Questions tagged [auxiliary-variable]

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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 ...
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2answers
259 views

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 ...
3
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1answer
55 views

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,...
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1answer
62 views

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 ...
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1answer
39 views

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? https://...
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1answer
605 views

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 $...
3
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1answer
226 views

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 ...
2
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1answer
33 views

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 ...
3
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1answer
552 views

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 ...