idx int64 1 56k | question stringlengths 15 155 | answer stringlengths 2 29.2k ⌀ | question_cut stringlengths 15 100 | answer_cut stringlengths 2 200 ⌀ | conversation stringlengths 47 29.3k | conversation_cut stringlengths 47 301 |
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7,201 | Why is using squared error the standard when absolute error is more relevant to most problems? [duplicate] | Suppose one rolls one die (numered 1-6), and wants to compute its average deviation from the average value of 3.5. Two rolls would differ by 0.5, two by 1.5, and two by 2.5, for an average deviation of 1.5. If one takes the average of the squares of the values, one would have one deviation of 0.25, one of 2.25, and o... | Why is using squared error the standard when absolute error is more relevant to most problems? [dupl | Suppose one rolls one die (numered 1-6), and wants to compute its average deviation from the average value of 3.5. Two rolls would differ by 0.5, two by 1.5, and two by 2.5, for an average deviation | Why is using squared error the standard when absolute error is more relevant to most problems? [duplicate]
Suppose one rolls one die (numered 1-6), and wants to compute its average deviation from the average value of 3.5. Two rolls would differ by 0.5, two by 1.5, and two by 2.5, for an average deviation of 1.5. If o... | Why is using squared error the standard when absolute error is more relevant to most problems? [dupl
Suppose one rolls one die (numered 1-6), and wants to compute its average deviation from the average value of 3.5. Two rolls would differ by 0.5, two by 1.5, and two by 2.5, for an average deviation |
7,202 | Why is using squared error the standard when absolute error is more relevant to most problems? [duplicate] | In my opinion, it boils to that the squared error guarantees a unique solution, easier to work with and hence much more intuition. By only two main assumptions (and linearity of the error term), a quadratic loss function guarantees that the estimated coefficient is the unique minimized. Least-absolute deviations does... | Why is using squared error the standard when absolute error is more relevant to most problems? [dupl | In my opinion, it boils to that the squared error guarantees a unique solution, easier to work with and hence much more intuition. By only two main assumptions (and linearity of the error term), a qu | Why is using squared error the standard when absolute error is more relevant to most problems? [duplicate]
In my opinion, it boils to that the squared error guarantees a unique solution, easier to work with and hence much more intuition. By only two main assumptions (and linearity of the error term), a quadratic loss ... | Why is using squared error the standard when absolute error is more relevant to most problems? [dupl
In my opinion, it boils to that the squared error guarantees a unique solution, easier to work with and hence much more intuition. By only two main assumptions (and linearity of the error term), a qu |
7,203 | Independent variable = Random variable? | There are two common formulations of linear regression. To focus on the concepts, I will abstract them somewhat. The mathematical description is a little more involved than the English description, so let's begin with the latter:
Linear regression is a model in which a response $Y$ is assumed to be random with a dis... | Independent variable = Random variable? | There are two common formulations of linear regression. To focus on the concepts, I will abstract them somewhat. The mathematical description is a little more involved than the English description, | Independent variable = Random variable?
There are two common formulations of linear regression. To focus on the concepts, I will abstract them somewhat. The mathematical description is a little more involved than the English description, so let's begin with the latter:
Linear regression is a model in which a respons... | Independent variable = Random variable?
There are two common formulations of linear regression. To focus on the concepts, I will abstract them somewhat. The mathematical description is a little more involved than the English description, |
7,204 | Independent variable = Random variable? | First of all, @whuber gave an excellent answer. I'll give it a different take, maybe simpler in some sense, also with a reference to a text.
MOTIVATION
$X$ can be random or fixed in the regression formulation. This depends on your problem. For so called observational studies it has to be random, and for experiments it ... | Independent variable = Random variable? | First of all, @whuber gave an excellent answer. I'll give it a different take, maybe simpler in some sense, also with a reference to a text.
MOTIVATION
$X$ can be random or fixed in the regression for | Independent variable = Random variable?
First of all, @whuber gave an excellent answer. I'll give it a different take, maybe simpler in some sense, also with a reference to a text.
MOTIVATION
$X$ can be random or fixed in the regression formulation. This depends on your problem. For so called observational studies it h... | Independent variable = Random variable?
First of all, @whuber gave an excellent answer. I'll give it a different take, maybe simpler in some sense, also with a reference to a text.
MOTIVATION
$X$ can be random or fixed in the regression for |
7,205 | Independent variable = Random variable? | In statistics a random variable is quantity that varies randomly in some way. You can find a good discussion in this excellent CV thread: What is meant by a “random variable”?
In a regression model, the predictor variables (X-variables, explanatory variables, covariates, etc.) are assumed to be fixed and known. They... | Independent variable = Random variable? | In statistics a random variable is quantity that varies randomly in some way. You can find a good discussion in this excellent CV thread: What is meant by a “random variable”?
In a regression model, | Independent variable = Random variable?
In statistics a random variable is quantity that varies randomly in some way. You can find a good discussion in this excellent CV thread: What is meant by a “random variable”?
In a regression model, the predictor variables (X-variables, explanatory variables, covariates, etc.) ... | Independent variable = Random variable?
In statistics a random variable is quantity that varies randomly in some way. You can find a good discussion in this excellent CV thread: What is meant by a “random variable”?
In a regression model, |
7,206 | Independent variable = Random variable? | Not sure if I understand the question, but if you're just asking, "must an independent variable always be a random variable", then the answer is no.
An independent variable is a variable which is hypothesised to be correlated with the dependent variable. You then test whether this is the case through modelling (presu... | Independent variable = Random variable? | Not sure if I understand the question, but if you're just asking, "must an independent variable always be a random variable", then the answer is no.
An independent variable is a variable which is hyp | Independent variable = Random variable?
Not sure if I understand the question, but if you're just asking, "must an independent variable always be a random variable", then the answer is no.
An independent variable is a variable which is hypothesised to be correlated with the dependent variable. You then test whether t... | Independent variable = Random variable?
Not sure if I understand the question, but if you're just asking, "must an independent variable always be a random variable", then the answer is no.
An independent variable is a variable which is hyp |
7,207 | Will the mean of a set of means always be the same as the mean obtained from the entire set of raw data? | No, the averages of the averages of subsets is not the same as the average of the whole set. It will only be the same value if the subsets are the same sample size. If you want the average of the population, multiply each average by the size of the sample it came from to get the population total, then divide by the tot... | Will the mean of a set of means always be the same as the mean obtained from the entire set of raw d | No, the averages of the averages of subsets is not the same as the average of the whole set. It will only be the same value if the subsets are the same sample size. If you want the average of the popu | Will the mean of a set of means always be the same as the mean obtained from the entire set of raw data?
No, the averages of the averages of subsets is not the same as the average of the whole set. It will only be the same value if the subsets are the same sample size. If you want the average of the population, multipl... | Will the mean of a set of means always be the same as the mean obtained from the entire set of raw d
No, the averages of the averages of subsets is not the same as the average of the whole set. It will only be the same value if the subsets are the same sample size. If you want the average of the popu |
7,208 | Will the mean of a set of means always be the same as the mean obtained from the entire set of raw data? | Let's try it and see if we can figure it out. The following example is coded in R, which is free and will let you reproduce the example, but hopefully the code is self-explanatory:
group1 = c(1,2,3)
group2 = c(4,5,6,7,8,9)
mean(group1)
# 2
mean(group2)
# 6.5
mean(c(group1, group2))
# 5
mean(c(mean(group1), mean(g... | Will the mean of a set of means always be the same as the mean obtained from the entire set of raw d | Let's try it and see if we can figure it out. The following example is coded in R, which is free and will let you reproduce the example, but hopefully the code is self-explanatory:
group1 = c(1,2,3 | Will the mean of a set of means always be the same as the mean obtained from the entire set of raw data?
