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 ...

learn more… | top users | synonyms

0
votes
2answers
116 views

How to I find the distribution of $\log p(X)$ given an $X$ drawn from $p$?

I have a feeling there's no general solution to this problem, but I'll ask anyway. I have a multivariate PDF $p$ and, given a random vector $X\sim p$, I'd like to find the the PDF of $\log p(X)$. ...
1
vote
2answers
14 views

Survival bias and probability

Imagine the following situation: A new virus is discovered that is believed to have infected 20% of the population. Anyone infected with the virus has a chance of 50% of dying in their sleep every ...
3
votes
1answer
32 views

Determine how likely it is that a set of boolean data is produced by a distribution

Suppose we have a collection of independent Boolean random variables $X_i$ and $Y_i$ (for $1 \le i \le N$), and are told $p_i = P(X_i = 1)$ for all $i$. We are now given a set of values $x_i$ that was ...
0
votes
0answers
23 views

Is Bayesian Inference what I need? [on hold]

I'm not sure if I need a mathematician or a developer (or both) for this question. 1)There is a framework called Infer.NET that uses Bayesian inference for probabilistic programming. 2) I'm ...
0
votes
1answer
26 views

An explanation of how this solution is derived

I am having difficulty understanding the solution to this problem. Since the solution is in the form of Bayes theorem I expected something along the lines that looked similar to Bayes theorem. ...
0
votes
0answers
19 views

Nando de Freitas' Machine Learning Homework 2 Questions 1 & 2 Solutions

I've been following Nando de Freitas' Machine Learning course from UBC. While I have been enjoying the course I thought it would be good to see if I could do the homework along with it. So I'm on ...
1
vote
1answer
12 views

Prior that incentives dissimilarity of 2 parameters

I have some binary data. I have a proposed partition of this data into partitions 1 and 2. I want to test whether the data in models 1 and 2 were generated by two Bernoullis such that their ...
0
votes
2answers
37 views

A priori probability in Bayesian inference problem

The problem A psychic uses a five-card deck to demonstrate ESP, claiming to be able to guess a card correctly with $0.5$ probability (of course, ordinary guessing is $0.2$). A single experiment ...
5
votes
1answer
233 views

Hillary Clinton's Iowa Caucus Coin Toss Wins and Bayesian Inference

In yesterday's Iowa Caucus, Hillary Clinton beat Bernie Sanders in six out of six tied counties by a coin-toss*. I believe we would have heard the uproar about it by now if this was somehow rigged in ...
2
votes
2answers
397 views

Simple Bayes Theorem question

You know there are 3 boys and an unknown number of girls in a nursery at a hospital. Then a woman gives birth a baby, but you do not know its gender, and it is placed in the nursery. Then a nurse ...
0
votes
1answer
10 views

Combining two Gaussian posterior distributions from different data to refine estimated distribution.

If we apply Bayesian inference to try and determine the distribution of a multivariate Gaussian $\textbf{x}$, and we have two predictions $$ \textbf{x}\sim N(\textbf{a}_1,\Sigma _1)~~ and ~~ ...
1
vote
1answer
17 views

Bernoulli Naive Bayes Classification

I am having trouble understanding the following text regarding Bernoulli Naive Bayes. Specifically, the author mentions that $i$ is a feature. However, what is the difference between $x_i$ and $i$? ...
2
votes
0answers
31 views

Example of Kalman filter with irregular time steps/weights to observations

I am trying to find a Kalman filter implementation which does not make the assumption that each observation is equally spaced and of equal weight. In particular, I have measurements of a process ...
0
votes
0answers
16 views

Bayesian estimation of $x_m$ for Pareto distribution

The Pareto distribution has pdf $$f\left(x\right)=\alpha x_m^\alpha x^{-\alpha-1}$$ for $x\geq x_m$ with $\alpha,\,x_m$ positive parameters. I've been researching maximum-likelihood and Bayesian ...
0
votes
1answer
36 views

How to solve conditional probability problem using bayesian algorithm

I am trying to solve An agent learning to categorise news articles in two topics, World (W) and Finance (F). Out of $100$ articles, $40$ were classified as W, and $20$ of the articles were ...
0
votes
0answers
12 views

calculation probability : bayesian network

I want to ask some questions based on this link : http://artint.info/html/ArtInt_148.html about Bayesian Network , this is the following conditional probability and the bayesian network: Image ...
0
votes
0answers
12 views

How to sort list with Bayesian inference?

