Can anyone give a concrete example to illustrate what is an uniform prior?Given an observed sample from a binomial distribution and a known prior, how can I update the probability distribution of possible 'p' values?Probablity of getting sequence of K equal results while tossing coin N timesWhy doesn't ML point estimate equal MAP point estimate even though I'm using uniform prior?Long-run behavior in coin tossing experimentProbability of $k$ successes in no more than $n$ Bernoulli trialsParadoxical results when performing simple Bayesian analysis. Need help explain resultsHow to calculate probability distribution of rolling n dice? (with a twist!)How does a Bayesian update his belief when something with probability 0 happened?Bayesian posterior pmf for weighted dice with uniform priorWhat is the likelihood function of having heads 8 times out of 10 tossHypothesis test between two coins
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Can anyone give a concrete example to illustrate what is an uniform prior?
Given an observed sample from a binomial distribution and a known prior, how can I update the probability distribution of possible 'p' values?Probablity of getting sequence of K equal results while tossing coin N timesWhy doesn't ML point estimate equal MAP point estimate even though I'm using uniform prior?Long-run behavior in coin tossing experimentProbability of $k$ successes in no more than $n$ Bernoulli trialsParadoxical results when performing simple Bayesian analysis. Need help explain resultsHow to calculate probability distribution of rolling n dice? (with a twist!)How does a Bayesian update his belief when something with probability 0 happened?Bayesian posterior pmf for weighted dice with uniform priorWhat is the likelihood function of having heads 8 times out of 10 tossHypothesis test between two coins
.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty margin-bottom:0;
$begingroup$
I googled "uniform prior" and got a link to Prior probability, which uses the term without an explanation or a definition.
anther link is to quora, which does not give an concrete example.
Can anyone give a concrete example, such as coin flipping or dice tossing, to illustrate the uniform prior?
probability bayesian mathematical-statistics
asked 9 hours ago
czlswsczlsws
1696 bronze badges
$endgroup$
add a comment |
$begingroup$
I googled "uniform prior" and got a link to Prior probability, which uses the term without an explanation or a definition.
anther link is to quora, which does not give an concrete example.
Can anyone give a concrete example, such as coin flipping or dice tossing, to illustrate the uniform prior?
probability bayesian mathematical-statistics
asked 9 hours ago
czlswsczlsws
1696 bronze badges
$endgroup$
$begingroup$
Possibly useful link.
$endgroup$
– BruceET
8 hours ago
add a comment |
$begingroup$
I googled "uniform prior" and got a link to Prior probability, which uses the term without an explanation or a definition.
anther link is to quora, which does not give an concrete example.
Can anyone give a concrete example, such as coin flipping or dice tossing, to illustrate the uniform prior?
probability bayesian mathematical-statistics
asked 9 hours ago
czlswsczlsws
1696 bronze badges
$endgroup$
I googled "uniform prior" and got a link to Prior probability, which uses the term without an explanation or a definition.
anther link is to quora, which does not give an concrete example.
Can anyone give a concrete example, such as coin flipping or dice tossing, to illustrate the uniform prior?
probability bayesian mathematical-statistics
probability bayesian mathematical-statistics
asked 9 hours ago
czlswsczlsws
1696 bronze badges
asked 9 hours ago
czlswsczlsws
1696 bronze badges
asked 9 hours ago
czlswsczlsws
1696 bronze badges
asked 9 hours ago
czlswsczlsws
1696 bronze badges
asked 9 hours ago
czlswsczlsws
1696 bronze badges
1696 bronze badges
$begingroup$
Possibly useful link.
$endgroup$
– BruceET
8 hours ago
add a comment |
$begingroup$
Possibly useful link.
$endgroup$
– BruceET
8 hours ago
$begingroup$
Possibly useful link.
$endgroup$
– BruceET
8 hours ago
$begingroup$
Possibly useful link.
$endgroup$
– BruceET
8 hours ago
add a comment |
3 Answers
3
active
oldest
votes
$begingroup$
Let's say you don't know the probability of head, $p$, of a coin. You decide to conduct an experiment to estimate what it is, via Bayesian analysis. It requires you to choose a prior, and in general you're free to choose one of the feasible ones. If you don't know or don't want to assume anything about this $p$, you can say that it is uniformly distributed in $[0,1]$, in which $f_P(p)=1, 0leq pleq 1$, $0$ otherwise. This is quite similar to saying that any $p$ value in $[0,1]$ is equally likely. This prior distribution is a uniform prior.
