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Questions tagged [auxiliary-variable]

12 questions
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Auxiliary variables for imputation in survey data

I have a situation where I have a survey that contains two parts, everyone answers all of the questions on the first part, and a sample (10 percent) of the people are selected to answer some further questions. The 10 percent is selected using a…
astel
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Auxiliary variable Gibbs sampler

Suppose we want to sample from a pdf $f(x_1,x_2)$. It's easy to sample from $x_1 \vert x_2$, but not $x_2 \vert x_1$, so we introduce an auxiliary variable $u$ such that $\int f(x_1,x_2,u) du = f(x_1,x_2)$, and it's easier to sample $x_2 \vert x_1,…
user3294195
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Two algorithms are given for rejection sampling. I can not relate these two algorithms

Algorithm 1) Step 1:Obtain a sample $y$ from distribution $Y$ and a sample $u$ from $(0,1)$ Step 2: Check whether or not $u < f(y)/ M.g(y)$ if true accept $y$ as a sample from $f$ Else, reject the value of $y$ return to the sampling…
Animate_Ant
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Does the Auxiliary Particle Filter not ordinarily yield estimates for $p(y_t|y_{1:t-1})$

Background Say you're implementing basic importance sampling. To approximate a distribution $p(x)$, you utilize an importance density $q(x)$ that you can sample from. Also, assume that you can only evaluate $p_u(x) = C_p p(x)$, the target density…
Taylor
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Generating random samples from a marginal distribution

I have a joint distribution $p(a,b)$ that I obtained through numerical integration- that is, I don't have a formula for $p(a,b)$ but a bunch of samples drawn from this joint distribution. I would like to obtain samples from the marginal…
TheBean
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Does one impute auxiliary variables (multiple imputation)

Auxiliary variables may have themselves missing values. According to the following website, one (can) include(s) auxiliary variables also as variables to be imputed. Is this common practice?…
user18075
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Auxiliary random experiment

This question is from Robert Hogg's Introduction to Mathematical Statistic 6th version exercise 8.5.2 page 461. The question is: Let $X_1, X_2,...,X_{10}$ be a random sample of size 10 from a Poisson distribution with parameter $\theta$. Let…
Deep North
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Why do we draw parameters to draw from a marginal distribution that does not contain the parameters?

I'm sure this is dreadfully simple to everyone who sees it, but I'm completely lost. From what I've read, I think this concept must be so fundamental to Bayesian statistics that no one bothers to explain it. Anyway, here's a concept I'm trying to…
lazer-guided-lazerbeam
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What is an auxiliary density/distribution?

I am currently reading an academic paper where, without definition, the concept of an "auxiliary distribution" has been invoked. Additional expressions used are "auxiliary density function" and "auxiliary model" I have been googling and I can't find…
jmars
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Determining the order in which to impute variables (multiple imputation by FCS)

I am working with SPSS and am using multiple imputation to handle missings on 11 variables of interest. I intend to conduct multiple linear regressions on these variables after I impute them; 7 of them will be predictors and 4 of them will be…
tim9800
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Can dichotomous variable be used as auxiliary variable in conventional way to design an estimator?

I have a variable Y that can assume a range of values, and an auxiliary variable X that assumes value 1 if it possesses a characteristic, 0 otherwise. My first assumption here is that I can substitute mean by proportion for X, since $\frac1n\sum…
Diya
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Multiple imputation of a categorical variable using underlying continuous variable as auxiliary

I have a continuous variable with some values missing at random (MAR) that has to be categorized for further analysis. As far as I know it is not a good idea to categorize the continuous variable after multiple imputation, therfore, it has to be…
Gregory
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