I have long list of Instagram accounts with the following data: number of followers of the account (N); number of users, who follows both this and mine accounts (n). I would like to get list of ...
1
vote
1answer
31 views

Conditional Probability with two subsets

Question: A man plans to ship six boxes. Two of the boxes are insured, while the other four aren't. Each package that is shipped has a 10% chance of being damaged. What is the probability that: ...
0
votes
0answers
18 views

Bayesian serial chain

I am trying to understand Bayesian networks and particularly causal (serial) chains. It is defined as P(C|A&B) = P(C|B).This means that the probability of C, ...
0
votes
0answers
22 views

Bayesian formula with multiple events

I am trying to predict next location of the user knowing his current (t) and previous location (t-1). I am trying to use Bayesian networks for this. Lets assume that we have following path: ...
2
votes
1answer
379 views

Calculating Probabilities for Substitution Ciphers using Frequency Analysis

I have been trying to put together a tool that can take in cipher text encrypted via a simple substitution cipher and calculate the most likely "key" (that is, how the plain text letters were mapped ...
0
votes
0answers
32 views

$P(A=0, B=0)$ is what given the following graph?

Graph and Probabilities Given this graph and respective probabilities, what would be the value for $P(A=0, B=0)$? I computed $P(A=0, B=0)=P(A=0)P(B=0)=0.24$ because A & B are independent of D. ...
0
votes
1answer
15 views

Is it possible to have multiple Conjugate Priors?

In Bayesian probability theory, can a probability distribution have more than one conjugate prior for the same model parameters? I know that the Normal distribution has another Normal distribution ...
0
votes
0answers
11 views

How to find the conjugate prior of a probability distribution?

I am looking for a procedure for finding the conjugate prior, given a probability distribution. I am more interested in the exponential family of distributions of the form $$ F(x|\theta) = ...
0
votes
0answers
23 views

Undefined notation in Causality book

I'm reading the book Causality - Models, Reasoning and Inference (Second edition). On page 11 the Decomposition property uses the notation $YW$, which is not defined before. What does $YW$ mean, ...
0
votes
0answers
14 views

Variational inference on a Normal distribution: is my choice of priors passable?

I am trying to understand the basics of Variational Inference. In order to do so I designed a very simple problem: using the free-form mean field method to approximate the posteriori distribution of ...
0
votes
1answer
14 views

Determining posterior gaussian distribution having marginalised over hyperparameters.

When applying gaussian process machine learning to regression problems where we want to determine the value a function $f$ takes at a new input point $x_{n+1}$, given observations of function values ...
0
votes
0answers
22 views

Which is the best indicator of probability here? Bayes

I am part of a group of teachers in DFW area. We are very competitive when it comes to our profession. So we like to have a little fun throughout the year by having “test battles”. We simply ...
1
vote
2answers
50 views

How to derive the posterior predictive distribution?

I often seen the posterior predictive distribution mentioned in the context of machine learning and bayesian inference. The definition is as follows: $ p(D'|D) = \int_\theta p(D'|\theta)p(\theta|D)$ ...
1
vote
1answer
24 views

Bayes' rule where the realization of random vector is a subset of the realization of a different random variable?

I have realizations of two different random vectors, where one is a subset (is that proper terminology here?) of the other $$s^t = (x_1,x_2,x_3,\dots x_\tau, x_{\tau +1},\dots x_t)$$ and $$ s^\tau = ...
2
votes
1answer
622 views

Bayesian versus Classical (frequentist) Statistics

Very often in text-books the comparison of Bayesian vs. Classical Statistics are presented upfront in a very abstract way. For example, in the current book I'm studying there's the following ...
1
vote
0answers
16 views

Expected utility of action, given probability model

We record measurements of an appartus every day. If apparatus doesn't break (it has probability equal to $1-p_2$), it will measure zero with probability $p_1$. If apparatus breaks (probability $p2$), ...
1
vote
0answers
29 views

Find a conditional probability of a Bayes' Net knowing only the prior probability of the root.

Given three nodes A,B,C that form a Bayes Network as the following: (A)-->(B)-->(C) If we know the prior probability of A is 0.3, i.e. P(A)=0.3, is this ...
1
vote
1answer
729 views

Improper Uniform Prior Distribution

In Bayesian method, choosing the prior distribution is an important step when using the Bayesian method. When choosing prior, we consider the prior knowledge to choose which prior distribution is the ...
6
votes
1answer
328 views

Is there an introduction to probability and statistics that balances frequentist and bayesian views?