You can also choose other priors, that focus on different regions in $[0,1]$, for example, if you choose a prior like $f_P(p)=frac32(1-(1-2p)^2), 0leq pleq 1$, you'll assume that $p$ is more likely to be around $0.5$ compared to edge cases, such as $p=0,p=1$.
answered 8 hours ago
gunesgunes
12.2k1 gold badge5 silver badges22 bronze badges
$endgroup$
$begingroup$
Thank you so much! Does the function $f_P(p)$ represent the random variables, Bernoulli random variable in this case?
$endgroup$
– czlsws
1 hour ago
add a comment |
$begingroup$
The notion of uniform prior as a prior with a constant density is not well-defined (or even meaningful) as it depends on both
- the dominating measure that determines the density function of the prior
- the parameterisation of the model for which the prior is constructed.
If either entry is modified, the density of the prior changes as well and stops being constant.
answered 8 hours ago
Xi'anXi'an
61.8k8 gold badges99 silver badges377 bronze badges
$endgroup$
2
$begingroup$
+1. Another way to express this, perhaps a little more forcibly, is that all (absolutely continuous) priors are uniform.
$endgroup$
– whuber♦
7 hours ago
add a comment |
$begingroup$
When the prior distribution $pi$, of the parameter $theta$ to be estimated is the Uniform distribution, i.e. $pi(theta)sim U(a,b)$, we refer to prior $pi$ as a uniform or uninformative prior. I'm not sure what's not to understand here except the basics of Bayesian inference and the Uniform distribution.
The best way to understand the uniform distribution is via a Monte Carlo sample of fair die rolls. The probability of every outcome $P(X=x_i),~ i=1,...,6$ is equal to $1/6$ and the histogram of the empirical distribution should be approximating a horizontal line (i.e. is uniform).
answered 5 hours ago
DigioDigio
1,8738 silver badges17 bronze badges
$endgroup$
add a comment |
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3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Let's say you don't know the probability of head, $p$, of a coin. You decide to conduct an experiment to estimate what it is, via Bayesian analysis. It requires you to choose a prior, and in general you're free to choose one of the feasible ones. If you don't know or don't want to assume anything about this $p$, you can say that it is uniformly distributed in $[0,1]$, in which $f_P(p)=1, 0leq pleq 1$, $0$ otherwise. This is quite similar to saying that any $p$ value in $[0,1]$ is equally likely. This prior distribution is a uniform prior.
You can also choose other priors, that focus on different regions in $[0,1]$, for example, if you choose a prior like $f_P(p)=frac32(1-(1-2p)^2), 0leq pleq 1$, you'll assume that $p$ is more likely to be around $0.5$ compared to edge cases, such as $p=0,p=1$.
answered 8 hours ago
gunesgunes
12.2k1 gold badge5 silver badges22 bronze badges
$endgroup$
$begingroup$
Thank you so much! Does the function $f_P(p)$ represent the random variables, Bernoulli random variable in this case?
$endgroup$
– czlsws
1 hour ago
add a comment |
$begingroup$
Let's say you don't know the probability of head, $p$, of a coin. You decide to conduct an experiment to estimate what it is, via Bayesian analysis. It requires you to choose a prior, and in general you're free to choose one of the feasible ones. If you don't know or don't want to assume anything about this $p$, you can say that it is uniformly distributed in $[0,1]$, in which $f_P(p)=1, 0leq pleq 1$, $0$ otherwise. This is quite similar to saying that any $p$ value in $[0,1]$ is equally likely. This prior distribution is a uniform prior.
You can also choose other priors, that focus on different regions in $[0,1]$, for example, if you choose a prior like $f_P(p)=frac32(1-(1-2p)^2), 0leq pleq 1$, you'll assume that $p$ is more likely to be around $0.5$ compared to edge cases, such as $p=0,p=1$.
answered 8 hours ago
gunesgunes
12.2k1 gold badge5 silver badges22 bronze badges
$endgroup$
$begingroup$
Thank you so much! Does the function $f_P(p)$ represent the random variables, Bernoulli random variable in this case?
$endgroup$
– czlsws
1 hour ago
add a comment |
$begingroup$
Let's say you don't know the probability of head, $p$, of a coin. You decide to conduct an experiment to estimate what it is, via Bayesian analysis. It requires you to choose a prior, and in general you're free to choose one of the feasible ones. If you don't know or don't want to assume anything about this $p$, you can say that it is uniformly distributed in $[0,1]$, in which $f_P(p)=1, 0leq pleq 1$, $0$ otherwise. This is quite similar to saying that any $p$ value in $[0,1]$ is equally likely. This prior distribution is a uniform prior.