Let's try it and see if we can figure it out. The following example is coded in R, which is free and will let you reproduce the example, but hopefully the code is self-explanatory:
group1 = c(1,2,3)
group2 = c(4,... | Will the mean of a set of means always be the same as the mean obtained from the entire set of raw d
Let's try it and see if we can figure it out. The following example is coded in R, which is free and will let you reproduce the example, but hopefully the code is self-explanatory:
group1 = c(1,2,3 |
7,209 | Will the mean of a set of means always be the same as the mean obtained from the entire set of raw data? | In general, if you have a set of $m$ groups with respective sizes $n_1,...,n_m$ and means $\bar{x}_1,...,\bar{x}_m$ then the overall sample mean of all the data is:
$$\bar{x} = \sum_{k=1}^m \frac{n_k}{n} \cdot \bar{x}_k
\quad \quad \quad \quad \quad
n = \sum_{i=1}^m n_k.$$
Thus, the overall mean is always a weighted av... | Will the mean of a set of means always be the same as the mean obtained from the entire set of raw d | In general, if you have a set of $m$ groups with respective sizes $n_1,...,n_m$ and means $\bar{x}_1,...,\bar{x}_m$ then the overall sample mean of all the data is:
$$\bar{x} = \sum_{k=1}^m \frac{n_k} | Will the mean of a set of means always be the same as the mean obtained from the entire set of raw data?
In general, if you have a set of $m$ groups with respective sizes $n_1,...,n_m$ and means $\bar{x}_1,...,\bar{x}_m$ then the overall sample mean of all the data is:
$$\bar{x} = \sum_{k=1}^m \frac{n_k}{n} \cdot \bar{... | Will the mean of a set of means always be the same as the mean obtained from the entire set of raw d
In general, if you have a set of $m$ groups with respective sizes $n_1,...,n_m$ and means $\bar{x}_1,...,\bar{x}_m$ then the overall sample mean of all the data is:
$$\bar{x} = \sum_{k=1}^m \frac{n_k} |
7,210 | Will the mean of a set of means always be the same as the mean obtained from the entire set of raw data? | Just want to give an (extreme) example: if we have a hit rate of (1/10000) in one sample, and a hit rate of (1/2) in another example, then $\sum \frac{hit_i}{total_i} \neq \frac{\sum hit_i}{\sum total_i}$. In the first case (mean of means), we have an "average" hit rate of 0.5001/2 while in the second case (mean of tot... | Will the mean of a set of means always be the same as the mean obtained from the entire set of raw d | Just want to give an (extreme) example: if we have a hit rate of (1/10000) in one sample, and a hit rate of (1/2) in another example, then $\sum \frac{hit_i}{total_i} \neq \frac{\sum hit_i}{\sum total | Will the mean of a set of means always be the same as the mean obtained from the entire set of raw data?
Just want to give an (extreme) example: if we have a hit rate of (1/10000) in one sample, and a hit rate of (1/2) in another example, then $\sum \frac{hit_i}{total_i} \neq \frac{\sum hit_i}{\sum total_i}$. In the fi... | Will the mean of a set of means always be the same as the mean obtained from the entire set of raw d
Just want to give an (extreme) example: if we have a hit rate of (1/10000) in one sample, and a hit rate of (1/2) in another example, then $\sum \frac{hit_i}{total_i} \neq \frac{\sum hit_i}{\sum total |
7,211 | Will the mean of a set of means always be the same as the mean obtained from the entire set of raw data? | Here's a simple counter-example that shows that the relation in the posted question cannot be true in general. Let us begin by defining the function mean that simply takes a set of outcomes and outputs the mean of those outcomes:
mean({x_1, ..., x_n}) := (x_1 + ... + x_n)/n,
where n = #{x_1, ..., x_n} (number of elem... | Will the mean of a set of means always be the same as the mean obtained from the entire set of raw d | Here's a simple counter-example that shows that the relation in the posted question cannot be true in general. Let us begin by defining the function mean that simply takes a set of outcomes and output | Will the mean of a set of means always be the same as the mean obtained from the entire set of raw data?
Here's a simple counter-example that shows that the relation in the posted question cannot be true in general. Let us begin by defining the function mean that simply takes a set of outcomes and outputs the mean of t... | Will the mean of a set of means always be the same as the mean obtained from the entire set of raw d
Here's a simple counter-example that shows that the relation in the posted question cannot be true in general. Let us begin by defining the function mean that simply takes a set of outcomes and output |
7,212 | The moose must flow, but how? | As you have already pointed out, the question is whether you are dealing with a vector field $v$ from your polygon $P$ to $\mathbb{R}^2$, $v:P \to \mathbb R^2$, and since it is supposed to be normalized, your field maps to the unit circle $\mathbf{S}^1$, i.e. $v:P\to\mathbf{S^1}$.
First, let's consider the idea of a gr... | The moose must flow, but how? | As you have already pointed out, the question is whether you are dealing with a vector field $v$ from your polygon $P$ to $\mathbb{R}^2$, $v:P \to \mathbb R^2$, and since it is supposed to be normaliz | The moose must flow, but how?
As you have already pointed out, the question is whether you are dealing with a vector field $v$ from your polygon $P$ to $\mathbb{R}^2$, $v:P \to \mathbb R^2$, and since it is supposed to be normalized, your field maps to the unit circle $\mathbf{S}^1$, i.e. $v:P\to\mathbf{S^1}$.
First, l... | The moose must flow, but how?
As you have already pointed out, the question is whether you are dealing with a vector field $v$ from your polygon $P$ to $\mathbb{R}^2$, $v:P \to \mathbb R^2$, and since it is supposed to be normaliz |
7,213 | The moose must flow, but how? | Windy moose
You may have few data points to really "model" this. But this does not mean that you could not see the patterns in data.
The trick is that, instead of a spherical cow, you may generalize your beloved moose as wind, and each footprint as a weather station that indicates the observed direction on each point.
... | The moose must flow, but how? | Windy moose
You may have few data points to really "model" this. But this does not mean that you could not see the patterns in data.
The trick is that, instead of a spherical cow, you may generalize y | The moose must flow, but how?
Windy moose
You may have few data points to really "model" this. But this does not mean that you could not see the patterns in data.
The trick is that, instead of a spherical cow, you may generalize your beloved moose as wind, and each footprint as a weather station that indicates the obse... | The moose must flow, but how?
Windy moose
You may have few data points to really "model" this. But this does not mean that you could not see the patterns in data.
The trick is that, instead of a spherical cow, you may generalize y |
7,214 | The moose must flow, but how? | My thoughts from an ecologist's perspective, especially in the context of:
The ultimate goal is to estimate likely paths that the moose are
taking into and then out of the bounded region.
