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

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Confused about maximum a posteriori estimation

I am new to Bayesian statistics, and I just came across MAP. When our prior is a continuous distribution (pdf) on $\theta$ how can we calculate $g(\theta)$ in the numerator?
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Bayesian linear regression on complex : how to use the prior laws and more

My model is as follows : With $y\in\mathbb{C}^{40},A\in\mathbb{C}^{40\times10},x\in\mathbb{C}^{10},b\in\mathbb{C}^{40}$ : $$y=Ax+b$$ $y$ and $A$ are known and I have a normal prior law on the module ...
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6 views

beta binomial hierarchical model with two groups, inference on the group hyperparameters

The problem I want to solve: Lets imagine that I have two factories A and B, where each factory produces coins. What I suspect is that the probability of tails (denoted as $\theta$) varies ...
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Help with computing message on TrueSkill factor graph

I want to better understand the step for calculating the message from the game factor $h_{g}$ down to the difference variable $d_g$ on the TrueSkill factor. Such message is shown in the Rasmussen's ...
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11 views

P-values Calculation as significance (Pseudo-counts and Hypergeometric)

I am looking for a way to solve this problem I have run k-means to obtain a set of clusters with elements, some of this clusters have 1 or 2 elements in them. I use the hypergeometric function to ...
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13 views

Model Selection: Goodness-of-Fit Statistic when Noise is Unknown (vs Reduced Chi-Squared)

I have data D_k and different models M_i, and I would like to calculate a goodness-of-fit statistic for undertaking model comparison between the different M_i's, in the case of unknown uncertainties ...
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21 views

Informative priors

I have a general query regarding informativeness of priors, since my laptops gone down and not able to run this on Stan to check (but from previous runs I think this was the case). If the priors used ...
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25 views

difference between MAP and MML

I am new to Bayesian inference and Gaussian Processes. I am writing to ask what is the difference between MAP (maximum a posteriori) and MML (maximum marginal likelihood). They both seem to enable us ...
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307 views

Does multiplying the likelihood by a constant change the Bayesian inference using MCMC?

For numerical Bayesian inference we have Posterior~Prior*Likelihood. In MCMC we do not need to calculate the denominator in Bayes rule. My question is that can I multiply the Likelihood by a large ...
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25 views

Constructing credible interval for store opening times

Overview: Suppose I have a log which records the time at which customers visit a store. For the sake of this example, say I have 10 stores in the dataset. Example data for Store 1: Customer 828: 9:...
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13 views

Estimate wear distribution based on smal amount of samples

This is a task where I think bayesian statistics can help, but as I only know the basics about it and the question is rather complex I have troubles to get started... Assume a machine where some ...
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uninformative prior for something dependent on states?

Say I have a model which predicts something say abc over time I define 3 states, S1, S2, S3. I define transition transitional probs. I have another variable say, xyz which has value of 0 to 5. xyz ...
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Understanding parameter as a random variable in Bayesian statistics

If I understand correctly*, in Bayesian statistics, a parameter is a random variable. When estimating the parameter, a prior distribution is combined with the data to yield a posterior distribution. ...
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Overconfidence of Bayesian classifiers on out-of-distribution samples

I am trying to find a principled way around the following problem: consider a Bayesian classifier $p(x|c)$ where $x$ is the input and $c$ is the class label. According to Bayes rule the class ...
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31 views

Naive Bayes for probability estimates

I am using a naive bayes algorithm to derive probabilities of a certain object's belonging to a class. I know that naive bayes is a classifier and doesn't yield the most accurate probabilities, the ...
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12 views

How can I run script about Bayesian Spatio-temporal model in MATLAB [on hold]

In order to Run this Script about "Bayesian Spatio-temporal model in MATLAB" which is located at the following site: https://github.com/zhangz19/BST_CAR_AR I first run 'mainProBST.m' , then run ...
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Coding resources: Accessible introductions to Bayesian Structural Time series?

