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To obtain a random draw from the posterior predictive distribution I would concatenate the $(y_{rep}^{(1)}, \ldots, y_{rep}^{(B)})$ vectors, marginalising out the posterior distribution (see for example … At that point, I would overlay the KDE of the observed outcome with the KDE of (what I believe is) the posterior predictive distribution. …

predictive distribution for (j in 1:length(pvr)){ pmu[j] <- alpha + b.vr*pvr[j] + b.ir*pir[j] pri[j] ~ dnorm(pmu[j],tau) } #priors for regression alpha ~ dnorm(0,0.01 … ) b.vr ~ dunif(-10,0) b.ir ~ dunif(0,10) #prior for precision tau ~ dgamma(0.001,0.001) sigma <- 1/sqrt(tau) } I am trying to calculate the posterior predictive distribution with …

I am confused about the posterior predictive distribution. This is from Murphy's Machine Learning: A Probabilistic Perspective. … Should the posterior predictive distribution sum to 1? …

I want to draw data from the posterior predictive distribution p(y|D). … my model has a complicated posterior predictive distribution p(y|D), so I cannot derive CDF. if I can use monte Carlo, can I draw data with pdf? …

However, instead of deriving a posterior predictive distribution, the authors resort to ranking (Eq. 1). … Can you please clearly explain the differences between ranking and predictive posterior distribution for prediction? …

=\theta^{T}x^{(i)}+e^{(i)}$$ where: $$P(y^{(i)}|x^{(i)},\theta)=\frac{1}{\sqrt{2\pi}\sigma}exp(-\frac{(y^{(i)}-\theta^{T}x^{(i)})^{2}}{2\sigma^{2}})$$ Then using Bayes Rule we obtain some parameter distribution … My problem is with derivation of posterior predictive distribution which is given in notes as follows: Given new test point $x_{*}$ probability distribution over possible outputs(posterior predictive …

I think the struggle is in relation to the posterior predictive distribution. … Could anyone walk me through the probability/integration steps necessary to come up with this specific posterior predictive distribution? 1. Schofield et al. 2016↩ 2. …

As I understand it, in Bayesian inference, the posterior predictive distribution is the probability distribution of a new data point, as opposed to the posterior distribution which is a distribution of … However, to obtain the posterior predictive distribution, you marginalise over the parameter by integrating over it. …

of a new data sample $y_{n+1}$ $$ p(y_{n+1} | y_1, \ldots, y_n; \mu_0, \sigma^2) \sim \mathcal{N}\left(\alpha_n, \sigma^2 +\tau_n^2\right) $$ I am interested in computing the posterior predictive distribution … I can draw samples $\tilde{y}^i_{n+1}$ from the posterior predictive distribution of the data and construct an approximate average $\frac{1}{S} \sum_{i=1}^S p(\mu_{n+1} | y_1, \ldots, y_n, y^i_{n+1}; \ …

In my minimum reproducible example, I have data for 9 observations and would like to find a posterior predictive distribution for the 10th observation. … To do this, I include the 10th observation as an NA and estimate its posterior predictive distribution as the variable pi10. …

In my situation, I have a set of data points: $$ z_{0:n} = \\{ (x_0, y_0),\dots ,(x_{n-1}, y_{n-1}) \\} $$ I am trying to figure out how to derive the fully expanded form for the conditional posterior … predictive distribution: $$p(y|x, \mathcal{z}_{0:n})$$ from the definition of the posterior predictive distribution $(z=(x,y))$: $$p(z|z_{0:n}) = \int p(z | \theta)p(\theta|z_{0:n}) d\theta$$ where $$p …

I'd like use this information ($n$, $\bar{x}_1$, $s_1$, and $m$) to formulate closed-form expectations of $\bar{x}_2$ and $s_2$, and, after some research, it seems like posterior predictive distributions …

I am considering writing an article that discusses the Bayesian MMSE and MAP of the posterior predictive distribution. … I was wondering if there are acronyms that have been used so that instead of always saying: "The MMSE of the posterior predictive distribution..." …

I am trying to figure out how to prove a result about the expectation of a random variable under the posterior predictive distribution, that may or may not be true. … expectation is taken under the posterior distribution. …

predictive distribution is analytic and is student t. … Is there an analytic form for the posterior predictive distribution in this case? Can I just plug my estimate of it into a multivariate student t? …