Bayesian inference is a method of statistical inference that relies on turning the model parameters into random variables and applying Bayes' theorem to deduce probability statements about the parameters or hypotheses, conditional on the observed dataset.

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Python Bayesian invgamma.rvs - joint posterior of normal distribution sampling

I have some code I'm trying to figure out but doesn't make sense to me. I am proficient with c# and not python although I've done a lot of PERL. I think I'm misunderstanding something in the code ...
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Handling the “positive bias” in percentages of positive variables

Say we run an experiment and notice the following impact on a variable of interest (one row per experimental unit): ...
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30 views

How would a bayesian and a frequentist answer this question? [on hold]

I have a site which which in which there are lets say 1000 visitors every month and out of 1000, 10 people actually sign up on my site which leads to a 1% conversion rate. Now I invest in the ...
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Bayes factors and ROC curves

The question comes from Kevin Murphy's book, Ch 5, Ex 5.6. Could somebody suggest a solution? Let $B=p(D|H_1)/p(D|H_0)$ be the bayes factor in favor of model 1. Suppose we plot two ROC curves, one ...
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coding a JAGS error model for a dependent variable that has increasing variance as a function of the magnitude of the dependent variable

I am running a model in JAGS. I have a situation where y is a linear function of x, but the error in ...
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R packages for Bayesian online change point detection of multi-dimensional time series

With respect to Bayesian online change point detection, are there any R packages that can handle multi-dimensional time series? Looks like BCP package can only ...
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Estimation of Large Seemingly Unrelated Regressions Systems [migrated]

I'm using Bayesian methods to estimate a system of Seemingly Unrelated Regressions (SUR). The system I'm estimating, however, is large, and I'm trying to find a computationally feasible way to ...
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35 views

Gaussian Process in single dimension

Suppose that I start with a two-dimensional (zero-mean) Gaussian process; following Rasmussen and Williams, I denote it by $$ f(x, y) \sim \mathcal{GP}(0, k(x, y, x', y')), $$ where $(x, y) \in \...
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Find Bayesian estimator with random sample from poisson and prior distribution from exponential distribution

Let $X_{1}$ .....$X_n$ be a random sample from Poisson distribution, prior distribution with parameter $\pi(\lambda) = \beta e^{-\beta\lambda}$. Find Bayesian estimator I couldn't take integration ...
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30 views

Over-parameterization in Bayesian Hierarchical Model

Can someone explain the influence of adding parameters to a Bayesian model? I have read from Kruschke that Bayesian analysis 'accounts' for model complexity by way of multiple priors, however I don't ...
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How to understand difference between Frequentist Statistics and Bayesian Statistics [on hold]

I have already searched about following . Couldn't find any which suffice a layman on topic like me to build up the concept. How do the frequentist and bayesian approaches compare each other (e.g., ...
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bayesmh and mixed-effects logit [closed]

first post here. I'm trying to replicate the results from the Bayesian Analysis Reference Manual of Stata v.14, pp. 130, mixed-effects logit: use http://www.stata-press.com/data/r14/bangladesh set ...
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Calculating prediction variance from JAGS model of a bernoulli outcome in R

I have a model of a bernoulli random process I fit using JAGS via the rjags package in R. Here are some example data, as well as code to fit the given models in ...
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When 2% of the Bayesian Model have not converged?

I have model with 20000 latent parameters, set up in a Gibb's sampler. 98% of the parameters and sometimes 99.5% of the parameters satisfy the Geweke convergence statistic, have low autocorrelation ...
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1answer
68 views

Does JAGS have an R front end like brms for Stan? [closed]

Does JAGS have an R front end like brms / rstanarm for Stan? Is anyone working on one for JAGS?
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1answer
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What are the hyperparameters? [duplicate]

I find the meaning of hyperparameters not always clear. The hyperparameters are defined as "the parameters of the prior". Suppose that one has prior information about a certain parameter $\theta$. ...
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18 views

