Questions tagged [prior]
In Bayesian statistics a prior distribution formalizes information or knowledge (often subjective), available before a sample is seen, in the form of a probability distribution. A distribution with large spread is used when little is known about the parameter(s), while a more narrow prior distribution represents a greater degree of information.
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Variance of marginal posterior distribution
Suppose $Y_1,\dots,Y_n\mid\mu,\sigma^2 \sim \text{ iid } N(\mu,\sigma^2)$ and suppose the priors $\mu \mid \sigma^2 \sim N(\mu_0, \sigma^2 / \kappa_0)$ and $1/\sigma^2 \sim \text{gamma}(\nu_0/2, \nu_0 ...
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How to choose default uninformative prior in the R Package BAS
I'm conducting a Bayesian multilevel logistic regression based on the Rpackage BAS. I'm a beginner in Bayesian statistics.
But in bas.glm, I don't understand and I don't know how to specify my prior. ...
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If a credible interval has a flat prior, is a 95% confidence interval equal to a 95% credible interval?
I'm very new to Bayesian statistics, and this may be a silly question. Nevertheless:
Consider a credible interval with a prior that specifies a uniform distribution. For example, from 0 to 1, where 0 ...
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What are the implications of setting off-diagonal elements of estimated covariance to 0?
I have sometimes seen in published work that when estimating covariance matrices, off-diagonal elements are set to 0. For example, in this paper, $N$ neurons are recorded and authors wish to use the $...
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how can predictive distributions be considered as expectations?
I guess that the prior and posterior predictive distributions can be considered expectation of $p(y|\theta )$ (in case of prior predictive distribution) and $p(\widetilde{y}|\theta )$ (in case of ...
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How to obtain likelihood ($P(B/R)$ given the prior $P(R)$ and the posterior $P(R/B)$
I am working on a topic related to multiple-choice response. I would like to measure the efficiency of the information source (or a student’s information search) and I believe Bayesian statistics is ...
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Can I use the Mean Squared Prediction Error to select the prior SD in a CausalImpact model?
I'm using the CausalImpact package (in R), and (as I expect is typical) the findings are very sensitive to the prior being used.
I have an OK understanding, I think, of what the prior is doing in this ...
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Estimating Markov Chain Probabilities with Limited Data
Suppose I have some data on transitions between states of a Discrete Time Markov Chain. Let's say that transitions between some events are observed more frequently from others. For example, in a 3 ...
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Priors and nested random effects in MCMCglmm?
I am trying to construct a zero inflation Poisson GLMM using MCMCglmm(). I am new to Bayesian Statistics and this function and I am struggling to understand a couple of things.
For my data I am ...
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How to get around to "Argument 'coef' may not be specified when using boundaries."?
I have a model, the brms code is given below. It is a system of equations (I am estimating demand for two categories of goods). Economic theory tells me that the ...
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Does the example given correspond to a prior predictive check?
Could someone explain to me precisely what is meant by prior predictive check, in Bayesian inference? In some documents, one uses observed data (“in which we ...
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How to decide the parameters of a Gamma distribution for a Gamma-Poisson model?
In Bayesian inference, the Gamma-Poisson model uses usually a Gamma($\alpha$,$\beta$) prior on the $\lambda$ parameter of the Poisson distribution.
Are there any rules for setting appropriate values ...
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Understanding PRIOR option in SCORE statement for PROC LOGISTIC (SAS)
Say I have a binary response which I want to model with logistic regression on covariates $x$. Fitting a model with PROC LOGISTIC will fit MLE coefficients for the model
$$
\text{logit}(\pi) = \alpha +...
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How to calculate the confidence interval with weighted data?
I've done some search for similar questions, but they're not the same as what I'm trying to get.
Assume that there's a server that handles requests $r$ and returns a set of items $I_{r}$ of random ...
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Avoid singular fits in mixed models in R with blme - checking layman's priors
While fitting linear mixed models, I would like to avoid zero random-effects (ranef(model)) and cluster-level SD estimates (...
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