Movement ecology
I mentioned this in a comment, but movement ecology might be the place to look. It focuses a lot on movement data... | The moose must flow, but how? | My thoughts from an ecologist's perspective, especially in the context of:
The ultimate goal is to estimate likely paths that the moose are
taking into and then out of the bounded region.
Movement e | The moose must flow, but how?
My thoughts from an ecologist's perspective, especially in the context of:
The ultimate goal is to estimate likely paths that the moose are
taking into and then out of the bounded region.
Movement ecology
I mentioned this in a comment, but movement ecology might be the place to look. It ... | The moose must flow, but how?
My thoughts from an ecologist's perspective, especially in the context of:
The ultimate goal is to estimate likely paths that the moose are
taking into and then out of the bounded region.
Movement e |
7,215 | The moose must flow, but how? | Not an answer, just an extended comment.
First, if you have no temporal data and it can be assumed that not all tracks were found, some could have been damaged, etc, then it is not possible to exactly recreate the path. Only the approximate, "educated guesses" are possible.
If you look at the picture you posted, there ... | The moose must flow, but how? | Not an answer, just an extended comment.
First, if you have no temporal data and it can be assumed that not all tracks were found, some could have been damaged, etc, then it is not possible to exactly | The moose must flow, but how?
Not an answer, just an extended comment.
First, if you have no temporal data and it can be assumed that not all tracks were found, some could have been damaged, etc, then it is not possible to exactly recreate the path. Only the approximate, "educated guesses" are possible.
If you look at ... | The moose must flow, but how?
Not an answer, just an extended comment.
First, if you have no temporal data and it can be assumed that not all tracks were found, some could have been damaged, etc, then it is not possible to exactly |
7,216 | The moose must flow, but how? | This approach of finding best-fit vector paths through a bounded volume with directed point measurements is the overall principle of Diffusion Tensor Imaging. There is a large volume of methodology and mathematics around finding paths under these constraints. An example of an introduction article: https://www.ncbi.nlm.... | The moose must flow, but how? | This approach of finding best-fit vector paths through a bounded volume with directed point measurements is the overall principle of Diffusion Tensor Imaging. There is a large volume of methodology an | The moose must flow, but how?
This approach of finding best-fit vector paths through a bounded volume with directed point measurements is the overall principle of Diffusion Tensor Imaging. There is a large volume of methodology and mathematics around finding paths under these constraints. An example of an introduction ... | The moose must flow, but how?
This approach of finding best-fit vector paths through a bounded volume with directed point measurements is the overall principle of Diffusion Tensor Imaging. There is a large volume of methodology an |
7,217 | The moose must flow, but how? | Building on the answer of Betterthan Kwora, here is one possible approach.
You can view your vector field as a function $\{(x_i, y_i)\}_{1 \le i \le n} \subset \mathbb{R}^2 \rightarrow [0, 2\pi]$, because each moose vector has unit length. You can use interpolation to extend this to a function defined on the whole of $... | The moose must flow, but how? | Building on the answer of Betterthan Kwora, here is one possible approach.
You can view your vector field as a function $\{(x_i, y_i)\}_{1 \le i \le n} \subset \mathbb{R}^2 \rightarrow [0, 2\pi]$, bec | The moose must flow, but how?
Building on the answer of Betterthan Kwora, here is one possible approach.
You can view your vector field as a function $\{(x_i, y_i)\}_{1 \le i \le n} \subset \mathbb{R}^2 \rightarrow [0, 2\pi]$, because each moose vector has unit length. You can use interpolation to extend this to a func... | The moose must flow, but how?
Building on the answer of Betterthan Kwora, here is one possible approach.
You can view your vector field as a function $\{(x_i, y_i)\}_{1 \le i \le n} \subset \mathbb{R}^2 \rightarrow [0, 2\pi]$, bec |
7,218 | The moose must flow, but how? | It appears that you can break this down into separate problems.
First, you can attempt to infer a moose movement vector for each point in your polygon. This will take the form of learning a function $f: \mathbb{R}^2 \mapsto \mathbb{R}^2$. Better yet, this would be a stochastic function, yielding a distribution over mov... | The moose must flow, but how? | It appears that you can break this down into separate problems.
First, you can attempt to infer a moose movement vector for each point in your polygon. This will take the form of learning a function $ | The moose must flow, but how?
It appears that you can break this down into separate problems.
First, you can attempt to infer a moose movement vector for each point in your polygon. This will take the form of learning a function $f: \mathbb{R}^2 \mapsto \mathbb{R}^2$. Better yet, this would be a stochastic function, yi... | The moose must flow, but how?
It appears that you can break this down into separate problems.
First, you can attempt to infer a moose movement vector for each point in your polygon. This will take the form of learning a function $ |
7,219 | The moose must flow, but how? | Moose density
While other answers have taken more sophisticated approaches I'd suggest neglecting the vector data for a moment - does your sampling mean that you can estimate the density of moose (regardless of direction) from your observed tracks? That will in itself be worthwhile.
You can then add data points using t... | The moose must flow, but how? | Moose density
While other answers have taken more sophisticated approaches I'd suggest neglecting the vector data for a moment - does your sampling mean that you can estimate the density of moose (reg | The moose must flow, but how?
Moose density
While other answers have taken more sophisticated approaches I'd suggest neglecting the vector data for a moment - does your sampling mean that you can estimate the density of moose (regardless of direction) from your observed tracks? That will in itself be worthwhile.
You ca... | The moose must flow, but how?
Moose density
While other answers have taken more sophisticated approaches I'd suggest neglecting the vector data for a moment - does your sampling mean that you can estimate the density of moose (reg |
7,220 | The moose must flow, but how? | Let's first propose a fairly general description of the underlying moose motion, and then consider how the hoofprint observations can help infer the specific dynamics.
We start with an assumption that the observations cover either a large enough number of moose, or a long enough period of time, so that a continuous moo... | The moose must flow, but how? | Let's first propose a fairly general description of the underlying moose motion, and then consider how the hoofprint observations can help infer the specific dynamics.
We start with an assumption that | The moose must flow, but how?
Let's first propose a fairly general description of the underlying moose motion, and then consider how the hoofprint observations can help infer the specific dynamics.
We start with an assumption that the observations cover either a large enough number of moose, or a long enough period of ... | The moose must flow, but how?
Let's first propose a fairly general description of the underlying moose motion, and then consider how the hoofprint observations can help infer the specific dynamics.
We start with an assumption that |
7,221 | The moose must flow, but how? | One thing you could consider would be a discrete model. The idea is this: using your measurement points, make a Voronoi diagram to divide your polygon up into cells. The direction measurement gives a directed graph on the cells, as it points to a unique adjacent cell, and you could consider moose to travel deterministi... | The moose must flow, but how? | One thing you could consider would be a discrete model. The idea is this: using your measurement points, make a Voronoi diagram to divide your polygon up into cells. The direction measurement gives a | The moose must flow, but how?
One thing you could consider would be a discrete model. The idea is this: using your measurement points, make a Voronoi diagram to divide your polygon up into cells. The direction measurement gives a directed graph on the cells, as it points to a unique adjacent cell, and you could conside... | The moose must flow, but how?
