JonasMoss

#' Sample from a kernel density with the Epanechnikov kernel.
#' 
#' @param n Number of observations to sample.
#' @param x The data from which the estimate is to be computed.
#' @param bw Desired bandwidth.
#' @return A numeric vector with n sampled data points from the kernel
#' density estimator.
#' @details The factor sqrt(5) in is needed since the standard deviation of 
#' the kernel is 1/sqrt(5). This makes the normal kernel and the Epanchnikov
#' kernel comparable.

JonasMoss

### Here's some more info about default values! 
### Especially when they are difficult to understand.

### An easy example of default values.
def f(x, a = True): 
    if a:
        return (x + 1)
    if not a:
        return (x + 2)

JonasMoss

from collections import Counter
def f(i, s):
    total = np.cumsum([0] + list(Counter(coding(s)).values()))
    total = total / total[-1]
    values = np.diff(total)
    return values[i-1]

coding(data_student['apply'],f

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JonasMoss

First Reading

On the Consistency Rule in Causal Inference Axiom, Definition, Assumption, or Theorem? (Pearl, 2010, 4 page) One of the big problems with the causality literature is the terminology and the lack of foundationas for everyone to agree on.(Think about a vector space -- everyone agrees what it is. That's where we want to be.) The consistency rule appears to me to be the corner-stone of an axiomatic development of causality theory.

The following papers are mentioned in the Pearl paper and are a part of the assignment:

1. The consistency statement in causal inference: a definition or an assumption

2. Concerning the consistency assumption in causal inference

JonasMoss

#' Hide non-function variables from function.
#' 
#' @param ... Named functions and function definitions.
#' @return Nothing.

H = function(...) {
  
  function_names = names(as.list(substitute((...)))[-1])
  function_defs = list(...)
  envir = parent.env(parent.frame())

JonasMoss

# Create a covariance matrix for the covariates.
rho12 = -0.1
rho13 = 0.65
rho23 = -0.3

covariance = matrix(c(1,     rho12, rho13,
                      rho12, 1,     rho23,
                      rho13, rho23, 1), nrow = 3)

# Simulate a linear regression with all betas equal to 1.

JonasMoss

#' Graph of number of tries needed to obtain K successes.
#' @param K number of studies.
#' @return NULL.

plotter = function(K){
  kk = 0:(K*70)
  plot(kk + K, dnbinom(kk, K, 0.05), bty = "l", type = "b", pch = 20,
       xlab = "Number of studies", 
       ylab = "Probability",
       main =  paste0("Number of studies before ", K, " successes"))

JonasMoss

#' Find the cumulative maximal streak length in a vector of bools.
#' 
#' @param bools Logical vector.
#' @return An integer vector. The \code{i}th element is the maximal streak
#' length in \code{x[1:i]}.
#' @example
#'     bools1 = c(FALSE, TRUE, FALSE, TRUE, TRUE, TRUE, FALSE)
#'     streaks(bools1) [1] 0 1 1 1 2 3 3
#'     
#'     bools2 = c(FALSE, FALSE, TRUE, TRUE, TRUE, TRUE, FALSE, TRUE)