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详细笔记 变量四则运算 🔗 两个独立Cauchy相加 = Cauchy
Key notes: likelihood uncensored pts contribute to survival + hazard; censored pts contribute only to survival –> survival is a function of hazard –> likelihood is a function of hazard; Two assumptions: A1. independent censoring (t_tilde indep censoring given covariates) and A2. non-informative censoring (censoring distribution does not involve params of interest, so it can be dropped out from the likelihood) continuous time: exp/pois identity. homogeneous Poisson process (for each
详细笔记
详细笔记 point estimators 🔗 MOM MLE MAP EM trace: sum of the diagonal elements of a $square$ matrix, 不要求full rank Hat matrix: map the observed value to the predicted value Y_hat = H Y_obs
一些概念笔记 🔗 trace: sum of the diagonal elements of a $square$ matrix, 不要求full rank Hat matrix: map the observed value to the predicted value Y_hat = H Y_obs
MLE properties笔记 🔗 1)consistent: likelihood maximized at $\hat theta$ (LHS), RHS maximized at $\theta_0$, so $\hat theta$ converge in prob to $\theta_0$ as n goes to infinity. 2)asymptotically normality: score function 在 $\theta_0$处的泰勒展开–>
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Binomial model 🔗 posterior dist. of theta ~beta(alpha+y, beta) E(theta) = alpha/(alpha+beta), Var(theta) =(alpha*beta)/(..) Normal model 🔗 Assume tau known, mu: normal prior to normal posterior Assume mu known, tau: gamma(alpha,beta) prior to gamma posterior E(tau) = alpha/beta, var(tau) = beta/alpha both mu and tau unknown. Prior : conditional dist of mu prior is normal (conditional on tau) marginal dist of tau prior is a gamma Posterior: conditional dist of
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总结outline： 🔗 model time? e.g., log T = Z/linear predictor –> censoring/ missing data problem. the out come time-to-event is not always observed due to censoring/competing risk. Model rate: the aggregated data: known the total number of years and the total number of events why rate works? the rate param captures the instantaneous occurrence of the outcome at any given t
总结outline： 🔗 Poisson(expected total count), exponential(waiting time) [connected by homogeneous poisson process], and binomial(# of success)[connected by h ->0, N -> infinity] connection. 所以我们在写likelihood的时候可以从这三种模型出发来写. Poisson 是aggr
总结outline： 🔗 Poisson(expected total count), exponential(waiting time) [connected by homogeneous poisson process], and binomial(# of success)[connected by h ->0, N -> infinity] connection. 所以我们在写likelihood的时候可以从这三种模型出发来写. 2024-06-09 comment: 我这在胡
手机预览点这里 see CHL5223 HW3 Q3(a) 由于X Y indep, 所以我们可以根据他们的marginal PDF 先求到他们的joint PDF， 然后在这个PDF里面把其中一个vari
总结outline： 1. what is a RV? 🔗1.1 defn: it’s a function from sample space D to real line. 1.2 randomness: before we do the experiment, we have random experiment, and we assign different prob. to experiment. 2. Discrete RV 🔗2.1 Bernoulli 🔗2.2 Binomial: sum of n indep Bernoulli 🔗 sum of two