Perhaps, roughly, I might be described as advanced undergraduate regarding mathematics. However, I have not learned statistics and have only learned elementary probability. Does there exist a book or ...
1
vote
1answer
28 views

Understanding Bayes' theorem through an example

Suppose I have three nodes A,B,C such that A and B are independent and pointed to C as the following: A --> C <-- B Also Suppose that each node takes a peobability between (0,1) so that the ...
0
votes
0answers
7 views

Interpreting data from a Gaussian Mixture Model using Gibbs sampling

I have data from a population with suspected subtypes within it. I have used a Gibbs sampler with different numbers of potential subtypes to produce Markov chains and posterior distributions. I am ...
0
votes
0answers
42 views

how to calculate expected utility for probability decision problem?

consider a decision problem: classifying $x$ as belonging to one of two classes $C_1, C_2$. there are prior probabilities for each class, $p(C_1), p(C_2)$ and likelihood probabilities for data given ...
0
votes
0answers
8 views

Bayesian Networks: simple example when to use discrete network and when to use linear Gaussian network

So I am not sure when to use which. Is there a simple example that a non maths pro would understand when to use which? I use libpgm and the pgmlearner provides different functions to train on data. I ...
3
votes
1answer
28 views

What assumptions did I make when I strengthened my independence criterion across a new random variable?

I have an algorithm which tries to calculate some $\operatorname{Pr(X | Y_1 Y_2 \dots )}$ (where juxtaposition means event intersection, "given $Y_1$ and $Y_2$ and ... have happened".) We have some ...
1
vote
1answer
41 views

Bayesian Approach: Is a die from a 3-D printer fair?

In a recent post "Fair die or not from 3-D printer"on this site @Eumel reported making a die on a 3-D printer, providing data on the faces seen in 150 rolls, and wondered about "the chances that the ...
0
votes
0answers
14 views

Bayes classification

What are the synonyms for 1) Bayes classifier 2) Bayes decision rule 3) Bayes decision function for uniform distribution I found many terms in literature and got confused because they look similar ...
2
votes
2answers
43 views

Simple example of “Maximum A Posteriori”

I've been immersing myself into Bayesian statistics in school and I'm having a very difficult time grasping argmax and ...
0
votes
1answer
37 views

ANSML - Proof of Naive Bayes Derivation

I was working through one proof of the Naive Bayes and got stuck at the last step. The setup is as follows: Given a dataset $\left\{ (x^{(i)},y^{(i)}), \cdots\right\}$ for $i=1,\cdots,m$, $y$ can ...
0
votes
0answers
32 views

How to work out $P(B\mid\neg A)$ using Bayes' formula

I am trying to work out the probability of something using Bayes' theorem: $$P(A \mid B) =\frac{P(B\mid A)P(A)}{P(B\mid A)P(A) + P(B\mid \neg A)P(\neg A)}$$ So in the question I know what $P(B\mid ...
0
votes
1answer
41 views

Conditional Probability calcualtion

In the following BBN network, 1)what is meant by P(Martin Late|train strike,Norman Late)? Does this mean probability of martin Late given that Train Strike And ...
0
votes
2answers
107 views

Bayesian Network vs Markov Decision Process

I am wondering if somebody can tell me anything about the practical differences between using Markov Decision Processes and and Bayesian Networks in reasoning about probabilistic processes?
0
votes
0answers
33 views

Change of Variable technique for two variables?

If, $\theta_1 = ln \frac p{1-p}$ $\theta_2 = ln \frac q{1-q}$ $\theta_2|\theta_1 \sim N(\theta_1, \sigma^2)$ which means $f(\theta_1,\theta_2) \propto ...
1
vote
1answer
42 views

When do we expand the numerator of the Bayes' Theorem

I am trying to understand why the proposed solution below to the following question is wrong:- A box contains three cards: a card that is black on both sides, one that is white on both sides and a ...
9
votes
1answer
172 views

Is Entropy = Information circular or trivial?

I have seen several "maximum entropy distributions" used in the mathematical and statistical literature, often with the justification that they are "minimally informed" beyond the assumptions and data ...