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Planar point processes. N(A) = #{(  j,  j ) in A} cp. N(t) = #{0 <  j  t} Data r j = (  j,  j ) j=1,...,J Empirical rate: N(A)/|A|

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Presentation on theme: "Planar point processes. N(A) = #{(  j,  j ) in A} cp. N(t) = #{0 <  j  t} Data r j = (  j,  j ) j=1,...,J Empirical rate: N(A)/|A|"— Presentation transcript:

1 Planar point processes. N(A) = #{(  j,  j ) in A} cp. N(t) = #{0 <  j  t} Data r j = (  j,  j ) j=1,...,J Empirical rate: N(A)/|A|

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3 Special trees on UCB campus

4 Wildfires in Oregon Federal Lands, 1989-1996

5 Brillinger, Stewart and Littnan (2008) Monk seal locations - Molokai

6 Line process - set of lines {l 1, l 2, l s,...} Point process {(p(l 1 ),  (l 1 )),(p(l 2 ),  (l 2 )),...} p: distance  : angle

7 Cedar Fire - near San Diego, 2003 dot is fire origin

8 t.s. ==> p.p. in R 2 P.p. {  j,X(  j )}

9 Marked point process. planar case (r j,M j } = {(  j,  j ), M j } j=1,...,J Signed measure J(I) =  {M j | r j in I} dJ(s,t) =  j M j  (s-  j, t-  j ) dsdt

10 Loma Prieta 1989

11 ordinal values

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15 Arrays, graphs

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