In RobinHankin/hyper2: The Hyperdirichlet Distribution, Mark 2

knitr::opts_chunk$set(echo = TRUE)
library("hyper2")

Formula 1 grand prix racing, 2022 season. We wonder whether placing well at a race helps the team in some way in the next race. The "help" might be an $\alpha$ weighting term for just the winners, or a $\alpha^n$ term for placing $n$-th in the previous race. I would have thought $\alpha>1$ [the help accruing from a win is positive] but it is possible that $\alpha<1$ which would correspond to it being a hindrance in some way. Perhaps winning leads to overconfidence or complacency in the next one?

setwd("~/rstudio/hyper2/inst")
finish <- read.table("formula1_2023.txt",header=TRUE)
finish <- finish[,seq_len(ncol(finish)-1)]
finish[1:9,1:5]

f <- function(i){ # this is column 'i' of finish
    ordertable2supp(finish[,i,drop=FALSE])
}
g <- function(i){
    suppressWarnings(out <- as.numeric(finish[,i,drop=TRUE]))
    out[is.na(out)] <- length(out)
    names(out) <- rownames(finish)
    return(out)
}

    weightedlikelihood <- function(alpha){
        out <- hyper3()
        for(i in seq(from=2,to=ncol(finish))){
            H <- f(i)
            previous <- g(i-1)
            H[names(previous)] <- as.weight(alpha^previous)
            out <- out + H
        }
        return(out)
}

H <- weightedlikelihood(0.9)
mH <- maxp(H)

mH
dotchart(mH)
loglik(mH,H)

H91 <- weightedlikelihood(0.91)
mH91 <- maxp(H91)

mH91
dotchart(mH91)
loglik(mH91,H91)

likealpha <- function(alpha){
    H <- weightedlikelihood(alpha)
    mH <- maxp(H)
    return(loglik(mH,H))
}

alpha <- seq(from=0.95,to=1.02,by=0.01)
likes <- sapply(alpha,likealpha)

plot(alpha,likes-max(likes),type='b')
abline(h=c(0,-2))
abline(v=1)

RobinHankin/hyper2 documentation built on May 6, 2024, 4:25 p.m.