Jags Implementation of Multivariate Response Probit Model

I am trying to implement the latent variable interpretation of a probit model with vector response (described on wiki here), but am receiving an error. In this model, we have a matrix $X$, $n \times ...
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13 views

transdimensional Markov chain Monte Carlo (MCMC) method, bayesian

I'm studying psychology and i need help with satistics. I have to use the transdimensional Markov chain Monte Carlo method, to compare the mean of three groups with jags on R. 1) mean=91.3, n=30, ...
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2answers
443 views

Bayes's Theorem with specificity = 1

Given Bayes's Theorem: $$\text{P}(A|B)=\frac{\text{P}(B|A)\text{P}(A)}{\text{P}(B|A)\text{P}(A)+\text{P}(B|\neg A)\text{P}(\neg A)}$$ and a specificity of 1: $$\text{P}(\neg B|\neg A)=1$$ Then: $$...
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44 views

Are there any non exponential family distributions with conjugate priors? [duplicate]

I believed I had been taught that only exponential family distributions have conjugate priors but I have recently read that ' all exponential family distributions have conjugate priors', leaving the ...
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What's the point of 'predictive matching criteria' in Bayesian Statistics?

In this paper, the authors refer to a 'predictive matching criteria'. I fail to see the link between what they write at the beginning of paragraph in page 5(the wrong scale/factor increasing with the ...
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1answer
44 views

Interpretation in histogram of empirical posterior distribution

I'm having trouble to understand the following histograms I know that the posterior distribution in this case is just the empirical cumulative $$P(\rho\leq c)=\frac{1}{n}\sum_{i=1}^n \mathbb{...
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2answers
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How does Naive Bayes work with continuous variables?

To my (very basic) understanding, Naive Bayes estimates probabilities based on the class frequencies of each feature in the training data. But how does it calculate the frequency of continuous ...
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34 views

Statistical Decision Problem and Prior Sensitivity

At a critical stage in the development of a new aeroplane, a decision must be taken to continue or to abandon the project. The financial viability of the project can be measured by a parameter $\...
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1answer
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Vector Outcome Logistic Regression

Question: What model (Likelihood/prior family) is appropriate to use when attempting to do inference on a vector of boolean outcomes given continuous factors? Elaboration: I am only aware of ...
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49 views

Gibbs sampling, what to use?

My question concerns Gibbs sampling. Suppose that I have three unknown quantities, $\mu, \sigma^2$ and $c$. I have given prior information and I have given the likelihood which allows me to compute ...
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1answer
31 views

Uncertainty on fitted parameters in extrapolation

Consider a time evolving phenomenon represented by a variable $y(t)$, whose dynamics is dependent on a parameter, say the temperature $\theta$. We have two series of measurements at different ...
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1answer
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generate uncertainty for a prediction using JAGS via rjags in R

Say I have a relationship between two variables, that I have successfully fit using JAGS via the rjags package for R. Below is the code to generate the data, and ...
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RJMCMC acceptance probability of split/combine move

I have a question about the acceptance probability of Richardson & Green's RJMCMC split/combine move from their paper "On Bayesian Analysis of Mixtures with an Unknown Number of Components". In ...
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1answer
75 views

Posterior of Dirichlet distribution parameters

I want to obtain posterior distribution for parameters of a Dirichlet distribution $x = (p_1,p_2,p_3) \sim Dir(p_1,p_2,p_3; a_1,a_2,a_3)$ with uniform $P(a_1,a_2,a_3)$ and observed data $X=\{x_1,x_2,.....
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Errors-in-variables mutual instrument calibration with unknown “true” value

The problem: I have two measurement techniques, X and Y, measuring the same variable, crack depths in a metallic structure. Based on previous studies, I know the i.i.d. random error associated with ...
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193 views

Making a Bayesian prior from a frequentist result

How should one go about turning a frequentist result into a Bayesian prior? Consider the following pretty generic scenario: An experiment was conducted in the past and a result on some parameter $\...
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Bayesian MCMC Fitting

I am doing a Bayesian MCMC fit using emcee in python. I first maximize the log of the likelihood and use the results as initial parameter starting points in my MCMC. I am using a uniform prior and ...
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Nuisance Parameter in Bayesian MCMC

I am doing a Bayesian MCMC fit to some data using a simple model and I want to understand how to handle nuisance parameters. I am looking at this tutorial. The model is a line: $$y = m x + b$$. The ...
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1answer
32 views

Bayesian networks and weird probabilities

I have to solve the following problem: Suppose we have a bayesian net in which we have the following variables: R, PA and PR Let: P(R) = 0.1, P(PA) = 0.5, P(PR|R, PA) = 0.6, P(PR|¬R, PA) = 0.4, P(...
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Does it make sense to compare DIC of model with and without transformed response?

