Alternative to chi2 test in model comparison
$begingroup$
I have three curves ( 1.> observation: yobs , 2.> theory-1: yth1 , 3.> theory-2: yth2 ). All of these curves are functions of a single variable (say variable x.) From a computational perspective, all these curves can be thought of as arrays with discrete values. Alongside these curves, I also have 100 simulations of observations. I use these simulations to get error bars around yobs.
Below is a schematic diagram of yobs, yth1 and yth2. The orange shaded region around yobs shows error bars gotten from 100 simulations.
I want to get quantitative comparisons of the two theory functions (yth1 and yth2) with the observation curve yobs within the fitting region [x1, x2]. The main aim of doing this is to get a quantitative idea of which theory (yth1 or yth2) matches better with yobs.
One way of doing that is through the use of 
analysis. This is shown in the two formulae given below. In the two formulae given below, the symbol 
denotes covariance matrix obtained from the 100 simulations. However, for a variety of reasons, the 
values that I get for comparisons are very big (~100). Because of this, I want to find methods other than 
analysis to find which theory (yth1 or yth2) matches better with observation ( yobs ).
One alternative would be the use of fractional errors in a manner as shown in the two equations given below. But, these methods do not use errors from simulations. So, I am not sure how much I can trust the method of fractional errors to find which theory matches better with observation.
Given the nature of my problem, what is the best statistical method to find which of the theories (yth1 or yth2) matches better with observation ( yobs )?
model-selection
asked 4 mins ago
Siddharth SatpathySiddharth Satpathy
1011
New contributor
Siddharth Satpathy is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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add a comment |
$begingroup$
I have three curves ( 1.> observation: yobs , 2.> theory-1: yth1 , 3.> theory-2: yth2 ). All of these curves are functions of a single variable (say variable x.) From a computational perspective, all these curves can be thought of as arrays with discrete values. Alongside these curves, I also have 100 simulations of observations. I use these simulations to get error bars around yobs.
Below is a schematic diagram of yobs, yth1 and yth2. The orange shaded region around yobs shows error bars gotten from 100 simulations.
I want to get quantitative comparisons of the two theory functions (yth1 and yth2) with the observation curve yobs within the fitting region [x1, x2]. The main aim of doing this is to get a quantitative idea of which theory (yth1 or yth2) matches better with yobs.
One way of doing that is through the use of analysis. This is shown in the two formulae given below. In the two formulae given below, the symbol denotes covariance matrix obtained from the 100 simulations. However, for a variety of reasons, the values that I get for comparisons are very big (~100). Because of this, I want to find methods other than analysis to find which theory (yth1 or yth2) matches better with observation ( yobs ).
One alternative would be the use of fractional errors in a manner as shown in the two equations given below. But, these methods do not use errors from simulations. So, I am not sure how much I can trust the method of fractional errors to find which theory matches better with observation.
Given the nature of my problem, what is the best statistical method to find which of the theories (yth1 or yth2) matches better with observation ( yobs )?
model-selection
asked 4 mins ago
Siddharth SatpathySiddharth Satpathy
1011
New contributor
Siddharth Satpathy is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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add a comment |
$begingroup$
I have three curves ( 1.> observation: yobs , 2.> theory-1: yth1 , 3.> theory-2: yth2 ). All of these curves are functions of a single variable (say variable x.) From a computational perspective, all these curves can be thought of as arrays with discrete values. Alongside these curves, I also have 100 simulations of observations. I use these simulations to get error bars around yobs.
Below is a schematic diagram of yobs, yth1 and yth2. The orange shaded region around yobs shows error bars gotten from 100 simulations.
I want to get quantitative comparisons of the two theory functions (yth1 and yth2) with the observation curve yobs within the fitting region [x1, x2]. The main aim of doing this is to get a quantitative idea of which theory (yth1 or yth2) matches better with yobs.
One way of doing that is through the use of analysis. This is shown in the two formulae given below. In the two formulae given below, the symbol denotes covariance matrix obtained from the 100 simulations. However, for a variety of reasons, the values that I get for comparisons are very big (~100). Because of this, I want to find methods other than analysis to find which theory (yth1 or yth2) matches better with observation ( yobs ).
One alternative would be the use of fractional errors in a manner as shown in the two equations given below. But, these methods do not use errors from simulations. So, I am not sure how much I can trust the method of fractional errors to find which theory matches better with observation.
Given the nature of my problem, what is the best statistical method to find which of the theories (yth1 or yth2) matches better with observation ( yobs )?
model-selection
asked 4 mins ago
Siddharth SatpathySiddharth Satpathy
1011
New contributor
Siddharth Satpathy is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
I have three curves ( 1.> observation: yobs , 2.> theory-1: yth1 , 3.> theory-2: yth2 ). All of these curves are functions of a single variable (say variable x.) From a computational perspective, all these curves can be thought of as arrays with discrete values. Alongside these curves, I also have 100 simulations of observations. I use these simulations to get error bars around yobs.
Below is a schematic diagram of yobs, yth1 and yth2. The orange shaded region around yobs shows error bars gotten from 100 simulations.
I want to get quantitative comparisons of the two theory functions (yth1 and yth2) with the observation curve yobs within the fitting region [x1, x2]. The main aim of doing this is to get a quantitative idea of which theory (yth1 or yth2) matches better with yobs.
One way of doing that is through the use of analysis. This is shown in the two formulae given below. In the two formulae given below, the symbol denotes covariance matrix obtained from the 100 simulations. However, for a variety of reasons, the values that I get for comparisons are very big (~100). Because of this, I want to find methods other than analysis to find which theory (yth1 or yth2) matches better with observation ( yobs ).
One alternative would be the use of fractional errors in a manner as shown in the two equations given below. But, these methods do not use errors from simulations. So, I am not sure how much I can trust the method of fractional errors to find which theory matches better with observation.
Given the nature of my problem, what is the best statistical method to find which of the theories (yth1 or yth2) matches better with observation ( yobs )?
model-selection
model-selection
asked 4 mins ago
Siddharth SatpathySiddharth Satpathy
1011
New contributor
Siddharth Satpathy is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 4 mins ago
Siddharth SatpathySiddharth Satpathy
1011
New contributor
Siddharth Satpathy is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 4 mins ago
Siddharth SatpathySiddharth Satpathy
1011
New contributor
Siddharth Satpathy is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 4 mins ago
Siddharth SatpathySiddharth Satpathy
1011
asked 4 mins ago
Siddharth SatpathySiddharth Satpathy
1011
1011
New contributor
Siddharth Satpathy is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Siddharth Satpathy is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Siddharth Satpathy is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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