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Lecture 4 Startup
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lacorreia65 committed Jan 19, 2023
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4 changes: 2 additions & 2 deletions .Rproj.user/B584AE7E/sources/prop/EA93BB00
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"path": "C:/Users/lacor/OneDrive/100. Personal/SelfDevelopment/25. Project 2022/Statistical-Thinking-2023/Statistical Thinking 2023_v2.qmd",
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Expand Up @@ -362,3 +362,31 @@ true_pos <- sapply(p, function (q) (ptr*q)/(ptr*q+(1-ptr)*(1-q)))

plot(true_pos, p, col=2, lwd=3)
```

```{r}
n=20
logYs = -9.89
A = sum(logYs)-1
B = 2*n-1+sum(logYs)
C = n

theta_hat = (-B-sqrt(B^2-4*A*C))/(2*A) ##Quadratic formula

theta_vec = seq(0, 6, length=500)
post_prop = theta_vec^n*(theta_vec+1)^n*exp(-theta_vec)*(exp(sum(logYs)))^theta_vec

# pdf(file = "~/Dropbox/pubh8442/2015/Asymptotic_Posterior_Approximation_thetaDens.pdf", width = 7, height=4)

plot(theta_vec,post_prop,xlim = c(0,6), ylab = "Unormalized density", xlab = "theta", type = 'l', lwd = 2, main = "")
abline(v=theta_hat, col = 'red')
#dev.off()

var = (1/20)*(theta_hat^2*(1+theta_hat)^2)/(theta_hat^2+(theta_hat+1)^2)
post_approx = dnorm(theta_vec, theta_hat,sqrt(var))

#pdf(file = "~/Dropbox/pubh8442/2015/Asymptotic_Posterior_Approximation_NormApp##.pdf", width = 7, height=4)

plot(theta_vec,post_approx,xlim = c(0,6), ylab = "Density", xlab = "theta", type = 'l', lwd = 2, main = "")
abline(v=theta_hat, col = 'red')
#dev.off()
```
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14 changes: 14 additions & 0 deletions ....user/shared/notebooks/39C21CC9-Statistical Thinking 2023_v2/1/s/cwqxet0zexx43/000017.csv
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"0","#dev.off()"
"0",""
"0","var = (1/20)*(theta_hat^2*(1+theta_hat)^2)/(theta_hat^2+(theta_hat+1)^2)"
"0","post_approx = dnorm(theta_vec, theta_hat,sqrt(var))"
"0",""
"0","#pdf(file = ""~/Dropbox/pubh8442/2015/Asymptotic_Posterior_Approximation_NormApp##.pdf"", width = 7, height=4)"
"0",""
"0","plot(theta_vec,post_approx,xlim = c(0,6), ylab = ""Density"", xlab = ""theta"", type = 'l', lwd = 2, main = """")"
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"0","abline(v=theta_hat, col = 'red')"
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