Publications by Daniel
Poisson regression
Poisson regression \[ \mathrm{P}(Y=y \mid \lambda)=\frac{e^{-\lambda} \lambda^y}{y !} \] Poisson distribution not equal Poisson regression # numbers from x<-seq(0,30,1) # calculate the distribution function # based on the parameters pdf1<- dpois(x, 1) pdf2<- dpois(x, 7) pdf3<- dpois(x, 12) # Plotting the PDF plot(x,pdf1,type = "l") ...
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Poisson regression
Poisson regression Negative binomial regression is a popular generalization of Poisson regression because it loosens the highly restrictive assumption that the variance is equal to the mean made by the Poisson model. The traditional negative binomial regression model is based on the Poisson-gamma mixture distribution. This model is popular beca...
1810 sym R (3659 sym/12 pcs) 4 img
Common statistical distribution
References and D. Joyce Continuous Distributions Normal distribution The Central Limit Theorem says sample means and sample sums approach normal distributions as the sample size approaches infinity (normal, t, chisq, f distributions). Probaility density function \[ f(x)=\frac{e^{-(x-\mu)^2 /\left(2 \sigma^2\right)}}{\sigma \sqrt{2 \pi}} \] ...
15596 sym Python (8074 sym/39 pcs) 38 img
Common statistical distribution
Continuous Distributions Normal distribution Probaility density function \[ f(x)=\frac{e^{-(x-\mu)^2 /\left(2 \sigma^2\right)}}{\sigma \sqrt{2 \pi}} \] where \(\mu\) is the location (shift the graph)/center parameter and \(\sigma\) is the scale (stretch out the graph)/spread parameter. # numbers from x<-seq(-5,5,0.1) # calculate the dist...
12196 sym Python (7189 sym/35 pcs) 35 img
Bayesian Inference in R
Reference etc Bayesian inference Let Y be a random variable representing the data. We have a (parametric) model for Y with Y∼f(y∣θ),θ∈Θ, Θ the parameter space. That is probability density function and can result in the likelihood function. Then we have a prior distribution represented by π(θ). Given an observation of Y, the posteri...
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Bayesian Inference in R
Reference etc Bayes’ theorem Let Y be a random variable representing the data. We have a (parametric) model for Y with Y∼f(y∣θ),θ∈Θ, Θ the parameter space. That is probability density function and can result in the likelihood function. Then we have a prior distribution represented by π(θ). Given an observation of Y, the posterior...
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Bayesian Inference in R
Reference etc Bayes’ theorem Let Y be a random variable representing the data. We have a (parametric) model for Y with Y∼f(y∣θ),θ∈Θ, Θ the parameter space. That is probability density function and can result in the likelihood function. Then we have a prior distribution represented by π(θ). Given an observation of Y, the posterior...
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Bias analysis and control
Refrerence Selection Bias Selection Bias, occurs when the study selected population doesn’t represent the target population (like refuse answer and leave study). No selection bias if the response rate is 100%. bias_parms is 4 probabilities: among cases exposed (1), among cases unexposed(2), among noncases exposed(3), and among noncases un...
5042 sym R (18864 sym/52 pcs)
Statistics in clinical trial
Brief summary from the book Introduction The clinical statistician determines the statistical methodology for the trial; evaluates the trial length; for randomized trials, randomizes group allocations for subjects; monitors the data; analyzes the data; and provides the interim data reports for DSMBs and the final FDA (EC/EMEA) report. A typic...
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Mixed effect model- Introduction
Brief summary from the book Random Intercept Model It is assumed that there is a within-subject correlation of the response variable across time, whereas the between-subject correlation is negligible. A random intercept model has the form \[ y_{i j}=\beta_{0}+\beta_{1} x_{1 i j}+\cdots+\beta_{p} x_{p i j}+\beta_{p+1} t_{j}+u_{i}+\varepsilon_...
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