You can also choose other priors, that focus on different regions in $[0,1]$, for example, if you choose a prior like $f_P(p)=frac32(1-(1-2p)^2), 0leq pleq 1$, you'll assume that $p$ is more likely to be around $0.5$ compared to edge cases, such as $p=0,p=1$.
answered 8 hours ago
gunesgunes
12.2k1 gold badge5 silver badges22 bronze badges
$endgroup$
Let's say you don't know the probability of head, $p$, of a coin. You decide to conduct an experiment to estimate what it is, via Bayesian analysis. It requires you to choose a prior, and in general you're free to choose one of the feasible ones. If you don't know or don't want to assume anything about this $p$, you can say that it is uniformly distributed in $[0,1]$, in which $f_P(p)=1, 0leq pleq 1$, $0$ otherwise. This is quite similar to saying that any $p$ value in $[0,1]$ is equally likely. This prior distribution is a uniform prior.
You can also choose other priors, that focus on different regions in $[0,1]$, for example, if you choose a prior like $f_P(p)=frac32(1-(1-2p)^2), 0leq pleq 1$, you'll assume that $p$ is more likely to be around $0.5$ compared to edge cases, such as $p=0,p=1$.
answered 8 hours ago
gunesgunes
12.2k1 gold badge5 silver badges22 bronze badges
edited 8 hours ago
answered 8 hours ago
gunesgunes
12.2k1 gold badge5 silver badges22 bronze badges
answered 8 hours ago
gunesgunes
12.2k1 gold badge5 silver badges22 bronze badges
answered 8 hours ago
gunesgunes
12.2k1 gold badge5 silver badges22 bronze badges
12.2k1 gold badge5 silver badges22 bronze badges
$begingroup$
Thank you so much! Does the function $f_P(p)$ represent the random variables, Bernoulli random variable in this case?
$endgroup$
– czlsws
1 hour ago
add a comment |
$begingroup$
Thank you so much! Does the function $f_P(p)$ represent the random variables, Bernoulli random variable in this case?
$endgroup$
– czlsws
1 hour ago
$begingroup$
Thank you so much! Does the function $f_P(p)$ represent the random variables, Bernoulli random variable in this case?
$endgroup$
– czlsws
1 hour ago
$begingroup$
Thank you so much! Does the function $f_P(p)$ represent the random variables, Bernoulli random variable in this case?
$endgroup$
– czlsws
1 hour ago
add a comment |
$begingroup$
The notion of uniform prior as a prior with a constant density is not well-defined (or even meaningful) as it depends on both
- the dominating measure that determines the density function of the prior
- the parameterisation of the model for which the prior is constructed.
If either entry is modified, the density of the prior changes as well and stops being constant.
answered 8 hours ago
Xi'anXi'an
61.8k8 gold badges99 silver badges377 bronze badges
$endgroup$
2
$begingroup$
+1. Another way to express this, perhaps a little more forcibly, is that all (absolutely continuous) priors are uniform.
$endgroup$
– whuber♦
7 hours ago
add a comment |
$begingroup$
The notion of uniform prior as a prior with a constant density is not well-defined (or even meaningful) as it depends on both
- the dominating measure that determines the density function of the prior
- the parameterisation of the model for which the prior is constructed.
If either entry is modified, the density of the prior changes as well and stops being constant.
answered 8 hours ago
Xi'anXi'an
61.8k8 gold badges99 silver badges377 bronze badges
$endgroup$
2
$begingroup$
+1. Another way to express this, perhaps a little more forcibly, is that all (absolutely continuous) priors are uniform.
$endgroup$
– whuber♦
7 hours ago
add a comment |
$begingroup$
The notion of uniform prior as a prior with a constant density is not well-defined (or even meaningful) as it depends on both
- the dominating measure that determines the density function of the prior
- the parameterisation of the model for which the prior is constructed.
If either entry is modified, the density of the prior changes as well and stops being constant.
answered 8 hours ago
Xi'anXi'an
61.8k8 gold badges99 silver badges377 bronze badges
$endgroup$
The notion of uniform prior as a prior with a constant density is not well-defined (or even meaningful) as it depends on both
- the dominating measure that determines the density function of the prior
- the parameterisation of the model for which the prior is constructed.