One thing you could consider would be a discrete model. The idea is this: using your measurement points, make a Voronoi diagram to divide your polygon up into cells. The direction measurement gives a |
7,222 | Covariance of a random vector after a linear transformation | For a random (column) vector $\mathbf Z$ with mean vector $\mathbf{m} = E[\mathbf{Z}]$, the covariance matrix is defined as $\operatorname{cov}(\mathbf{Z}) = E[(\mathbf{Z}-\mathbf{m})(\mathbf{Z}-\mathbf{m})^T]$. Thus,
the covariance matrix of $A\mathbf{Z}$, whose mean vector is $A\mathbf{m}$,
is given by
$$\begin{ali... | Covariance of a random vector after a linear transformation | For a random (column) vector $\mathbf Z$ with mean vector $\mathbf{m} = E[\mathbf{Z}]$, the covariance matrix is defined as $\operatorname{cov}(\mathbf{Z}) = E[(\mathbf{Z}-\mathbf{m})(\mathbf{Z}-\math | Covariance of a random vector after a linear transformation
For a random (column) vector $\mathbf Z$ with mean vector $\mathbf{m} = E[\mathbf{Z}]$, the covariance matrix is defined as $\operatorname{cov}(\mathbf{Z}) = E[(\mathbf{Z}-\mathbf{m})(\mathbf{Z}-\mathbf{m})^T]$. Thus,
the covariance matrix of $A\mathbf{Z}$, w... | Covariance of a random vector after a linear transformation
For a random (column) vector $\mathbf Z$ with mean vector $\mathbf{m} = E[\mathbf{Z}]$, the covariance matrix is defined as $\operatorname{cov}(\mathbf{Z}) = E[(\mathbf{Z}-\mathbf{m})(\mathbf{Z}-\math |
7,223 | How to Handle Many Times Series Simultaneously? | As Ben mentioned, the text book methods for multiple time series are VAR and VARIMA models. In practice though, I have not seen them used that often in the context of demand forecasting.
Much more common, including what my team currently uses, is hierarchical forecasting (see here as well). Hierarchical forecasting is... | How to Handle Many Times Series Simultaneously? | As Ben mentioned, the text book methods for multiple time series are VAR and VARIMA models. In practice though, I have not seen them used that often in the context of demand forecasting.
Much more co | How to Handle Many Times Series Simultaneously?
As Ben mentioned, the text book methods for multiple time series are VAR and VARIMA models. In practice though, I have not seen them used that often in the context of demand forecasting.
Much more common, including what my team currently uses, is hierarchical forecasting... | How to Handle Many Times Series Simultaneously?
As Ben mentioned, the text book methods for multiple time series are VAR and VARIMA models. In practice though, I have not seen them used that often in the context of demand forecasting.
Much more co |
7,224 | How to Handle Many Times Series Simultaneously? | Generally when you have multiple time-series you would use some kind of vector-based model to model them all simultaneously. The natural extension of the ARIMA model for this purpose is the VARIMA (Vector ARIMA) model. The fact that you have $1200$ time-series means that you will need to specify some heavy parametric... | How to Handle Many Times Series Simultaneously? | Generally when you have multiple time-series you would use some kind of vector-based model to model them all simultaneously. The natural extension of the ARIMA model for this purpose is the VARIMA (V | How to Handle Many Times Series Simultaneously?
Generally when you have multiple time-series you would use some kind of vector-based model to model them all simultaneously. The natural extension of the ARIMA model for this purpose is the VARIMA (Vector ARIMA) model. The fact that you have $1200$ time-series means tha... | How to Handle Many Times Series Simultaneously?
Generally when you have multiple time-series you would use some kind of vector-based model to model them all simultaneously. The natural extension of the ARIMA model for this purpose is the VARIMA (V |
7,225 | How to Handle Many Times Series Simultaneously? | The problem with the mass-fitting packages that have been suggested is they uniformly fail to deal with latent deterministic structure such as pulses, level/step shifts, seasonal pulses and time trends or efficiently deal with user-suggested causals as per https://autobox.com/pdfs/SARMAX.pdf
Additionally the compute ti... | How to Handle Many Times Series Simultaneously? | The problem with the mass-fitting packages that have been suggested is they uniformly fail to deal with latent deterministic structure such as pulses, level/step shifts, seasonal pulses and time trend | How to Handle Many Times Series Simultaneously?
The problem with the mass-fitting packages that have been suggested is they uniformly fail to deal with latent deterministic structure such as pulses, level/step shifts, seasonal pulses and time trends or efficiently deal with user-suggested causals as per https://autobox... | How to Handle Many Times Series Simultaneously?
The problem with the mass-fitting packages that have been suggested is they uniformly fail to deal with latent deterministic structure such as pulses, level/step shifts, seasonal pulses and time trend |
7,226 | How to Handle Many Times Series Simultaneously? | 1200 products is the main driver of the dimensionality of your problem. Now you have only 25 periods. This is very little data, insufficient to do any kind of blanket correlation analysis. In other words you don't have data to have a simultaneous forecast of all products without reducing the dimensionality. This pretty... | How to Handle Many Times Series Simultaneously? | 1200 products is the main driver of the dimensionality of your problem. Now you have only 25 periods. This is very little data, insufficient to do any kind of blanket correlation analysis. In other wo | How to Handle Many Times Series Simultaneously?
1200 products is the main driver of the dimensionality of your problem. Now you have only 25 periods. This is very little data, insufficient to do any kind of blanket correlation analysis. In other words you don't have data to have a simultaneous forecast of all products ... | How to Handle Many Times Series Simultaneously?
1200 products is the main driver of the dimensionality of your problem. Now you have only 25 periods. This is very little data, insufficient to do any kind of blanket correlation analysis. In other wo |
7,227 | How to Handle Many Times Series Simultaneously? | I am not sure if you are interested in cloud-based solutions, but Amazon makes an algorithm they call "DeepAR" available through AWS SageMaker, as seen here.
This algorithm is specifically intended to be able to learn from multiple input time series in order to create forecasts, including static and dynamic features; a... | How to Handle Many Times Series Simultaneously? | I am not sure if you are interested in cloud-based solutions, but Amazon makes an algorithm they call "DeepAR" available through AWS SageMaker, as seen here.
This algorithm is specifically intended to | How to Handle Many Times Series Simultaneously?
I am not sure if you are interested in cloud-based solutions, but Amazon makes an algorithm they call "DeepAR" available through AWS SageMaker, as seen here.
This algorithm is specifically intended to be able to learn from multiple input time series in order to create for... | How to Handle Many Times Series Simultaneously?
I am not sure if you are interested in cloud-based solutions, but Amazon makes an algorithm they call "DeepAR" available through AWS SageMaker, as seen here.
This algorithm is specifically intended to |
7,228 | What are the advantages of kernel PCA over standard PCA? | PCA (as a dimensionality reduction technique) tries to find a low-dimensional linear subspace that the data are confined to. But it might be that the data are confined to low-dimensional nonlinear subspace. What will happen then?
Take a look at this Figure, taken from Bishop's "Pattern recognition and Machine Learning"... | What are the advantages of kernel PCA over standard PCA? | PCA (as a dimensionality reduction technique) tries to find a low-dimensional linear subspace that the data are confined to. But it might be that the data are confined to low-dimensional nonlinear sub | What are the advantages of kernel PCA over standard PCA?
