What is a "filter" and what does "filtering" mean in statistics/engineering/computer science? I see the term "filter" in many neuroscience papers including those with heavy statistical content ("spatial filter", "temporal filter", etc.), as well as those with little or no statistical content (it seems that this term is overused). See for example https://www.jneurosci.org/content/27/31/8366.short.

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*What are a "filter" and "filtering" in statistics/engineering/computer science?

*What are the different contexts in which they can be used (e.g., does it make sense in the way it's used in the linked paper)? Do they have the same meaning in all contexts?

 A: The term 'filter' can have many meanings in science. Science is messy and terminology can be used in different ways between disciplines and even within disciplines. Filtering as I encounter it most, being in the acoustic field of Neuroscience is in the context of:

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*signal processing, where signals, often time series of measurements, are filtered in terms of frequency, including but not limited to: the classical analogue filters (e.g., Wiener filter)and their current digital counterparts, FFT Filters, Impulse filters, wavelet analyses, moving filters and so on.

But as you say, it's also used in other fields, such as in

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*Neuroscience as in your linked abstract where it's used as a term to express the weight change in neural signals. Often signals are funneled in the brain, like in the thalamus. The thalamus is sometimes referred to as a filter as well (although that's disputable). In anyway, in the awake state the high-frequency sensory inputs are funneled and passed through to the brain. During sleep, however, the various sensory inputs (barred smell) don't pass through the thalamus but are swamped by thalamic low-frequency waves. In a way, the peripheral inputs are filtered out by the thalamus helping the brain to maintain the sleeping state.

It's as such applied in many other fields, like in

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*Statistics to filter data

*Machine learning to make predictions based on large data sets

etc.
But it's also used in colloquial language, think coffee filters and particle filters in industry.
A: From Simon Haykin’s Adaptive Filter Theory I could gather the following.
The term “filter” can be understood to mean an “estimator” that extracts information about a quantity of interest from noisy data. A filter is thus a formula or algorithm that can be implemented in software or hardware.
As an example, in a digital communication system consisting of a transmitter, channel, and receiver, the (analog) channel typically suffers from noise. Consequently, the receiver only receives a corrupted version of what the transmitter sends. Thus, the receiver must have a way to produce a reliable estimate of the original message sent by the transmitter. This estimation is called filtering.
It seems to me that in a discipline such as neuroscience the term filtering is used to imply a transformation. In the example of the paper linked above, the term appears exactly four times, with one of those being irrelevant to the main findings and another being in the title. In this paper, the term seems to refer to the response of neurons to reward over multiple timescales. This is interpreted to mean that the neurons filter (i.e., extract) the reward information over time.
In sum, it appears that the more accurate and descriptive word for the operation of a filter is “estimator.”
