7 deleted 142 characters in body edited Mar 31 at 6:47 Bahgat Nassour 1,14711 gold badge66 silver badges1818 bronze badges I think you misunderstand the concept of conditional probability, when we sample from the prior and plug the sampled value into the likelihood , we do not evaluate a probability value at a particular point we just get a conditional distribution given the sampled value from the prior .In the following is an example from a frequentist point of view but it is very straightforward to be understandable in the bayesian context. Suppose that the target distribution is the joint probability distribution of two variables, a discrete variable $$\delta \in \{1,2,3\}$$ and a continuous variable $$\theta \in \mathbb{R}$$ then the target density will be defined as : I think you misunderstand the concept of conditional probability, when we sample from the prior and plug the sampled value into the likelihood , we do not evaluate a probability value at a particular point we just get a conditional distribution given the sampled value from the prior .In the following is an example from a frequentist point of view but it is very straightforward to be understandable in the bayesian context. Suppose that the target distribution is the joint probability distribution of two variables, a discrete variable $$\delta \in \{1,2,3\}$$ and a continuous variable $$\theta \in \mathbb{R}$$ then the target density will be defined as : I think you misunderstand the concept of conditional probability, when we sample from the prior and plug the sampled value into the likelihood , we do not evaluate a probability value at a particular point we just get a conditional distribution given the sampled value from the prior. Suppose that the target distribution is the joint probability distribution of two variables, a discrete variable $$\delta \in \{1,2,3\}$$ and a continuous variable $$\theta \in \mathbb{R}$$ then the target density will be defined as : 6 added 250 characters in body edited Sep 12 '16 at 21:04 Bahgat Nassour 1,14711 gold badge66 silver badges1818 bronze badges I think you misunderstand the concept of conditional probability, when we sample from the prior and plug in the sampled value ininto the likelihood , we do not evaluate a probability value at a particular point we just get a conditional distribution given the sampled value from the prior .Anyway I want to give youIn the following is an example from a frequentist point of view but it is very straightforward to be understandable in the bayesian context. Suppose that the target distribution is the joint probability distribution of two variables, a discrete variable $$\delta \in \{1,2,3\}$$ and a continuous variable $$\theta \in \mathbb{R}$$ then the target density will be defined as : For more details see A First Course in Bayesian Statistical Methods the book provides also a very good comparison between MC and MCMC Chapter 6 section "Introduction to MCMC diagnostics ". I think you misunderstand the concept of conditional probability, when we sample from the prior and plug in the sampled value in the likelihood , we do not evaluate a probability value at a particular point we just get a conditional distribution given the sampled value from the prior .Anyway I want to give you an example from a frequentist point of view but it is very straightforward to be understandable in the bayesian context. Suppose that the target distribution is the joint probability distribution of two variables, a discrete variable $$\delta \in \{1,2,3\}$$ and a continuous variable $$\theta \in \mathbb{R}$$ then the target density will be defined as : I think you misunderstand the concept of conditional probability, when we sample from the prior and plug the sampled value into the likelihood , we do not evaluate a probability value at a particular point we just get a conditional distribution given the sampled value from the prior .In the following is an example from a frequentist point of view but it is very straightforward to be understandable in the bayesian context. Suppose that the target distribution is the joint probability distribution of two variables, a discrete variable $$\delta \in \{1,2,3\}$$ and a continuous variable $$\theta \in \mathbb{R}$$ then the target density will be defined as : For more details see A First Course in Bayesian Statistical Methods the book provides also a very good comparison between MC and MCMC Chapter 6 section "Introduction to MCMC diagnostics ". 5 edited body edited Sep 10 '16 at 7:32 Bahgat Nassour 1,14711 gold badge66 silver badges1818 bronze badges I think you misunderstand the concept of conditional probability, when we sample formfrom the prior and plug in the sampled value in the likelihood , we do not evaluate a probability value at a particular point we just get a conditional distribution given the sampled value from the prior .Anyway I want to give you an example from a frequentist point of view but it is very straightforward to be understandable in the bayesian context. Suppose that the target distribution is the joint probability distribution of two variables, a discrete variable $$\delta \in \{1,2,3\}$$ and a continuous variable $$\theta \in \mathbb{R}$$ then the target density will be defined as : I think you misunderstand the concept of conditional probability, when we sample form the prior and plug in the sampled value in the likelihood , we do not evaluate a probability value at a particular point we just get a conditional distribution given the sampled value from the prior .Anyway I want to give you an example from a frequentist point of view but it is very straightforward to be understandable in the bayesian context. Suppose that the target distribution is the joint probability distribution of two variables, a discrete variable $$\delta \in \{1,2,3\}$$ and a continuous variable $$\theta \in \mathbb{R}$$ then the target density will be defined as : I think you misunderstand the concept of conditional probability, when we sample from the prior and plug in the sampled value in the likelihood , we do not evaluate a probability value at a particular point we just get a conditional distribution given the sampled value from the prior .Anyway I want to give you an example from a frequentist point of view but it is very straightforward to be understandable in the bayesian context. Suppose that the target distribution is the joint probability distribution of two variables, a discrete variable $$\delta \in \{1,2,3\}$$ and a continuous variable $$\theta \in \mathbb{R}$$ then the target density will be defined as : 4 added 558 characters in body edited Sep 10 '16 at 7:24 Bahgat Nassour 1,14711 gold badge66 silver badges1818 bronze badges 3 deleted 25 characters in body edited Sep 7 '16 at 16:57 Bahgat Nassour 1,14711 gold badge66 silver badges1818 bronze badges 2 deleted 120 characters in body edited Sep 7 '16 at 6:50 Bahgat Nassour 1,14711 gold badge66 silver badges1818 bronze badges 1 answered Sep 7 '16 at 5:49 Bahgat Nassour 1,14711 gold badge66 silver badges1818 bronze badges