# Questions tagged [bayesian]

The approach and interpretation of probability associated with Bayes' theorem; usually used as opposed to the frequentist approach. It can be seen as an extension of logic that enables reasoning with propositions whose truth or falsity is uncertain. A Bayesian probabilist starts with some prior probability, and evaluates the evidence in favour of a hypothesis by combining the prior with the likelihood function of the observed data.

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### Using Bayesian statistics in time series forecasting

I would like to forecast demand count time series of taxi fleets at different locations on the map at different points in time. I.e. multivariate demand Time series forecasting. Given hierarchinal ...
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### Bayesian statistics - explanation of evidence

Despite trying to read multiple resources about Bayesian statistics, I cannot find a (free) resource which explains what is exactly $P(D)$. Most of the resources explain it somehow conceptually ...
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### Monty Hall problem with no guarantee

There 's an 80% chance a ball is in a chest of drawers with 4 drawers. If we open 3 and find they're empty ,what is the probability it s in the 4th (all drawers have an identical chance of having the ...
1 vote
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### Deriving the expression for the posterior predictive distribution.

We have $Y \mid \Theta=\theta \sim \operatorname{Po}(\theta)$ and $\Theta \sim \operatorname{Gamma}\left(\alpha_0, \lambda_0\right)$, the expression for the posterior predictive distribution is ...
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Given two normal distribution $y_* | \mathbf{x}_*, \mathbf{w} \sim N( \mathbf{x}_*^T \mathbf{w}, \sigma_n^2)$ and $\mathbf{w} \sim N(\mathbf{\bar{w}}, A^{-1})$. I am trying to show that $$y_* | \... 0 votes 0 answers 19 views ### Bayesian updating with cyclically interdependent observations Let a,b,c be independent normally distributed variables with mean 0 and standard deviation \sigma_a,\sigma_b,\sigma_c, respectively. What is the posterior distribution of the variables a,b,c ... 0 votes 0 answers 17 views ### Intuitive utility of the Jeffreys prior, eg. in Bernoulli trials I understand the computation the Jeffreys prior, and also its historical motivation. I (somewhat) understand the theoretical desirability of a "prior-construction principle/method" that is ... 1 vote 0 answers 60 views ### Is \int_{0}^{1}\exp\left(-\frac{n(x-Ks)^2}{2Ks}\right)s^{\alpha-3/2}(1-s)^{\beta-1}\mathop{\mathrm ds} approximately Gaussian as K\rightarrow 0? Suppose that$$X\mid p\sim\mathcal{N}\left(Kp,\frac{Kp}{n}\right)$$for K^2\approx 0. Now, if p\sim\text{Beta}(\alpha,\beta) for large \alpha,\beta (say \alpha\geq1.5 and \beta\geq 1), what ... 2 votes 0 answers 32 views ### Maximum entropy for continuous distributions, optimization problem Reading E. T. Jaynes book. In chapter 12 he introduces an extension to Shannon's entropy for continuous distributions: (*) H_{I}^{c} = - \int \text{d}z \, p(z|I) \log{\frac{p(z|I)}{m(z)}} which has ... 0 votes 0 answers 20 views ### Bayesian Updating with Conditional Independence of two tests I have the following scenario of Bayes updating with which I struggle quite a bit. Imagine we are interested in the probability that a given person has a disease D. We perform two different tests ... 2 votes 2 answers 85 views ### How to understand the Posterior hyperparameters for Bernoulli in Beta conjugate prior? From here: https://en.wikipedia.org/wiki/Conjugate_prior#When_the_likelihood_function_is_a_discrete_distribution I know \text{posterior} = \frac{\text{proir} \cdot \text{likelyhood}}{\text{evidence}}... 0 votes 0 answers 17 views ### Recursive formulas for the distributions in the state space model I am having difficulty understanding the recursive formula for the posterior distribution p(x_{0:t+1}|y_{1:t+1}) of the state space model in which we assume x_t is Markovian and y_t are ... 0 votes 0 answers 20 views ### Probability problem with uncertainty [duplicate] In a City there are 2 Taxi companies: Blue and Green. 85% of the Taxis are Green, 15% of the taxis are Blue A man has been hit by a taxi and he claims the taxi was blue but in tribunal the Judge ... 1 vote 2 answers 147 views ### What is the probability that the man is guilty? Problem I try to build some connection between those text provided figure to formulate a bayes equation when I want to solve : "What is the probability that the man is guilty?" I know that: ... 0 votes 1 answer 57 views ### Independence among random variables [closed] Say we have the random variables X_1, X_2, X_3, X_4, X_5. We know that: X_5 is influenced by X_3. X_4 is influenced by both X_2 and X_3. X_2 and X_3 are both influenced by ... 2 votes 0 answers 78 views ### 2 different answers, two different intuitions for Seattle raining probability problem, which one is correct? and why? You are waiting for your flight to Seattle, and to pass the time you call 3 friends in Seattle. You independently ask each one if it is raining. All 3 of your friends say “Yes, it is raining.” But ... -2 votes 1 answer 61 views ### A brilliant introductory course on machine learning (mathematical perspective) (simulation + implementation) [closed] I am a grad student with a relatively good understanding of stochastic analysis / probability theory, but only basic coding experience. What is a good source (textbook or lecture notes) for an ... 2 votes 1 answer 77 views ### If A,B indenpendent, and P(C|A),P(C|B) >P(C), what is relation P(C|A,B) with P(C)? [closed] If A,B indenpendent, and P(C|A),P(C|B) >P(C), what is relation P(C|A,B) with P(C)?(> or <) 0 votes 0 answers 63 views ### Exchangeability of y1 and y2. I'm working through one of Gelman's exercises on exchangeability and am stuck on a seemingly simple exercise. We are given a box with N black and white balls but we not know how many of each. Task ... 0 votes 0 answers 7 views ### Does likelihood function of your choice impact the asymptotic posterior of MCMC? The metropolis Hasting algorithm decides whether to jump based on posterior probability. Namely, likelihood x prior. Then it seems the density function that you choose (e.g., Poisson or Gaussian) can ... 0 votes 0 answers 12 views ### Bayesian inference on Gaussian process without conjugate prior but particular prior distribution I wondered if a well-known formula exists or if there is any reference I can look into for the following Bayesian inference problem. An observed data point y is a sum of true underlying value x ... 0 votes 0 answers 49 views ### Bayesian Learning: Finding the variance of signal Suppose x_i \sim N(10,4) - ie, the distribution is known. There is a noisy signal s_i \sim N(x_i, \sigma_e^2) and I want to estimate \sigma_e. I see some pairs (s_i, x_i) but they are not '... 0 votes 1 answer 53 views ### MAP estimation for conditional probability I'm studying bayesian estimation of model parameters and i noticed in several ML books (Deep Learning Goodfellow, ML a probabilistic perspective K. Murphy) that they used the bayesian rule in the ... 0 votes 1 answer 41 views ### Finding PDFs of conditional probability Y is a probability variable with only 0 and 1 as outcomes.$$ P(Y = 0) = P(Y = 1) = \dfrac{1}{2} $$f_{X|Y}(x|y) means the conditional probability function based on Y.$$ Y = 0, X \sim N(...
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I'm just curious about the following dynamic process: $$x_{t+1} = x_t\frac{y_t + \varepsilon_t}{y_t + x_t}$$ $$y_{t+1} = y_t + \varepsilon_t$$ Is there a name for this? I'm trying to find ...