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Questions tagged [conjugate-prior]

A prior distribution in Bayesian statistics that is such that, when combined with the likelihood, the resulting posterior is from the same family of distributions.

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Bayesian A/B test analysis for non-binary actions

When analyzing experiments with binary action (for example, will a user convert or not), then Beta-Binomial distribution is apt for that. But I am not able to figure out what distributions to use ...
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Conjuage priors for linear combination

My knwoledge of statistics in general and Bayesian statistics in particular is limited. With that in mind, I would sincerely appreciate if somebody could help me with the following problem that I have ...
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Mean of the posterior distribution in bayesian linear regression with infinitely broad prior

Currently reading from Christopher Bishop's Pattern Recognition and Machine Learning book about parameter distribution under a bayesian linear regression. On page 153, the author deduces that the ...
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Does Levy distribution has a conjugate prior?

I have searched a lot but can not find the conjugate prior of Levy distribution.
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Proving Matrix-Normal-Inverse-Wishart distribution is a conjugate prior for a Linear Model

How does one prove that the Matrix-Normal-Inverse-Wishart distribution is a conjugate prior for a Linear Model? This prior is a generalization of the Normal-Inverse-Wishart Distribution. By Matrix-...
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Truncated Gamma Distribution

The Gamma distribution is the conjugate prior of Poisson distribution. What about the Truncated Gamma distribution? Is it still the conjugate prior of Poisson distribution?
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Conjugate Prior for Student T distribution

Does the Student T distribution have a conjugate prior distribution? If so, what is it and what are the parameters?
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Is the posterior distribution for the model described in this question Gaussian?

I was in the middle of writing a long answer to Uncertainty estimation in high-dimensional inference problems without sampling? but I was suddenly struck by doubt: since the model assumes a Gaussian ...
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Survival time problem exponential with gamma prior

The survival times, in days, of patients diagnosed with a severe form of a terminal illness are thought to be well modelled by an exponential($\theta$) distribution. We observe the survival times ...
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Obtaining posteriors for multivariate Normal mixture models

So I want to fit a mixture model $$f(y) = \pi_1 f_1 (y) + \pi_2 f_2 (y)$$ where $\pi_k = P(S = k)$ and $S_i$ is a latent unobserved variable. I assume that, conditional on $S=k$, we have the model ...
Consider the following definition: A family $\cal F$ of probability distributions on $\Theta$ is said to be conjugate (or closed under sampling) for a likelihood function $f(x|\theta)$ if for every $\... 0answers 401 views Predictive Posterior Distribution of Normal Distribution with Unknown Mean and Variance Suppose that$x_{i}|\mu,\sigma^{2} \sim \mathcal{N}(\mu,\sigma^{2})$for$i = 1,...n$. Assume that the assigned prior distributions are$\mu$~$\mathcal{N}$($\mu_{0}$,$\sigma^{2}_{0}$) and$\tau \...
Bayesian Inference for the Normal Distribution, I use the following r code to obtain the posterior distribution. Let's say the data, $X\sim N(\mu, \sigma^{2})$ and $\mu \sim N(0,10)$ and \$\sigma \sim \...