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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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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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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Strange Variance Term for Normal Prior $w^2\sigma^2$
I've attached two screenshots, one with the question and one with the answer. It seems to me that the prior is wrong and it should include $w^2$ not $w^2\sigma^2$
I apologise for, including such a ...
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How to choose between gamma and Gaussian given a choice of gauges?
I'm trying to make the choice between the gamma and Gaussian distributions as a prior distribution for some data. When I learned statistics a while ago, I was given the rule of thumb: if your data ...
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BIC with non-negligible priors
I want to do model selection based on the best-fit/MAP/marginal posterior I find from an MCMC and likelihood maximization. I have a likelihood $\mathcal{L}(X|\theta)$, some informative priors $\pi(\...
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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
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\text{logit}(\pi) = \alpha +...
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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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Turning a list of cost into categorical probability mass distribution
Background
Given a noisy dataset $D$, I have to solve a classification problem where the possible anserwer is $i\in\{1,\dots,N\}$. So far I can get pretty decent result with an algorithm that, based ...
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How should uncertainties be treated when scaling data for optimisation
I have a large dataset for which I am using Bayesian statistics for parameter estimation and model selection (using MultiNest for more detail).
This involves setting a prior over which the nested ...
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How is data generated when using an improper prior
Let $X$ be an $\mathcal{X}$ valued random variable. We are doing Bayesian statistics. Suppose that $\theta$ is a $\Theta$ valued random variable with known prior distribution $\Pi$ and that the ...
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