integrated out

USAGE SUMMARY

The phrase "integrated out" is correct and usable in written English.
It is typically used in contexts related to mathematics, statistics, or physics, where certain variables are eliminated from consideration in a model or equation. Example: "In our analysis, we integrated out the nuisance parameters to focus on the primary effects of interest."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

51 human-written examples

The variable z and the two parameters of the distribution, α and β, can be matched with the terms in Eq. (11) and the density integrated out, leaving the integral proportional to a single non-constant term: begin{aligned} I propto c^{-frac{n-1}{2}} = left[ frac{(n+1)left(x^{2} + sum_{i=1}^{n} {x_{i}}^{2}right -left(x+sum_{i=1}^{2}right -left)^{2}}{n+1} right]^{-frac{n-1}{2}}. end{aligned} (14).

EURASIP Journal on Advances in Signal Processing

The frailty (random effect) can be integrated out (in closed form or by numerical or stochastically integration, depending on the frailty distribution) to get a likelihood function not depending on unobserved quantities [ 19].

BMC Gastroenterology

There is only one type of input, so the PDF Q is a delta function that can be integrated out.   2.

The Journal of Mathematical Neuroscience

In some specific situations, these chain orientational degrees of freedom can be integrated out, and the quasi-static approximation is valid.

Physics Reports

From (11), it is not difficult to see that ({E{tau (U,V |V}}), in which the random variable V is integrated out, has the same mean with ({tau (U,V }), yet a reduced variance.

Complex & Intelligent Systems

To go further in detail of the second approach, we may remark that for the given z, the expression of p f, z|g) as a function of f is Gaussian and so it can be easily integrated out and we obtain: p ( z g ) ∝ p ( g z ) p ( z ) ∝ N ( g 0, H ( v diag[ z j, j  = 1,..., n ] ) H ��� + v ε I ) × λ ∑ j z j ( 1 - λ ) ∑ j ( 1 - z j ) (75).

EURASIP Journal on Advances in Signal Processing

Human-verified similar examples from authoritative sources

Similar Expressions

8 human-written examples

So far, little is known about the differences in costs between an integrated out-of-hours care model and a separated out-of-hours care model.

BMC Family Practice

They already deliver the prevention, public health services and integrated out-of-hospital care that NHS England's Five Year Forward View and the health service financial sustainability agenda are crying out for.

The Guardian

The equations governing the displacement responses, relating the integrated out-of-plane displacement over the whole structural volume, i.e., the structural volume displacement (SVD), of a cylindrical shell to structural parameters of base structure and multiple PCLD patches, are derived using the energy approach and assumed-mode method.

Journal of Sound and Vibration

Currently, three regions in the Netherlands are working according to an integrated out-of-hours care system.

BMC Health Services Research

Two differently organised out-of-hours cooperatives are involved; a separated model and an integrated out-of-hours care model in two adjacent geographic regions in the Netherlands.

BMC Health Services Research

Expert writing Tips

Best practice

When using "integrated out", ensure that the mathematical or statistical operation is clearly defined and justified within the context of your analysis. Explicitly state the variable being integrated out and the reasons for doing so.

Common error

Avoid using "integrated out" loosely without a precise mathematical or statistical meaning. Incorrectly applying it can lead to flawed interpretations and inaccurate results. Clarify the nature of the variable and why it is suitable for integration.

Linguistic Context

The phrase "integrated out" functions as a verb phrase typically used in mathematical, statistical, and scientific contexts. According to Ludwig AI, it indicates the process of eliminating a variable through integration to simplify a model or analysis. This action affects the resultant equations or models.

Expression frequency: Common

Frequent in

Science

96%

News & Media

2%

Formal & Business

2%

Less common in

Academia

0%

Encyclopedias

0%

Wiki

0%

Ludwig's WRAP-UP

The phrase "integrated out" is primarily used within scientific and mathematical fields to denote the elimination of a variable through the process of integration. Ludwig AI confirms its proper usage in contexts where a variable's influence is accounted for mathematically, simplifying models or analyses. While predominantly found in science-related content, some examples appear in news and media discussing scientific topics. When employing this phrase, precision is key: ensure that the variable is clearly defined and that the integration process aligns with established mathematical principles. As an alternative, consider phrases like "eliminated from consideration" or "marginalized out". Avoiding vague usage is essential to maintaining the integrity of your analysis.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

removed from the equation

Directly states the elimination of a variable from the equation.

eliminated from consideration

Focuses on the removal of something from the scope of analysis, similar to integrating it out.

factored out

Indicates that the variable has been separated as a factor in the equation.

marginalized out

Highlights the process of reducing the influence or importance of a variable.

averaged out

Suggests calculating an average to remove the effect of a variable.

averaged over

Similar to "averaged out" but emphasizes that the average is taken across different values of the eliminated variable.

conditioned upon

Emphasizes that the analysis depends on specific conditions, effectively removing the influence of other variables.

collapsed over

Suggests merging or combining different values or categories of a variable.

accounted for

Implies that the variable's influence has been considered and addressed within the model.

taken into account

Indicates the influence of the factor has been considered when analyzing.

FAQs

What does "integrated out" mean in a statistical context?

In statistics, "integrated out" refers to the process of eliminating a variable from a probability distribution by integrating over all its possible values. This is often done to simplify the model or to focus on the effects of other variables.

When is it appropriate to "integrate out" a variable?

It's appropriate to "integrate out" a variable when it's considered a nuisance parameter, meaning it's not of primary interest but its presence complicates the analysis. It's also used when the variable is unobserved or when you want to obtain a marginal distribution for the remaining variables.

What are some alternatives to saying "integrated out"?

Depending on the context, you can use alternatives like "eliminated from consideration", "marginalized out", or "averaged out" to express the same concept.

How does "integrating out" a variable affect the remaining parameters?

When a variable is "integrated out", its uncertainty is incorporated into the remaining parameters. This can lead to wider confidence intervals or less precise estimates for those parameters, but it also provides a more robust analysis by accounting for the variability of the integrated variable.