PCA (as a dimensionality reduction technique) tries to find a low-dimensional linear subspace that the data are confined to. But it might be that the data are confined to low-dimensional nonlinear subspace. What will happen then?
Take a look at this Figure, taken... | What are the advantages of kernel PCA over standard PCA?
PCA (as a dimensionality reduction technique) tries to find a low-dimensional linear subspace that the data are confined to. But it might be that the data are confined to low-dimensional nonlinear sub |
7,229 | Is p-value essentially useless and dangerous to use? | Here are some thoughts:
As @whuber notes, I doubt Gelman said that (although he may have said something similar sounding). Five percent of cases where the null is true will yield significant results (type I errors) using an alpha of .05. If we assume that the true power for all studies where the null was false wer... | Is p-value essentially useless and dangerous to use? | Here are some thoughts:
As @whuber notes, I doubt Gelman said that (although he may have said something similar sounding). Five percent of cases where the null is true will yield significant resul | Is p-value essentially useless and dangerous to use?
Here are some thoughts:
As @whuber notes, I doubt Gelman said that (although he may have said something similar sounding). Five percent of cases where the null is true will yield significant results (type I errors) using an alpha of .05. If we assume that the tr... | Is p-value essentially useless and dangerous to use?
Here are some thoughts:
As @whuber notes, I doubt Gelman said that (although he may have said something similar sounding). Five percent of cases where the null is true will yield significant resul |
7,230 | Is p-value essentially useless and dangerous to use? | To me, one of the most interesting things about the p-hacking controversy is that the entire history of p<=0.05 as the "once in a blue moon" standard for statistical significance, as Joseph Kaldane noted in a JASA article on forensic statistics back in the 90s, rests on absolutely no statistical theory whatsoever. It's... | Is p-value essentially useless and dangerous to use? | To me, one of the most interesting things about the p-hacking controversy is that the entire history of p<=0.05 as the "once in a blue moon" standard for statistical significance, as Joseph Kaldane no | Is p-value essentially useless and dangerous to use?
To me, one of the most interesting things about the p-hacking controversy is that the entire history of p<=0.05 as the "once in a blue moon" standard for statistical significance, as Joseph Kaldane noted in a JASA article on forensic statistics back in the 90s, rests... | Is p-value essentially useless and dangerous to use?
To me, one of the most interesting things about the p-hacking controversy is that the entire history of p<=0.05 as the "once in a blue moon" standard for statistical significance, as Joseph Kaldane no |
7,231 | Is p-value essentially useless and dangerous to use? | Here are some of my thoughts regarding Question 3 after reading all the insightful comments and answers.
Perhaps one practical guidance in statistical analysis to avoid p-value hacking is to instead look at the scientifically (or, biologically, clinically, etc) significant/meaningful effect size.
Specifically, the res... | Is p-value essentially useless and dangerous to use? | Here are some of my thoughts regarding Question 3 after reading all the insightful comments and answers.
Perhaps one practical guidance in statistical analysis to avoid p-value hacking is to instead | Is p-value essentially useless and dangerous to use?
Here are some of my thoughts regarding Question 3 after reading all the insightful comments and answers.
Perhaps one practical guidance in statistical analysis to avoid p-value hacking is to instead look at the scientifically (or, biologically, clinically, etc) sign... | Is p-value essentially useless and dangerous to use?
Here are some of my thoughts regarding Question 3 after reading all the insightful comments and answers.
Perhaps one practical guidance in statistical analysis to avoid p-value hacking is to instead |
7,232 | Is p-value essentially useless and dangerous to use? | In contemporary usage the p-value refers to the cumulative probability of the data given the null hypothesis being at or greater than some threshold. I.e. $P(D|H_0)\le\alpha$. I think that $H_0$ tends to be a hypothesis of 'no effect' usually proxied by a comparison to the probability to a satisfactorily unlikely rando... | Is p-value essentially useless and dangerous to use? | In contemporary usage the p-value refers to the cumulative probability of the data given the null hypothesis being at or greater than some threshold. I.e. $P(D|H_0)\le\alpha$. I think that $H_0$ tends | Is p-value essentially useless and dangerous to use?
In contemporary usage the p-value refers to the cumulative probability of the data given the null hypothesis being at or greater than some threshold. I.e. $P(D|H_0)\le\alpha$. I think that $H_0$ tends to be a hypothesis of 'no effect' usually proxied by a comparison ... | Is p-value essentially useless and dangerous to use?
In contemporary usage the p-value refers to the cumulative probability of the data given the null hypothesis being at or greater than some threshold. I.e. $P(D|H_0)\le\alpha$. I think that $H_0$ tends |
7,233 | Is p-value essentially useless and dangerous to use? | Reproducibility of statistical test results
This is a short, simple exercise to assess the reproducibility of decisions based on statistical testing.
Consider a null hypothesis H0 with a set of alternative hypotheses containing H1 and H2. Setup the statistical hypothesis test procedure at a significance level of 0.05 ... | Is p-value essentially useless and dangerous to use? | Reproducibility of statistical test results
This is a short, simple exercise to assess the reproducibility of decisions based on statistical testing.
Consider a null hypothesis H0 with a set of alter | Is p-value essentially useless and dangerous to use?
Reproducibility of statistical test results
This is a short, simple exercise to assess the reproducibility of decisions based on statistical testing.
Consider a null hypothesis H0 with a set of alternative hypotheses containing H1 and H2. Setup the statistical hypot... | Is p-value essentially useless and dangerous to use?
Reproducibility of statistical test results
This is a short, simple exercise to assess the reproducibility of decisions based on statistical testing.
