Science?!

{Saket Choudhary}

Statinference

Probability

  • Population quantity summarizing the randomness of a random experiment
  • Inherently when we are talking about probability we are talking about population
  • Data in hand is just an aid to model this probability
  • $\alpha$ quantile: $F(x_\alpha)=\alpha$ About%100(1-\alpha)$ of the observations lie above this point

Baye’s Rule

  • $P(B A)=\frac{P(A B)P(B)}{P(A B)P(B)+P(A B^c)P(B^c)}$
  • Let
      • = Test results positive
      • = Test results positive
    • D = Person has disease in reality
    • D^c = Person does not have disease
  • Sensitivity = $P(+ D)$
  • Specificity = $P(- D^c)$
  • Positive Predictive Value(PPV) = $P(D +)$
  • Negative Predictive value = $P(D^c -)$
  • Prevalence of Diseae = $P(D)$
  • Likelihood ratio: $\frac{P(D +)}{P(D^c +)}= \frac{P(+ D)P(D)}{P(+ D^c)P(D^c)}$
  • Post test odds of D = $DLR_+$ x Pre test odds

Estimation

  • Sample mean is itself a random variable and will have it;s own distribution, expected value
  • The center of this distribution of the sample mean is same as that of observation making the sample mean an ‘unbiased’ estimator of population mean
  • Expected values are properties of distribution
  • Sample mean is an estimate of pipulation mean.
  • Center of mass of population = population mean
  • Center of mass of observations - Sample mean

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