If either entry is modified, the density of the prior changes as well and stops being constant.
answered 8 hours ago
Xi'anXi'an
61.8k8 gold badges99 silver badges377 bronze badges
edited 6 hours ago
answered 8 hours ago
Xi'anXi'an
61.8k8 gold badges99 silver badges377 bronze badges
answered 8 hours ago
Xi'anXi'an
61.8k8 gold badges99 silver badges377 bronze badges
answered 8 hours ago
Xi'anXi'an
61.8k8 gold badges99 silver badges377 bronze badges
61.8k8 gold badges99 silver badges377 bronze badges
2
$begingroup$
+1. Another way to express this, perhaps a little more forcibly, is that all (absolutely continuous) priors are uniform.
$endgroup$
– whuber♦
7 hours ago
add a comment |
2
$begingroup$
+1. Another way to express this, perhaps a little more forcibly, is that all (absolutely continuous) priors are uniform.
$endgroup$
– whuber♦
7 hours ago
2
2
$begingroup$
+1. Another way to express this, perhaps a little more forcibly, is that all (absolutely continuous) priors are uniform.
$endgroup$
– whuber♦
7 hours ago
$begingroup$
+1. Another way to express this, perhaps a little more forcibly, is that all (absolutely continuous) priors are uniform.
$endgroup$
– whuber♦
7 hours ago
add a comment |
$begingroup$
When the prior distribution $pi$, of the parameter $theta$ to be estimated is the Uniform distribution, i.e. $pi(theta)sim U(a,b)$, we refer to prior $pi$ as a uniform or uninformative prior. I'm not sure what's not to understand here except the basics of Bayesian inference and the Uniform distribution.
The best way to understand the uniform distribution is via a Monte Carlo sample of fair die rolls. The probability of every outcome $P(X=x_i),~ i=1,...,6$ is equal to $1/6$ and the histogram of the empirical distribution should be approximating a horizontal line (i.e. is uniform).
answered 5 hours ago
DigioDigio
1,8738 silver badges17 bronze badges
$endgroup$
add a comment |
$begingroup$
When the prior distribution $pi$, of the parameter $theta$ to be estimated is the Uniform distribution, i.e. $pi(theta)sim U(a,b)$, we refer to prior $pi$ as a uniform or uninformative prior. I'm not sure what's not to understand here except the basics of Bayesian inference and the Uniform distribution.
The best way to understand the uniform distribution is via a Monte Carlo sample of fair die rolls. The probability of every outcome $P(X=x_i),~ i=1,...,6$ is equal to $1/6$ and the histogram of the empirical distribution should be approximating a horizontal line (i.e. is uniform).
answered 5 hours ago
DigioDigio
1,8738 silver badges17 bronze badges
$endgroup$
add a comment |
$begingroup$
When the prior distribution $pi$, of the parameter $theta$ to be estimated is the Uniform distribution, i.e. $pi(theta)sim U(a,b)$, we refer to prior $pi$ as a uniform or uninformative prior. I'm not sure what's not to understand here except the basics of Bayesian inference and the Uniform distribution.
The best way to understand the uniform distribution is via a Monte Carlo sample of fair die rolls. The probability of every outcome $P(X=x_i),~ i=1,...,6$ is equal to $1/6$ and the histogram of the empirical distribution should be approximating a horizontal line (i.e. is uniform).
answered 5 hours ago
DigioDigio
1,8738 silver badges17 bronze badges
$endgroup$
When the prior distribution $pi$, of the parameter $theta$ to be estimated is the Uniform distribution, i.e. $pi(theta)sim U(a,b)$, we refer to prior $pi$ as a uniform or uninformative prior. I'm not sure what's not to understand here except the basics of Bayesian inference and the Uniform distribution.
The best way to understand the uniform distribution is via a Monte Carlo sample of fair die rolls. The probability of every outcome $P(X=x_i),~ i=1,...,6$ is equal to $1/6$ and the histogram of the empirical distribution should be approximating a horizontal line (i.e. is uniform).
answered 5 hours ago
DigioDigio
1,8738 silver badges17 bronze badges
answered 5 hours ago
DigioDigio
1,8738 silver badges17 bronze badges
answered 5 hours ago
DigioDigio
1,8738 silver badges17 bronze badges
answered 5 hours ago
DigioDigio
1,8738 silver badges17 bronze badges
1,8738 silver badges17 bronze badges
add a comment |
add a comment |
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$begingroup$
Possibly useful link.
$endgroup$
– BruceET
8 hours ago