Consider a null hypothesis H0 with a set of alter |
7,234 | Backpropagation vs Genetic Algorithm for Neural Network training | If you look carefully at the scientific literature you'll find contrasting results. Obviously, in some cases GA (and more in general, Evolutionary Algorithms) may help you to find an optimal NN design but normally they have so many drawbacks (algorithm parameters' tuning, computational complexity etc) and their use is ... | Backpropagation vs Genetic Algorithm for Neural Network training | If you look carefully at the scientific literature you'll find contrasting results. Obviously, in some cases GA (and more in general, Evolutionary Algorithms) may help you to find an optimal NN design | Backpropagation vs Genetic Algorithm for Neural Network training
If you look carefully at the scientific literature you'll find contrasting results. Obviously, in some cases GA (and more in general, Evolutionary Algorithms) may help you to find an optimal NN design but normally they have so many drawbacks (algorithm pa... | Backpropagation vs Genetic Algorithm for Neural Network training
If you look carefully at the scientific literature you'll find contrasting results. Obviously, in some cases GA (and more in general, Evolutionary Algorithms) may help you to find an optimal NN design |
7,235 | Backpropagation vs Genetic Algorithm for Neural Network training | One of the key problems with neural networks is over-fitting, which means that algorithms that try very hard to find a network that minimises some criterion based on a finite sample of data will end up with a network that works very well for that particular sample of data, but which will have poor generalisation. I am... | Backpropagation vs Genetic Algorithm for Neural Network training | One of the key problems with neural networks is over-fitting, which means that algorithms that try very hard to find a network that minimises some criterion based on a finite sample of data will end u | Backpropagation vs Genetic Algorithm for Neural Network training
One of the key problems with neural networks is over-fitting, which means that algorithms that try very hard to find a network that minimises some criterion based on a finite sample of data will end up with a network that works very well for that particul... | Backpropagation vs Genetic Algorithm for Neural Network training
One of the key problems with neural networks is over-fitting, which means that algorithms that try very hard to find a network that minimises some criterion based on a finite sample of data will end u |
7,236 | Backpropagation vs Genetic Algorithm for Neural Network training | Whenever you deal with huge amounts of data and you want to solve a supervised learning task with a feed-forward neural network, solutions based on backpropagation are much more feasible. The reason for this is, that for a complex neural network, the number of free parameters is very high. One industry project I am cur... | Backpropagation vs Genetic Algorithm for Neural Network training | Whenever you deal with huge amounts of data and you want to solve a supervised learning task with a feed-forward neural network, solutions based on backpropagation are much more feasible. The reason f | Backpropagation vs Genetic Algorithm for Neural Network training
Whenever you deal with huge amounts of data and you want to solve a supervised learning task with a feed-forward neural network, solutions based on backpropagation are much more feasible. The reason for this is, that for a complex neural network, the numb... | Backpropagation vs Genetic Algorithm for Neural Network training
Whenever you deal with huge amounts of data and you want to solve a supervised learning task with a feed-forward neural network, solutions based on backpropagation are much more feasible. The reason f |
7,237 | Backpropagation vs Genetic Algorithm for Neural Network training | Second answer is wrong. Overfitting isn't caused by optimization. Overfitting happens when your model is over-complicated and can fit all the datapoints without learning the actual rule that created them (i.e. just memorizing them, in the extreme case.) There are many ways to prevent overfitting such as choosing simple... | Backpropagation vs Genetic Algorithm for Neural Network training | Second answer is wrong. Overfitting isn't caused by optimization. Overfitting happens when your model is over-complicated and can fit all the datapoints without learning the actual rule that created t | Backpropagation vs Genetic Algorithm for Neural Network training
Second answer is wrong. Overfitting isn't caused by optimization. Overfitting happens when your model is over-complicated and can fit all the datapoints without learning the actual rule that created them (i.e. just memorizing them, in the extreme case.) T... | Backpropagation vs Genetic Algorithm for Neural Network training
Second answer is wrong. Overfitting isn't caused by optimization. Overfitting happens when your model is over-complicated and can fit all the datapoints without learning the actual rule that created t |
7,238 | Backpropagation vs Genetic Algorithm for Neural Network training | imho the difference between GA and backpropagation is that GA is based on random numbers and that backpropagation is based on a static algorithm such as stochastic gradient descent. GA being based on random numbers and add to that mutation means that it would likely avoid being caught in a local minima. But then GA bei... | Backpropagation vs Genetic Algorithm for Neural Network training | imho the difference between GA and backpropagation is that GA is based on random numbers and that backpropagation is based on a static algorithm such as stochastic gradient descent. GA being based on | Backpropagation vs Genetic Algorithm for Neural Network training
imho the difference between GA and backpropagation is that GA is based on random numbers and that backpropagation is based on a static algorithm such as stochastic gradient descent. GA being based on random numbers and add to that mutation means that it w... | Backpropagation vs Genetic Algorithm for Neural Network training
imho the difference between GA and backpropagation is that GA is based on random numbers and that backpropagation is based on a static algorithm such as stochastic gradient descent. GA being based on |
7,239 | Backpropagation vs Genetic Algorithm for Neural Network training | To answer your question, I have tried to write selective algo to train mnist without tensorflow or pytorch. Only using numpy. It works but terribly slow. So tried utilizing gpu using cupy. I optimized my code. I wrote a custom kernel to cupy etc etc ...
So I have invented binary minist :P . Very small dataset only wi... | Backpropagation vs Genetic Algorithm for Neural Network training | To answer your question, I have tried to write selective algo to train mnist without tensorflow or pytorch. Only using numpy. It works but terribly slow. So tried utilizing gpu using cupy. I optimiz | Backpropagation vs Genetic Algorithm for Neural Network training
To answer your question, I have tried to write selective algo to train mnist without tensorflow or pytorch. Only using numpy. It works but terribly slow. So tried utilizing gpu using cupy. I optimized my code. I wrote a custom kernel to cupy etc etc ...... | Backpropagation vs Genetic Algorithm for Neural Network training
To answer your question, I have tried to write selective algo to train mnist without tensorflow or pytorch. Only using numpy. It works but terribly slow. So tried utilizing gpu using cupy. I optimiz |
7,240 | Are decision trees almost always binary trees? | This is mainly a technical issue: if you don't restrict to binary choices, there are simply too many possibilities for the next split in the tree. So you are definitely right in all the points made in your question.
Be aware that most tree-type algorithms work stepwise and are even as such not guaranteed to give the be... | Are decision trees almost always binary trees? | This is mainly a technical issue: if you don't restrict to binary choices, there are simply too many possibilities for the next split in the tree. So you are definitely right in all the points made in | Are decision trees almost always binary trees?
This is mainly a technical issue: if you don't restrict to binary choices, there are simply too many possibilities for the next split in the tree. So you are definitely right in all the points made in your question.
Be aware that most tree-type algorithms work stepwise and... | Are decision trees almost always binary trees?
This is mainly a technical issue: if you don't restrict to binary choices, there are simply too many possibilities for the next split in the tree. So you are definitely right in all the points made in |
7,241 | Are decision trees almost always binary trees? | A two-way split followed by another two-way split on one of the children is not the same thing as a single three-way split
I'm not sure what you mean here. Any multi-way split can be represented as a series of two-way splits. For a three-way split, you can split into A, B, and C by first splitting into A&B versus C an... | Are decision trees almost always binary trees? | A two-way split followed by another two-way split on one of the children is not the same thing as a single three-way split
I'm not sure what you mean here. Any multi-way split can be represented as a | Are decision trees almost always binary trees?
A two-way split followed by another two-way split on one of the children is not the same thing as a single three-way split
I'm not sure what you mean here. Any multi-way split can be represented as a series of two-way splits. For a three-way split, you can split into A, B... | Are decision trees almost always binary trees?
A two-way split followed by another two-way split on one of the children is not the same thing as a single three-way split
I'm not sure what you mean here. Any multi-way split can be represented as a |
7,242 | Are decision trees almost always binary trees? | Regarding uses of decision tree and splitting (binary versus otherwise), I only know of CHAID that has non-binary splits but there are likely others. For me, the main use of a non binary split is in data mining exercises where I am looking at how to optimally bin a nominal variable with many levels. A series of binary ... | Are decision trees almost always binary trees? | Regarding uses of decision tree and splitting (binary versus otherwise), I only know of CHAID that has non-binary splits but there are likely others. For me, the main use of a non binary split is in d | Are decision trees almost always binary trees?
Regarding uses of decision tree and splitting (binary versus otherwise), I only know of CHAID that has non-binary splits but there are likely others. For me, the main use of a non binary split is in data mining exercises where I am looking at how to optimally bin a nominal... | Are decision trees almost always binary trees?
