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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How to match my prior beliefs to beta distribution?
I have some data that I believe comes from the binomial distribution. I also have some old data from a past-experiment that I would like to base my prior beliefs on. The old data observations are: $$6,...
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Using old posterior as new prior given new data [duplicate]
Suppose I have some data, and use this data to create a posterior distribution.
Now suppose I have some new data that I believe is from the same population as the data before. Can I now use my old ...
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Confusion forming prior beliefs
Let's say, for the sake of ease, I have a sample of data that I believe comes from the binomial distribution. Let's say I have 100 observations in my sample. Previous to this experiment, I have ...
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Why would I pick a beta prior for binomial data? More generally, how would I pick any prior distribution? [duplicate]
Obviously, being a conjugate prior is useful as it saves performing tricky integrals or using a simulation, but why would I want to use a beta distribution? More generally, how does one pick an ...
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Picking parameters for beta prior
I have some data that I believe come from a binomially distributed population. A beta prior seems like an appropriate choice, but I don't have any very strong prior beliefs. I could use a less ...
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Estimator of variance for a binomially distributed sample
I want to run some Bayesian analysis on some data. Suppose we have a sample that we believe comes from a binomial population. We have $m$ observations
$$X_i \sim \text{Bin}(n,p)
\quad \quad \quad
\...
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Posterior probability for $\theta$ with a discrete prior
I'm trying to find a posterior probability for this model but I can't find the solution. Help would be appreciated!
Prior distribution: $\theta$ follows a discrete probability function: $\mathbb{P}(\...
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Derivation of acceptance probability from Linero, Yang (2018)
I am wondering how this paper Bayesian Regression Tree Ensembles that Adapt to
Smoothness and Sparsity by Linero & Yang (2018) derived the acceptance probability for $\sigma$.
The authors give $\...
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Bayes estimator of possion distribution with Pareto prior
Consider a random sample of size $n$ following the possion distribution with parameter $\ln \theta$, that is
$$
f(x|\theta)=\frac{(\ln\theta)^x}{\theta x!}, x=0,1,2,\cdots
$$
and the prior of the ...
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Centering Priors on MLEs vs. Using MLEs as Initial Conditions for MCMC [duplicate]
Here:
Centering prior distributions on MLE/OLS estimates
I ask about centering priors on MLEs in the context of a logistic regression (in my case with only categorical predictors), which I've seen a ...
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posterior predictive of a normal distribution with normal prior over mean and Gamma prior over precision
What is the posterior predictive of a normal distribution with normal prior over mean and Gamma prior over precision. Thus, what is the distribution of x given:
\begin{equation}
x \sim \mathcal{N}(x; \...
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prior distribution for iid gaussian, with a known variance
I have been reading Pattern Recognition and Machine Learning by Bishop, and I have a question regarding the prior distribution of an iid Gaussian with known variance.
The relationship $\dfrac{n}{\...
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Why not use a half-normal distribution as a prior for variance parameters in Bayesian estimation?
Typically, distributions with fat tails, such as the inverse Gamma or the half-Cauchy are used as prior distributions for the variance parameters.
I am trying to understand why do we need a fat-tailed ...
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Prior probability distribution when we have a single estimate of the mean and no estimate of the variance
Say we have some real parameter $p$ we'd like to determine experimentally. If we have a single estimate of $p$ but no associated uncertainty, what prior probability distribution(s) can/should we use ...
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What should be the appropriate choice of prior for a dummy variable in a Bayesian Linear regression?
I have a dataset where the dependent variable is Sales. The independent variables are Media Spends 1, Media Spends 2 and Covid dummy. I am trying to build a Bayesian Linear Regression model. The covid ...
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