all. I am asking this question in not necessarily a "subjectively recommend something for me" approach, but with a clear focus on just an accessible beginner's reference. My situation is I have been ...
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53 views

Fitting Data to an Unknown Distribution

Consider a sample $x_1,\ldots,x_n \sim F$ from an unknown parametric distribution where $F$ is the cumulative distribution. We observe data in the form $F(x_1),\ldots,F(x_n)$. Stated differently, we ...
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42 views

Writing a conditional probability as a marginal

So I understand that using sum-rule one can write a probability as a marginal: \begin{equation*} P(x) = \int{P(x,\theta)d\theta} = \int{P(x|\theta)P(\theta)}d\theta \end{equation*} But how is this ...
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32 views

Likelihood term in Bayesian inferencing versus the general definition

In general we say that the likelihood function is defined as some $L(\theta|x)$, so that it is a function over some parameters: $\theta$ given some data: $x$. That is, $\theta$ is free to vary whilst $...
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13 views

How to get Historical prediction value from BSTS model in R

I have a BSTS model and need the forecast for the entire period. For example, My training set is between 2008 to 2016 and my testing is 2017 Jan to 2018 Jan. Now I need the predicted values for 2008 ...
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Avoiding underflow errors when marginalizing over a nuisance parameter in Bayesian inference

I was reading this question about how to marginalize over nuisance parameters in Bayesian inference, and the concern I have is how to deal with underflow errors. If we are interested only in the ...
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30 views

Bayesian predictions

I have a more general query about some confusion ive been having lately deciding what the bayesian predictions are in my model. Suppose I have a model, $y_{j} = \mu_{j} + e_{j}$, (for which i have ...
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13 views

How does WINBUGS determine the posterior density of a parameter with multiple chains?

I am a new user to WINBUGS. I am running a model with 2 chains. When my model has finished running I have the following posterior density plot of my parameter: The plot only shows one distribution (i....
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Smooth regression algorithms that produce zero training error

I am looking to fit three regression functions $f_1, f_2, f_3:\mathbb{R}^2 \to \mathbb{R}$. For example, let's say $X_1$ is time, $X_2$ is geographic latitude, $f_1$ is the temperature, $f_2$ is the ...
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76 views

Fourier transform of a Gaussian process

I would like to discuss and ask a question regarding the Fourier transform of a Gaussian process, if it makes sense. For that purpose, let me describe the following situation. Let $z(s)$ be a ...
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11 views

Training Bayesian network for Time series

I know we can find the structure and parameters for static Bayesian network using available packages. However assume we have a time series, can we train and learn the parameters for time series using ...
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16 views

Bayesian starred rating system

In chapter 4 of Bayesian Methods for Hackers (by Cameron Davidson-Pilon), the author mentioned an extension to starred rating system with the following method. Extension to Starred rating systems. ...
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21 views

Can the hidden states of a HMM be interpreted as number of clusters underlying the data?

Trying to understand the physical significance of the number of hidden states of a HMM. Should they be interpreted as number of clusters in the data? If not, why? Or they should be interpreted as the ...
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24 views

Link between dimensionality of feature vectors and estimation [closed]

I am wondering, how does the dimensionality of the feature space effect the estimation complexity? Best
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10 views

How to interpret low posterior probability of covariate's positive or negative association?

I am using the following model in WINBUGS to run a hierarchical Bayesian regression where the beta are my covariates: If I modify this model by adding the ...
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12 views

bayesian regression with a limited dependent variable

Good Morning, i have an answer regarding bayesian regression. I have studied the jags package with a book, but i dont get how to do a simple regression with a dependent variable that can take values ...
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37 views

Gaussian mixture as a prior of gaussian

I'm curious what would be the posterior distribution having prior dstribution as a mixture of two guassian with the likelihood dist as a gaussian. In other words: Likelihood: $p(x|\mu,\sigma) = \...
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Weighting Observations for Bayesian Updating

if you're totally unfamiliar with baseball you might just be better looking at the tl;dr. Any help is appreciated. I'm working on a baseball research project to predict the outcomes between ...
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9 views

