a�e��.cfm? ab���ac�_id=3398303) 22/43 /

  23. � � Wha� are Condi�ional A��o-Regressi�e models (CAR)? 23/43 /

  24. Condi�ional A��o-Reg�e��i�e model� (CAR) � � · CAR model� are a cla�� of �pa�ial model� ��ed �o e��ima�e �pa�ial a��ocorrela�ion. · The�e model� are �idel� ��ed in Ecolog�, Economic� and Epidemiolog�. · CAR �a� �r�� de�eloped b� J�lian Be�ag in hi� no� cla��ic 1974 paper Spa�ial �n�e�ac�ion and �he S�a�i��ical Anal��i� of La��ice S���em� . 24/43 /

  25. CAR ��ec�f�ca����� � · Single aggregated measure per spatial unit, it can be continuous, binar� or discrete count. Example: Number of car accidents at the count� level. · Finite set of non-overlapping spatial units. · For spatial units, the relationship is de�ned in terms of adjacenc�. 25/43 /

  26. CAR m�del � Let N be the total number of spatial units from a region. A neighbor relationship is de�ned as where . This relationship is s�mmetric (i.e if ) but not re�e�ive (i.e. a region cannot be neighbor of itself). 26/43 /

  27. Adjacenc�! There are two matrices describing di�erent measures of adjacenc� in this model. 1) Adjacenc� matri� , de�ning � neighbor relationship. � 27/43 /

  28. Adjacenc�! There are two matrices describing di�erent measures of adjacenc� in this model. 1) Diagonal matrix , de�ning number � of adjacent units. � 28/43 /

  29. CAR m�del S�a�ial in�e�ac�ion be��een a�eal �ni�� i� modelled c��di�i��a��� a� a no�mall� di���ib��ed �andom �a�iable, �e��e�en�ed b� �he -leng�h �ec�o� (i.e. ). The�efo�e, �he condi�ional di���ib��ion of EACH i� de�ned a� follo��, �he�e i� �he �eigh�ed �al�e� of �he neighbo��. F�om Bane�jee, Ca�lin, and Gelfand, 2004, �ec. 3.2, i� follo�� �ha� �he join� di���ib��ion 29/43 /

  30. CAR m�del Recap! · : between 0 and 1, it represents the strength of the spatial association, with 0 meaning spatial independence. · D is our diagonal matrix. · W is the adjacenc� matrix. 30/43 /

  31. � � Wha� is �he in�risic par� of �he In�rinsic A��o-Regressi�e models (ICAR)? 31/43 /

  32. The in��in�ic c�ndi�i�nal a����eg�e��i�e (�CAR) The di�e�ence be��een CAR and �CAR i� �ha� �he �a�ame�e� i� �e� �o 1. · = 1 · D i� o�� diagonal ma��i�. · W i� �he adjacenc� ma��i�. Ho�e�e�, �e��ing c�ea�e� a challenge beca��e become� a �ing�la� ma��i� (i.e. non-in�e��ible). Thankf�ll�, incl�ding �he con���ain� �ol�e� �hi� challenge. 32/43 /

  33. Pai��i�e de�i�a�ion �CAR c�����e�� �� ��e� de��ed a� f������, a�d af�e� ���e a�geb�a, ��e ��g ���bab����� de����� bec��e�: 33/43 /

  34. Stan � S�an i� an open-�o�rce probabili��ic programming lang�age. ��'� �ri��en in C++ and and genrall� �peaking, i� i� ��ed �o �pecif� Ba�e�ian ��a�i��ical model�. S�an e��ima�e parame�er� b� calc�la�ing �he l�g ���babili�� de��i�� . (Tr� m�l�ipl�ing a large n�mber of ob�er�a�ion� �i�h �in� n�mber�, �o� �ill q�ickl� r�n in�o n�merical error�.) 34/43 /

  35. S�a� m�del ����c���e // T�� ����� ���� �� � ������ '�' �� ������ 'N'. ���� � ���<�����=0> N; �������N� �; � // T�� ���������� �������� �� ��� �����. ���������� � ���� ��; ����<�����=0> �����; � // T�� ����� ����� '�' �� �������� ����������� ���� ���� '��' // ��� �������� ��������� '�����'. ����� � � � ������(��, �����); � 35/43 /

Download Presentation
Download Policy: The content available on the website is offered to you 'AS IS' for your personal information and use only. It cannot be commercialized, licensed, or distributed on other websites without prior consent from the author. To download a presentation, simply click this link. If you encounter any difficulties during the download process, it's possible that the publisher has removed the file from their server.

Recommend


More recommend