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| − | = Bayes Parameter Estimation (BPE) tutorial | + | = '''Bayes Parameter Estimation (BPE) tutorial''' = |
A [https://www.projectrhea.org/learning/slectures.php slecture] by [https://kiwi.ecn.purdue.edu/rhea/index.php/ECE ECE] student Haiguang Wen | A [https://www.projectrhea.org/learning/slectures.php slecture] by [https://kiwi.ecn.purdue.edu/rhea/index.php/ECE ECE] student Haiguang Wen | ||
| − | Partially based on the [https://kiwi.ecn.purdue.edu/rhea/index.php/2014_Spring_ECE_662_Boutin ECE662 lecture] material of [https://engineering.purdue.edu/~mboutin/ Prof. Mireille Boutin.] | + | Partially based on the [https://kiwi.ecn.purdue.edu/rhea/index.php/2014_Spring_ECE_662_Boutin ECE662 lecture] material of [https://engineering.purdue.edu/~mboutin/ Prof. Mireille Boutin.] |
| + | |||
| + | ---- | ||
| + | |||
| + | == ''' What will you learn from this slecture?'''<br> == | ||
| + | |||
| + | *Basic knowledge of Bayes parameter estimation | ||
| + | *An example to illustrate the concept and properties of BPE | ||
| + | *The effect of sample size on the posterior | ||
| + | *The effect of prior on the posterior | ||
| + | |||
| + | |||
| + | |||
| + | ---- | ||
| + | |||
| + | == '''Introduction''' == | ||
| + | Bayes parameter estimation (BPE) is a widely used technique for estimating the probability density function of random variables with unknown parameters. Suppose that we have an observable random variable X for an experiment and its distribution depends on unknown parameter θ taking values in a parameter space Θ. The probability density function of X for a given value of θ is denoted by p(x|θ ). It should be noted that the random variable X and the parameter θ can be vector-valued. Now we obtain a set of independent observations or samples S = {x1,x2,...,xn} from an experiment. Our goal is to compute p(x|S) which is as close as we can come to obtain the unknown p(x), the probability density function of X. | ||
Revision as of 10:42, 23 April 2014
Bayes Parameter Estimation (BPE) tutorial
A slecture by ECE student Haiguang Wen
Partially based on the ECE662 lecture material of Prof. Mireille Boutin.
What will you learn from this slecture?
- Basic knowledge of Bayes parameter estimation
- An example to illustrate the concept and properties of BPE
- The effect of sample size on the posterior
- The effect of prior on the posterior
Introduction
Bayes parameter estimation (BPE) is a widely used technique for estimating the probability density function of random variables with unknown parameters. Suppose that we have an observable random variable X for an experiment and its distribution depends on unknown parameter θ taking values in a parameter space Θ. The probability density function of X for a given value of θ is denoted by p(x|θ ). It should be noted that the random variable X and the parameter θ can be vector-valued. Now we obtain a set of independent observations or samples S = {x1,x2,...,xn} from an experiment. Our goal is to compute p(x|S) which is as close as we can come to obtain the unknown p(x), the probability density function of X.