Regarding uses of decision tree and splitting (binary versus otherwise), I only know of CHAID that has non-binary splits but there are likely others. For me, the main use of a non binary split is in d |
7,243 | Are decision trees almost always binary trees? | Please read this
For practical reasons (combinatorial explosion) most libraries implement decision trees with binary splits. The nice thing is that they are NP-complete (Hyafil, Laurent, and Ronald L. Rivest. "Constructing optimal binary decision trees is NP-complete." Information Processing Letters 5.1 (1976): 15-17.... | Are decision trees almost always binary trees? | Please read this
For practical reasons (combinatorial explosion) most libraries implement decision trees with binary splits. The nice thing is that they are NP-complete (Hyafil, Laurent, and Ronald L | Are decision trees almost always binary trees?
Please read this
For practical reasons (combinatorial explosion) most libraries implement decision trees with binary splits. The nice thing is that they are NP-complete (Hyafil, Laurent, and Ronald L. Rivest. "Constructing optimal binary decision trees is NP-complete." In... | Are decision trees almost always binary trees?
Please read this
For practical reasons (combinatorial explosion) most libraries implement decision trees with binary splits. The nice thing is that they are NP-complete (Hyafil, Laurent, and Ronald L |
7,244 | Are decision trees almost always binary trees? | The Quinlan family of tree models (including the C4.5 you mention) makes higher-arity splits for nominal variables, one branch for each level. | Are decision trees almost always binary trees? | The Quinlan family of tree models (including the C4.5 you mention) makes higher-arity splits for nominal variables, one branch for each level. | Are decision trees almost always binary trees?
The Quinlan family of tree models (including the C4.5 you mention) makes higher-arity splits for nominal variables, one branch for each level. | Are decision trees almost always binary trees?
The Quinlan family of tree models (including the C4.5 you mention) makes higher-arity splits for nominal variables, one branch for each level. |
7,245 | Will the fact that my Italian son is going to attend a primary school change the expected number of Italian children to be present in his class? | As always you need to consider a probabilistic model that describes how the school distributes children among classes. Possibilities:
The school takes care that all classes have the same number of foreign nationals.
The school even tries to make certain that each nationality is represented roughly the same in every cl... | Will the fact that my Italian son is going to attend a primary school change the expected number of | As always you need to consider a probabilistic model that describes how the school distributes children among classes. Possibilities:
The school takes care that all classes have the same number of fo | Will the fact that my Italian son is going to attend a primary school change the expected number of Italian children to be present in his class?
As always you need to consider a probabilistic model that describes how the school distributes children among classes. Possibilities:
The school takes care that all classes h... | Will the fact that my Italian son is going to attend a primary school change the expected number of
As always you need to consider a probabilistic model that describes how the school distributes children among classes. Possibilities:
The school takes care that all classes have the same number of fo |
7,246 | Will the fact that my Italian son is going to attend a primary school change the expected number of Italian children to be present in his class? | Another way to look a this is at the level of individual children. Assuming that 30 children drawn randomly from a population (which you've indicated we can), we can work backward to the rough probability of an Italian child being drawn from this population: $2/30$ = $1/15$.
Given that we know that one of the 30 is Ita... | Will the fact that my Italian son is going to attend a primary school change the expected number of | Another way to look a this is at the level of individual children. Assuming that 30 children drawn randomly from a population (which you've indicated we can), we can work backward to the rough probabi | Will the fact that my Italian son is going to attend a primary school change the expected number of Italian children to be present in his class?
Another way to look a this is at the level of individual children. Assuming that 30 children drawn randomly from a population (which you've indicated we can), we can work back... | Will the fact that my Italian son is going to attend a primary school change the expected number of
Another way to look a this is at the level of individual children. Assuming that 30 children drawn randomly from a population (which you've indicated we can), we can work backward to the rough probabi |
7,247 | Will the fact that my Italian son is going to attend a primary school change the expected number of Italian children to be present in his class? | Here's my thoughts on how to approach this:
Let the random variable $S_n$ denote the number of Italian children in a class that is currently of size $n$. Let $X$ be the indicator for a new child's being Italian. Suppose that we add child $X$ to this class. Then the expected number of Italian children in this augmented... | Will the fact that my Italian son is going to attend a primary school change the expected number of | Here's my thoughts on how to approach this:
Let the random variable $S_n$ denote the number of Italian children in a class that is currently of size $n$. Let $X$ be the indicator for a new child's be | Will the fact that my Italian son is going to attend a primary school change the expected number of Italian children to be present in his class?
Here's my thoughts on how to approach this:
Let the random variable $S_n$ denote the number of Italian children in a class that is currently of size $n$. Let $X$ be the indic... | Will the fact that my Italian son is going to attend a primary school change the expected number of
Here's my thoughts on how to approach this:
Let the random variable $S_n$ denote the number of Italian children in a class that is currently of size $n$. Let $X$ be the indicator for a new child's be |
7,248 | Will the fact that my Italian son is going to attend a primary school change the expected number of Italian children to be present in his class? | Based on the Admission Office info, the number of Italian children follows binomial $\mathrm{Binom}(30, 2/30)$, assuming independence. Now you know in your class, there is at least one Italian child, so the expectation becomes $\mathbb{E}(X|X\geq1)$. For $X\sim \mathrm{Binom}(30, 2/30)$, this evaluates to $2.28$ (if I ... | Will the fact that my Italian son is going to attend a primary school change the expected number of | Based on the Admission Office info, the number of Italian children follows binomial $\mathrm{Binom}(30, 2/30)$, assuming independence. Now you know in your class, there is at least one Italian child, | Will the fact that my Italian son is going to attend a primary school change the expected number of Italian children to be present in his class?
Based on the Admission Office info, the number of Italian children follows binomial $\mathrm{Binom}(30, 2/30)$, assuming independence. Now you know in your class, there is at ... | Will the fact that my Italian son is going to attend a primary school change the expected number of
Based on the Admission Office info, the number of Italian children follows binomial $\mathrm{Binom}(30, 2/30)$, assuming independence. Now you know in your class, there is at least one Italian child, |
7,249 | Will the fact that my Italian son is going to attend a primary school change the expected number of Italian children to be present in his class? | No.
Your knowledge of the impending events changes nothing about the school's typical experience. | Will the fact that my Italian son is going to attend a primary school change the expected number of | No.
Your knowledge of the impending events changes nothing about the school's typical experience. | Will the fact that my Italian son is going to attend a primary school change the expected number of Italian children to be present in his class?
No.
Your knowledge of the impending events changes nothing about the school's typical experience. | Will the fact that my Italian son is going to attend a primary school change the expected number of
No.
Your knowledge of the impending events changes nothing about the school's typical experience. |
7,250 | Am I creating bias by using the same random seed over and over? | There is no bias if the RNG is any good. By always using the same seed you are, however, creating a strong interdependence among all the simulations you perform in your career. This creates an unusual kind of risk.
By using the same seed each time, either you are always getting a pretty nice pseudorandom sequence a... | Am I creating bias by using the same random seed over and over? | There is no bias if the RNG is any good. By always using the same seed you are, however, creating a strong interdependence among all the simulations you perform in your career. This creates an unusu | Am I creating bias by using the same random seed over and over?
There is no bias if the RNG is any good. By always using the same seed you are, however, creating a strong interdependence among all the simulations you perform in your career. This creates an unusual kind of risk.
By using the same seed each time, eit... | Am I creating bias by using the same random seed over and over?
