testing_bias_distribution/Average_i-phi_idea.R at main · canmod/testing_bias_distribution · GitHub

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
library(tidyverse)
library(ggplot2); theme_set(theme_bw())
library(viridis)
library(bbmle)
library(pracma)
library(gsl)
library(deSolve)
source("testing_funs.R")
source("Single_variable_SIR.R")

maxtime<-150
ODEstep<-1e-1

SIR_Sys<- MASIR_Proc(0.40, 0.20, init_S = 0.999, ODEmaxTime=maxtime, ODEstep=ODEstep,TrackDyn = T)
SIR_Sys$R0
SIR_Sys$RInfinity
SIR_Curve <- SIR_Sys$Dynamic

timeseq <- seq(1,(maxtime+1)*(1/ODEstep),(1/ODEstep))
Curve_tseq <- SIR_Curve[timeseq,]
I_tseq <- Curve_tseq[,3]

phi_const <- 0.2
phi_seq <- rep(phi_const,length(timeseq))
set.seed(1746)
test_seq<-runif(length(timeseq),min=0.001,max = 0.01)

prop_seq <- prop_pos_test_new(I_tseq,test_seq,phi_seq,method="log")

prop_seq
plot(c(1:(maxtime+1)),prop_seq,type="l")

### LSS optimize
target_fn <- function(x,test_obs,prop_obs){
  inc_val <- x[1]
  phi_val <- x[2]
  ## LSS
  prop_pred1 <- prop_pos_test_new(inc_val,test_obs[1],phi_val,method="log")
  prop_pred2 <- prop_pos_test_new(inc_val,test_obs[2],phi_val,method="log")
  LSS <- (prop_pred1-prop_obs[1])^2+(prop_pred2-prop_obs[2])^2
  return(LSS)
}

test_case <- nlm(target_fn,c(0.01,0.2),test_obs=c(test_seq[55],test_seq[56]),prop_obs=c(prop_seq[55],prop_seq[56]), stepmax=0.008,iterlim = 1000,gradtol = 1e-12)

test_case$estimate

I_tseq[55]
I_tseq[56]

####### Fail to identify both phi and inc

# a<-prop_pos_test_new(test_case$estimate[1], test_seq[1], test_case$estimate[2], method = "log")
# b<-prop_pos_test_new(test_case$estimate[1], test_seq[2], test_case$estimate[2], method = "log")
#
# c<-prop_pos_test_new(I_tseq[1], test_seq[1], phi_const, method = "log")
# d<-prop_pos_test_new(I_tseq[2], test_seq[2], phi_const, method = "log")
#
# (a-c)^2+(b-d)^2

#### Brute-force heat map
target_fn2 <- function(inc,phi,test_obs,prop_obs){
  inc_val <- inc
  phi_val <- phi
  ## LSS
  prop_pred1 <- prop_pos_test_new(inc_val,test_obs[1],phi_val,method="log")
  prop_pred2 <- prop_pos_test_new(inc_val,test_obs[2],phi_val,method="log")
  LSS <- (prop_pred1-prop_obs[1])^2+(prop_pred2-prop_obs[2])^2
  return(LSS)
}

dd <- (expand.grid(phi=seq(from=0.001,to=0.5,by=0.001),
                   inc=seq(from=0.0001,to=0.05,by=0.0001))
       %>% as_tibble()
       %>% mutate(LSS=target_fn2(inc,phi,test_obs=c(test_seq[55],test_seq[56]),prop_obs=c(prop_seq[55],prop_seq[56])))
       )

print(ggplot(dd,aes(phi,inc,fill=log(LSS)))
      + geom_tile()
      #+ scale_y_log10()
      + scale_fill_viridis_c(expand=c(0,0))
      + ggtitle("LSS of phi and inc")
)

dd[which.min(dd$LSS),]
test_case$estimate

I_tseq[55]
I_tseq[56]

## If knowing phi=0.2
Opt_knowphi <-which.min(dd$LSS[which(dd$phi==phi_const)])
dd[which(dd$phi==phi_const)[Opt_knowphi],]

I_tseq[55]
I_tseq[56]

### If knowing phi, we area able to figure out inc

######## Time series:
## Idea: take 2-3 days as a whole, test_prop1=day1 test_prop2=day1+day2, test_prop3=day1+day2+day3
## data: tp1,tp2,tp3, pp1,pp2,pp3
## Input: test_prop1= tp1, test_prop2= tp1+tp2, test_prop3=tp1+tp2+tp3
## pos_prop1=pp1, pos_prop2= (tp1*pp1+tp2*pp2)/(tp1+tp2), test_prop3=(tp1*pp1+tp2*pp2+tp3*pp3)/(tp1+tp2+tp3)
## trying to figure out i (and phi)

## Need to think more carefully of the assumption
#### What is the impact of time theories/aggragation

target_fn3 <- function(inc,phi,test_obs,prop_obs){
  inc_val <- inc
  phi_val <- phi

  test_prop1 <- test_obs[1]
  test_prop2 <- test_obs[1]+test_obs[2]
  test_prop3 <- test_obs[1]+test_obs[2]+test_obs[3]

  pos_prop1 <- prop_obs[1]
  pos_prop2 <- (prop_obs[1]*test_obs[1]+prop_obs[2]*test_obs[2])/test_prop2
  pos_prop3 <- (prop_obs[1]*test_obs[1]+prop_obs[2]*test_obs[2]+prop_obs[3]*test_obs[3])/test_prop3

  ## LSS
  prop_pred1 <- prop_pos_test_new(inc_val,test_prop1,phi_val,method="log")
  prop_pred2 <- prop_pos_test_new(inc_val,test_prop2,phi_val,method="log")
  prop_pred3 <- prop_pos_test_new(inc_val,test_prop3,phi_val,method="log")

  LSS <- (prop_pred1-pos_prop1)^2+(prop_pred2-pos_prop2)^2+(prop_pred3-pos_prop3)^2
  return(LSS)
}


time <- 15
test_obs=c(test_seq[time],test_seq[time+1],test_seq[time+2])
prob_obs=c(prop_seq[time],prop_seq[time+1],prop_seq[time+2])


dd2 <- (expand.grid(phi=seq(from=0.001,to=0.5,by=0.001),
                   inc=seq(from=0.001,to=0.1,by=0.001))
       %>% as_tibble()
       %>% mutate(LSS=target_fn3(inc,phi,test_obs=test_obs,prop_obs=prob_obs))
)

print(ggplot(dd2,aes(phi,inc,fill=log(LSS)))
      + geom_tile()
      #+ scale_y_log10()
      + scale_fill_viridis_c(expand=c(0,0))
      + ggtitle("LSS of phi and inc")
)

dd2[which.min(dd2$LSS),]

print(dd2[which(dd2$phi==0.2),],n=100)

I_tseq[time]
I_tseq[time+1]
I_tseq[time+2]


## not working.