I have a dataset for which I have made two types of longitudinal models. Each of the models has a random intercept and random slope. If the first model has a response Y and covariate X (the random ...
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Human behaviour and waiting times.

I was calling my phone company the other day about some issue. At some point I was told that I'd be put on hold for a few minutes. 5, 10, 15, 20 minutes went by and I was contemplating whether to hang-...
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1answer
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Is it reasonable to have a zero mean Gaussian prior for the coefficients of an AR(p) process, assuming it is stable?

I wanna perform parameter estimation of an underlying AR(p) process given some data. Let's say it's stable. For example an AR(2) process is stable when the conditions $a_2 - a_1 < 1,$ $a_2 + a_1 &...
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Think Bayes - Chapter 7 Exercice 7.4

I'm reading this book by Allen B. Downey and trying to do the exercises http://greenteapress.com/wp/think-bayes/ I am a bit stuck at this one, 7.4. I tried looking for blogs and stuff like that where ...
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How do I perform Bayesian Updating for a function of multiple parameters, each with its own distribution?

I have a variable that is a recursive function involving other variables with known distributions (see problem below). Let $b(t+1) = b(t) + C \sqrt{b(t)}$ where I know $C \sim N(1.82, .0298)$ and ...
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Simplifying equation of bayesian linear regression with gaussian priors

I was reading the book Gaussian Processes for Machine Learning by C. E. Rasmussen & C. K. I. Williams. In the Regression chapter (chapter 2) they teach you how to do a linear regression for data $...
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Bayesian A/B/C testing

I built a Bayesian A/B testing tool - i.e. one which models A and B having posteriors $Beta(\alpha_i, \beta_i)$ where $\alpha_i, \beta_i$ are updated every iteration. After T iterations, I compare ...
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Applying Bayesian statistics to A/B testing, calculate credible intervals?

I do not know much about statistics but from my primitive research, I would like to explore how to apply Bayesian statistics in A/B testing. The best Bayesian-based A/B split test graphic calculator ...
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Bayesian parameter estimation

Here is an exercise from a past exam of my course in Time Series Analysis Suppose you have observations $(Y_{i,t}; x_{i,t})$ on $n$ units $i = 1, ..., n$ at time $t$, with $t = 1, 2, ...$. ...
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Diagnostic tests for Markov model in R package, “ChannelAttribution”

I am using R version 3.30 on windows OS. I have come across a business problem in marketing of channel attribution that's when I found the aforementioned package. But I wonder, is there a way to ...
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1answer
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How do you model unequal time intervals in an M-array CJS survival model in BUGS/JAGS?

I'm implementing a Bayesian Cormack-Jolly-Seber mark-recapture model in JAGS in the M-array format (based on code from Kery & Schaub's book "Bayesian population analysis using winbugs"). I am ...
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Bayesian approach to estimate expected run time of an algorithm

I have a task to estimate expected run time (in seconds) of a tool. The tool is essentially a black box which appears to run to completion in amount of time which seems to be non-deterministic. In ...
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1answer
32 views

Causal Graph using Bayesian Network

I am currently doing a project in which the dataset is a lung cancer dataset. There is a training file which consists of 7 unnamed parameters (Attributes) and each of them have around 1000 values ...
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Bayesian Data Analysis: Section 3.4 Sampling from the joint posterior distribution Example

For reference: $$ p(\sigma^{2}|y) \propto \tau_n N(\mu_n | \mu_0, \tau_0^{2}) \text{Inv}-\chi^{2}(\nu_0, \sigma^{2}_0) \prod_{i=1}^{n} N(y_i|\mu_n,\sigma^{2}) \tag{3.14} $$ The book states: As ...