# Tag Info

I would follow the same scheme as in importance sampling https://en.wikipedia.org/wiki/Importance_sampling, i.e I'll find a distribution $f(x)$ that I can easily sample from with the same domain as $\tilde{p}(x)$ and I'll approximate the normalizing constant as $$Z = \int \tilde{p}(x)\frac{f(x)}{f(x)}dx= \int \frac{\tilde{p}(x)}{f(x)}f(x)dx \approx \sum_{n=1}... 1 The Latin hypercube code you wrote may not be accomplishing what you want. This code draws 5 variables with marginals on U(0,1) with no stratification. You will not achieve any variance reduction this way: lhs_1 <- randomLHS(1, 5) ym_1 <- qnorm(lhs_1, sd = sqrt(5)) If you want one variable with 5 strata across [0,1]: lhs_2 <- randomLHS(5, 1) ym_2 &... 0 Considering a likelihood function$$\exp\{-(\mathbf d-F(\mathbf m))^2/\sigma^2\}$$is equivalent to assume the observation is Normal. The posterior distribution is hence$$\pi(\mathbf m|\mathbf d) \propto \exp\{-(\mathbf d-F(\mathbf m))^2/\sigma^2\} \pi(\mathbf m)$$which can be simulated by an MCMC algorithm, no matter how complex the transform F(\cdot) ... -1 I wrote a paper arxiv.org/abs/1907.09090 that describes how the pseudo-marginal approach can impute missing data. 400 covariates sounds tough, though, to be completely honest. Depends on what kind of distributions you want to put on the columns, the number of rows, how you program everything. Intractable in your case? Probably, yes. In section 3.3, we ... 0 Are you familiar with censorship in survival analysis modeling? Censorship means that a patient was removed from the study without explicitly dying (at least in the context of survival analysis.) There are appropriate architectures to handle censorship; however, it's more a question of model architecture than the underlying MCMC sampling algorithm. For ... 0 Currently, no- such a solution does not exist. Core developers on PyMC3 actually addressed this, noting that it's a high impact problem but the solution remains over the horizon. (I'll dig for a reference and add it in a comment if I find it.) The biggest issue is that HMC uses gradient information to explore the target distribution. Why is this helpful? ... 0 I am not an expert in bayesian non-parametrics but I think I can help a little. Others please correct me If i am wrong. Based on your model, you would have \boldsymbol{\pi}, \mu, \Sigma, \boldsymbol{Z} as your latent variables and \boldsymbol{X} as your observables. I use bold symbols to represent vectors. The objective is to find the posterior ... 0 I cannot find the connected earlier questions on \mathsf X validated but many addressed this issue of making a proposal q(\cdot;\cdot) that covers more than the support of the target distribution \pi(\cdot). This is not an issue: when$$x'\sim q(x;x_t)$$is such that$$\pi(x')=0$$the Metropolis-Hastings acceptance ratio$$1 \wedge \dfrac{q(x';x_t)\pi(x')}...
The question is not about the MCMC method, is not about the R code, but is rather about Bayesian inference. The sampling model is a Gamma model$$x_1,\ldots,x_n \sim \mathcal Ga(\alpha,\beta)$$whose parameters $\alpha$ and $\beta$ are unknown and inferred from the data $x_1,\ldots,x_n$ using Bayesian inference. The specific prior distribution on the parameter ...