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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Why is MCMC needed when estimating a parameter using MAP

Given the formula for MAP estimation of a parameter Why is a MCMC (or similar) approach needed, couldn't I just take the derivative, set it to zero and then solve for the parameter?
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20 views

Latent Dirichlet Allocation yields different posterior distribution than simple Bayesian model

Method A: out of the box LDA I am using a package to run LDA on a sample of size m with n words in the vocabulary. The end ...
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41 views

Algorithm for approximating a density by a mixture density

Given a density $f(x)$ (e.g. the log-normal distribution or log-$t_{\nu=3}$ distribution), I was wondering what algorithm are known/typically used to find a mixture of distributions $g_r(x)$ from ...
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Example of learning methods based on bayesian inference

People often say that Bayesian learning and maximum likelihood are two approaches used in machine learning. Main difference is that Bayesian learning tries to include the existing knowledge in the ...
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12 views

Forming a likelihood from an implicit function

My problem involves two signals on a common value where the signals are tied together by an implicit function. I want to figure out a generic approach for how to find the likelihood of the common ...
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28 views

Is that OK to have the same Prior and Proposal Distribution in MH?

Is this ok to choose the same proposal distribution as the prior in Metropolis algorithm? Perhaps it's a simple question and to me, it's totally fine but as I always see people choose different ...
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18 views

new bigginer in R [closed]

how to ceck this code. because I can not run in that postplot <- function(mu, tau, ybar, sigma, n){ denom <- sigma^2/n + tau^2 mu <- (sigma^2/n*mu + tau^2*ybar)/denom stdev <- ...
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10 views

Familywise error with Bayes Factor

Recently a paper indicated a method to calculate Bayes Factor for correlations (http://link.springer.com/article/10.3758/s13423-012-0295-x/fulltext.html). This method doesn't use significance testing ...
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7 views

Update TrueSkill with Gaussian Drift

The update equations for the Vanilla TrueSkill algorithm are given on page 3 of the linked paper. It also says that the algorithm assumes a Gaussian drift between subsequent time steps for skills. ...
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12 views

Finding influential characteristics in a chain of events

I have some data which is sequences of actions performed by individuals. All of these actions have properties (some catagorical, some binary, some continuous numeric). Individuals can have 1 to ...
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40 views

Conditional Probability of Bathroom Stall Availability

You're walking towards a bathroom which has two stalls, Stall A and Stall B. There can only be two people in the bathroom at one ...
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11 views

Conditional / Marginal Distributions with Absolute Values

I would like to model a process that I believe follows a multi-variate Gaussian distribution[*]. However, I can only determine the covariance between the $|x_i|$s, rather than $x_i$s, because the ...
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14 views

Local Version of Bernstein Von-Mises Theorem?

The Bernstein-Von Mises theorem says that, under reasonable conditions, the posterior distribution $p(\theta | x_{1},\ldots,x_{n})$ converges weakly to the normal distribution after suitable ...
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25 views

Efficiency in Metropolis Vs Gibbs sampling

I have read that Gibbs sampling is more efficient than Metropolis algorithm. Why? Is this due only to the fact the in Gibbs sampling the acceptance rate is $1$, so that the chain needs fewer ...
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55 views

Can you use a gaussian process to model the smoothness of residuals?

I see a lot of use of Gaussian Processes for regression - fitting a GP model to data points, with a prior specifying the smoothness of the function, and using it to predict new values. However, I'm ...
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17 views

Test hypothesis of rare event with real life data using a Bayesian Model

Since I found out what Bayesian Theory I got really interested in using it in my everyday life to find a numerous of things, but I wasn't able to get any result due to my lack of understanding of ...
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1answer
45 views

On a possible generalization of the Beta distribution

Imagine that Alice is flipping a coin with unknown bias $\theta$ and reporting the results to Bob, who is conducting Bayesian inference. If Bob begins with a uniform prior, then his posterior ...
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52 views