Update Class Probabilities using a Bayesian Filter

I am classifying images over time in categories such as office, bathroom, living room and so on. The idea is to use all these classification to categorize the room where a robot is. I want to use a ...
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56 views

initial vector h in Jacquier, Polson and Rossi (1994)

I was going through the paper Jacquier, Polson and Rossi (1994): Bayesian Analysis of Stochastic Volatility Models. While the model seems straight forward to implement. I'm not able to find how the ...
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R: icenReg: How do I fit a Bayesian model without any groups?

I've encountered a rather strange problem with the icenReg package. I'm trying to fit a Bayesian model to some interval-censored data. I'll illustrate this using ...
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Discrete and continuos parameters in MCMC sampler

I'm working with a 6-dimensional Bayesian model, and the affine-invariant sampler implemented in emcee. Four of those parameters are discrete, while the other two ...
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50 views

How to create a Bayesian network?

I have a question regarding a research article titles "Modeling Individualization in a Bayesian Networks Implementation of Knowledge Tracing". I am trying to create a bayesian network for the model ...
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31 views

Highest Posterior Density (HPD) region of the marginals vs. of the joint distribution

In a Bayesian context, to analyse the posterior distribution, one can define the Highest Posterior Density (HPD) region or interval as $$\{\theta; \pi(\theta \mid x) \geq k\} $$ in both unidimensional ...
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Does running a Bayesian Elastic Net Regression require centered data?

I plan to run a Bayesian Elastic Net Regression on some data. For example, let's say that my model is as follows: $\textbf{y} = \boldsymbol\beta_0e^{f_0g} + \boldsymbol\beta_1e^{f_1g} + ... + \...
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17 views

How to validate Bayesian hierarchical (mixed) model ?

I am new to Bayesian analysis and using the following WINBUGS example to understand Bayesian hierarchical modeling: This is a 'mixed' model with both fixed effects (covariates given by 'beta' terms) ...
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Assign labels on multi label classification

I have a multi class and multi label problem: each sample can be labelled with a number of labels between 1 and n out of N. So I train N binary classifiers, so that each of those can say if the ...
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How to incorporate confusion matrix (on validation data) into final classification probability

I have a machine learning classifier that I've trained to distinguish between two classes, and have calculated the confusion matrix on a validation set. I'd like to incorporate those priors into the ...
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8 views

Bayesian logistic regression with priors from previous experiments (in Stata)

I am new to the world of Bayesian statistics - so I apologize in advance if my question is very basic. I've been looking for an answer a for a few days with no success. In short: Optimally, I would ...
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1answer
60 views

Is parametric Bayesian inference a special case of nonparametric Bayesian inference?

I'm thinking about univariate density estimation. Original Question In parametric inference, you assume the data are generated from a density that can be summarized by finitely-many parameters. You ...
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How to find the “right” hyperparameters for the Gaussian process used Bayesian optimization

Suppose we are using Gaussian process as a surrogate model in Bayesian optimization.To compute the acquisition function using Gaussian process we need to know the right hyperparameter of the Gaussian ...
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How do interpret a vague prior for hierarchical modeling?

I am new to Bayesian analysis and using the following WINBUGS example to understand Bayesian hierarchical modeling: I have 2 questions: 1) For the fixed effects terms, i.e., the beta0 and beta1 ...
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8 views

Bayesian Additive Regression Trees - model assumptions?

BART builds on regression and classification tree models, and you can use it for continuous and binary outcomes (=probit). See Chipman 2010 for details. With normal regression methods there are a ...
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60 views

Would a simple Gibbs, or a Metropolis-Hastings algorithm work for a State-Space model?

I'm wondering if a MCMC algorithm, in a Gibbs or a Metropolis-Hastings style, work for a State-Space model. Would I also be able to learn about the state variable and not just the parameters? I've ...