Explanation on minimization of Expected values

Thread starter cutesteph
Start date Nov 3, 2012
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Explanation Minimization

In summary, the minimization of expected values is a statistical concept used in decision-making and risk analysis to find the smallest possible value for a given set of outcomes. It is important in scientific research as it allows researchers to make informed decisions and minimize potential risks. Common methods for minimizing expected values include mathematical models, experiments, and data analysis. It differs from maximization of expected values, which involves finding the largest possible value. Minimization of expected values can also be applied to non-numerical data by assigning numerical representations or weights to determine the likelihood of each outcome.

Nov 3, 2012

cutesteph

Why is the E[ Y - f(x) ]^2 minimized when choosing f(x) = E[Y|X] ?

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Nov 3, 2012

chiro

Science Advisor

Hye cutesteph.

Try finding when the expression is zero. Also since you are using two variables, what is the expectation with respect to?

Another thing to note is that E_y[E_x[Y|X]] = E[Y] (also known as conditional expectation).

What is minimization of Expected values?

The minimization of expected values is a statistical concept that involves finding the smallest possible value for a given set of outcomes, taking into account the likelihood of each outcome occurring. It is often used in decision-making and risk analysis to determine the best course of action.

Why is minimization of Expected values important in scientific research?

Minimization of expected values is important in scientific research because it allows researchers to make informed decisions by considering all possible outcomes and their likelihood. It can help identify the most favorable or optimal solution and minimize potential risks or losses.

What are some common methods for minimizing Expected values?

Some common methods for minimizing expected values include using mathematical models, conducting experiments or simulations, and analyzing data to determine the most likely outcomes. Other approaches may involve risk management strategies, such as diversification or hedging, to minimize potential losses.

How does minimization of Expected values differ from maximization of Expected values?

Minimization of expected values involves finding the smallest possible value, while maximization of expected values involves finding the largest possible value. Both concepts are used in decision-making and risk analysis, but they represent different approaches to identifying the best possible outcome.

Can minimization of Expected values be applied to non-numerical data?

Yes, minimization of expected values can be applied to non-numerical data. In such cases, the values may be assigned numerical representations or weights to determine the likelihood of each outcome occurring. This approach is often used in qualitative research or risk assessments involving non-numerical data.