New rare-event regression method somewhere between logistic and survival

I keep running into situations (in my job) where I need to predict relatively rare events that occur at most once per entity, across many entities, and over time (e.g. predicting mortality of cancer ...
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2answers
26 views

Problem with prior mean in MOE (Bayesian optimization)

I am playing with MOE package (yelp.github.io/MOE) - I try to optimize some function of one variable, adding one point for sample at a time. Here is the intermediate chart I got: Blue line is the ...
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22 views

Bayesian inference and a logistic weight control problem

Currently I have a lot of problems to select which I want to work on. For some I already got ideas on how to solve it. However, I haven't dived deep into Bayesian inference so far but, from what I ...
2
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1answer
91 views

Priors for Truncated Parameters - RJAGS

I would like to estimate the parameters of a specific model. The model specification is as follows: $p_t = k_t + B_t/(1-B_t) + \eta_t$, where $ \eta_t \sim N(0, \sigma^2)$ $R_{t+1} = R_{t} + R_t ...
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34 views

Seeking suggestions on a Bayesian updating problem

I have no training in Bayesian data analysis, so I can't wrap my head around how to start solving the following problem and am hoping you can help: I am using linear regression to forecast the net ...
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2answers
48 views

Metropolis-Hastings fails when the loglikelihood is monotonically increasing with a parameter

I'm trying to estimate the parameters of a Pareto distribution (actually the paretian tail of a generic distribution) via Metropolis-Hastings. The problem is that the loglikelihood, $$ l(\alpha, ...
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12answers
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Who Are The Bayesians?

As one becomes interested in statistics, the dichotomy "Frequentist" vs. "Bayesian" soon becomes commonplace (and who hasn't read Nate Silver's The Signal and the Noise, anyway?). In talks and ...
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Other than Normal prior

Let $X\sim\mathcal{N}(\mu, \sigma)$, where $\sigma$ is known, If the prior for $\mu$ is normal then the posterior for $\mu$ is also normal. My question: Is there any other prior for $\mu$ that makes ...
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1answer
25 views

Objective priors for simulator-based models?

I've read a bit about how to derive parametrization-invariant priors for models where we have access to derivatives of the likelihood function and can compute the Fisher Information Matrix: ...
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1answer
36 views

Is this posterior probability integral right?

From Wiki: where , k is binomially distributed, and I'm not sure about u. I'm thinking that the second line should be: I mean, if we let X represent the toss of a die, then $P(X = 1, 2, ...
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91 views

Is this denominator of a posterior distribution the marginal distribution of Y?

From Wikipedia: , where Is the denominator (above pics are from Wiki) the marginal distribution of Y? Intuitively, it seems that way so that when we cross-multiply, LHS and RHS are mirrors. ...
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27 views

delta function as the likelihood in Bayes theorem

I am reading a paper which is doing a MAP estimation on the following model: $$ \phi_t = \max_k p(\phi_w|\phi_t) p(\phi_t) $$ So we are seeking $\phi_t$ which maximizes that joint distribution. ...
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22 views

Prediction Error for a Poisson Process

So I have a fleet of cars. I've sampled their breakdown rates (per hour driven) for the last 10 years. Their breakdown rate follows the gamma distribution. I am trying to do two things. Predict ...
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1answer
75 views

How do frequentists guess a distribution?

With competing hypotheses such as testing if a coin is fair, frequentists and Bayesians have their own approaches. What about for coming up with a distribution? In An Essay towards solving a Problem ...
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61 views

Stuck on Bayes Theorem

I'm working on a example understanding Bayes, and wondering if my thought process is correct. So I have three users, and true or false if they own Nike or Reebok shoes, or both. I want to calculate ...
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1answer
16 views

Posterior predictive distribution - dirichlet multinomial model

i saw this derivation of the posterior predictive distribution of a dirichlet multinomial model. Is one always allowed, or are there special circumstances, in which one can split the integral in ...
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27 views

Appropriate priors for truncated regression model

I have a simple linear regression model with the constraint that my dependent variable y (response time) has to be greater than zero. I want to specify priors for intercept, slope and sigma (the ...
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1answer
89 views

What exactly does it mean to and why must one update prior?

I'm still trying to understand prior and posterior distributions in Bayesian inference. In this question, one flips a coin. Priors: unfair is 0.1, and being fair is 0.9 Coin is flipped 10x and ...
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48 views

Naive Bayes Classifier

I've been working with trying to understand and explain how Naive Bayes classifier works with the adjusted (prior and posterior) probabilities, and wanted to show my example to ensure I'm executing it ...
4
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1answer
42 views

Bayesian inference with unequal sampling

I have a "two-column" data set, with a multi-class categorical variable A, and two-class variable B. It is assumed that each observation is independent. For each category of variable $A$, I want to ...
11
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1answer
170 views

Do statisticians use the Jeffreys' prior in actual applied work?

When I learned about the Jeffreys' prior in my graduate statistical inference class my professors made it sound sort of like it was interesting mostly for historical reasons rather than because anyone ...
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Bayesian logit model in Psychometric or Behavioural Testing for Credit Scoring in Developing Countries

A lot of parameters in one title, I know. So there's credit scoring but not using credit history. Then there's using a Bayesian logit model. Then there's doing so in a developing country such as Haiti ...
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21 views

How are bayesian instrumental variables calculated?

So with regular frequentist statistics, I know that you can just regress on the first stage of two-stage least squares, get the predicted values, then plug them into the second stage. How does this ...
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14 views

Bayesian Classifier to predict a class probability?

I have a 2 input (independent) variables: 1) number of likes (numeric value between 0 and 99) 2) number of dislikes (numeric value between 0 and 99) and I would ...
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1answer
53 views

GARCH vs SV for Forecasting

I believe I am aware of how GARCH family and stochastic volatility models differ in their construction and assumptions on the volatility states, (i.e. GARCH family assumes deterministic volatility ...
2
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1answer
139 views

MLE and Bayesian methods

I saw in some lecture the fact that as the number of data points N goes to infinity, the prediction of the Bayesian method goes to the prediction of the MLE. Can someone explain what exactly this ...
0
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1answer
21 views

Effect of “parameters.to.save” in R2jags/ JAGS

I'm using the package R2jags in R, which uses the parameters.to.save argument to specify parameters. I'm interested in the statistical distinction between a ...
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15 views

I have a hierarchical bayesian logit model with large variation in outcome between units. Should I still use a hierarchical model?

So instead of using country and time fixed effects for a time series cross section data on country-years with a binary outcome, I'm using a hierarchical logit model with country and time random ...
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11 views

how to model and implement bayesian change point with longitudinal data

I am working on Bayesian change point of Poisson data with different identities that is longitudinal. I have understood to degree the hierarchical structure of the posterior with hyper priors for data ...
3
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1answer
45 views

What is the limiting distribution of the Bayesian Filtering

I've got a question about the iterative Bayesian filtering, the general form of which is shown as follows: $P(x|z_0,...z_{k+1})\propto P(z_{n+1}|x)P(x|z_0,...,z_k),\,k=0,1,\dots$. $P(x|z_0)=P_0(x)$ ...
2
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1answer
38 views

Closed form of conditional probability for a specific joint

I have a joint probability of a very specific form: $P(x_1,\cdots,x_n)=\phi(x_1)\psi(x_1,x_2)\phi(x_2)\cdots\psi(x_{n-1},x_n)\phi(x_n)=\prod_{i=1}^n \phi(x_i) \prod_{i=1}^{n-1} \psi(x_i,x_{i+1})$ I ...
3
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19 views

Linear regression with prior on $\arctan \beta_1$

Suppose we have $\hat{y} = \beta_1 x + \beta_0$ (I ask only for the univariate case.) A typical Bayesian approach might involve Normal priors on both parameters. I was thinking today about a ...
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26 views

What are the practical problems where the prior and posterior probabilities derivable from data are not reliable?

In Rough Baysian Model (Rough sets and Bayes Factor), authors always say that this model is very applicable to practical problems where the prior and posterior probabilities derivable from data or ...