There is no bias if the RNG is any good. By always using the same seed you are, however, creating a strong interdependence among all the simulations you perform in your career. This creates an unusu |
7,251 | Am I creating bias by using the same random seed over and over? | As stated above, a good RNG will not generate bias under from using the same seed. However, there will be a correlation among the results. (The same pseudo-random number will start each computation.) Whether this matters isn't a matter of mathematics.
Using the same seed is OK at times: for debugging or when you know... | Am I creating bias by using the same random seed over and over? | As stated above, a good RNG will not generate bias under from using the same seed. However, there will be a correlation among the results. (The same pseudo-random number will start each computation.) | Am I creating bias by using the same random seed over and over?
As stated above, a good RNG will not generate bias under from using the same seed. However, there will be a correlation among the results. (The same pseudo-random number will start each computation.) Whether this matters isn't a matter of mathematics.
Us... | Am I creating bias by using the same random seed over and over?
As stated above, a good RNG will not generate bias under from using the same seed. However, there will be a correlation among the results. (The same pseudo-random number will start each computation.) |
7,252 | What is a good use of the 'comment' function in R? | To second @Gavin, Frank Harrell has developed efficient ways to handle annotated data.frame in R in his Hmisc package. For example, the label() and units() functions allow to add dedicated attributes to R objects. I find them very handy when producing summary of data.frame (e.g., with describe()).
Another useful way of... | What is a good use of the 'comment' function in R? | To second @Gavin, Frank Harrell has developed efficient ways to handle annotated data.frame in R in his Hmisc package. For example, the label() and units() functions allow to add dedicated attributes | What is a good use of the 'comment' function in R?
To second @Gavin, Frank Harrell has developed efficient ways to handle annotated data.frame in R in his Hmisc package. For example, the label() and units() functions allow to add dedicated attributes to R objects. I find them very handy when producing summary of data.f... | What is a good use of the 'comment' function in R?
To second @Gavin, Frank Harrell has developed efficient ways to handle annotated data.frame in R in his Hmisc package. For example, the label() and units() functions allow to add dedicated attributes |
7,253 | What is a good use of the 'comment' function in R? | One thing I often find myself doing in my R scripts for a particular data analysis task is to include comments in the script about the units of variables in my data frames. I work with environmental data and chemists and ecologists seem to enjoy using a wide range of different units for the same things (mg L$^{-1}$ vs ... | What is a good use of the 'comment' function in R? | One thing I often find myself doing in my R scripts for a particular data analysis task is to include comments in the script about the units of variables in my data frames. I work with environmental d | What is a good use of the 'comment' function in R?
One thing I often find myself doing in my R scripts for a particular data analysis task is to include comments in the script about the units of variables in my data frames. I work with environmental data and chemists and ecologists seem to enjoy using a wide range of d... | What is a good use of the 'comment' function in R?
One thing I often find myself doing in my R scripts for a particular data analysis task is to include comments in the script about the units of variables in my data frames. I work with environmental d |
7,254 | What is a good use of the 'comment' function in R? | Similar facilities exist in other packages, such as the -notes- command in Stata. We use this to document full details of a variable, e.g. details of assay for a biochemical measurement, or exact wording of the question asked for questionnaire data. This is often too much info for the variable name or label, one or bot... | What is a good use of the 'comment' function in R? | Similar facilities exist in other packages, such as the -notes- command in Stata. We use this to document full details of a variable, e.g. details of assay for a biochemical measurement, or exact word | What is a good use of the 'comment' function in R?
Similar facilities exist in other packages, such as the -notes- command in Stata. We use this to document full details of a variable, e.g. details of assay for a biochemical measurement, or exact wording of the question asked for questionnaire data. This is often too m... | What is a good use of the 'comment' function in R?
Similar facilities exist in other packages, such as the -notes- command in Stata. We use this to document full details of a variable, e.g. details of assay for a biochemical measurement, or exact word |
7,255 | What is a good use of the 'comment' function in R? | One of the things I find myself doing a lot is tracking the commands used to generate data and objects, and have found the comment to be a useful tool for this.
The 'matched.call.data' and 'generate.command.string' do the trick. Not perfect, but helpful and a use for 'comment()'. :)
# Comments only accept strings...
#... | What is a good use of the 'comment' function in R? | One of the things I find myself doing a lot is tracking the commands used to generate data and objects, and have found the comment to be a useful tool for this.
The 'matched.call.data' and 'generate.c | What is a good use of the 'comment' function in R?
One of the things I find myself doing a lot is tracking the commands used to generate data and objects, and have found the comment to be a useful tool for this.
The 'matched.call.data' and 'generate.command.string' do the trick. Not perfect, but helpful and a use for ... | What is a good use of the 'comment' function in R?
One of the things I find myself doing a lot is tracking the commands used to generate data and objects, and have found the comment to be a useful tool for this.
The 'matched.call.data' and 'generate.c |
7,256 | What is a good use of the 'comment' function in R? | Allow me to suggest my general solution to object management in R: the repo package. Using it, you can assign each variable a long name, a description, a set of tags, a remote url, dependency relations and also attach figures or generic external files. For example, source code can be stored as a repository item and att... | What is a good use of the 'comment' function in R? | Allow me to suggest my general solution to object management in R: the repo package. Using it, you can assign each variable a long name, a description, a set of tags, a remote url, dependency relation | What is a good use of the 'comment' function in R?
Allow me to suggest my general solution to object management in R: the repo package. Using it, you can assign each variable a long name, a description, a set of tags, a remote url, dependency relations and also attach figures or generic external files. For example, sou... | What is a good use of the 'comment' function in R?
Allow me to suggest my general solution to object management in R: the repo package. Using it, you can assign each variable a long name, a description, a set of tags, a remote url, dependency relation |
7,257 | Bootstrap prediction interval | The method laid out below is the one
described in Section 6.3.3 of Davidson and Hinckley (1997),
Bootstrap Methods and Their Application. Thanks to Glen_b and his
comment here. Given that there were several questions on Cross Validated on this topic, I thought it was worth writing up.
The linear regression model is... | Bootstrap prediction interval | The method laid out below is the one
described in Section 6.3.3 of Davidson and Hinckley (1997),
Bootstrap Methods and Their Application. Thanks to Glen_b and his
comment here. Given that there were | Bootstrap prediction interval
The method laid out below is the one
described in Section 6.3.3 of Davidson and Hinckley (1997),
Bootstrap Methods and Their Application. Thanks to Glen_b and his
comment here. Given that there were several questions on Cross Validated on this topic, I thought it was worth writing up.
... | Bootstrap prediction interval
The method laid out below is the one
described in Section 6.3.3 of Davidson and Hinckley (1997),
Bootstrap Methods and Their Application. Thanks to Glen_b and his
comment here. Given that there were |
7,258 | Bootstrap prediction interval | Consider the much simpler solution than the excelent answer offered by Bill, that following the model based resampling of Sections 6.2.3 and 6.3.3 of Davidson and Hinckley (1997), Bootstrap Methods and Their Application consider X as fixed by design.
Simply add sample(resid(fit.b), size = 1) to the prediction line in S... | Bootstrap prediction interval | Consider the much simpler solution than the excelent answer offered by Bill, that following the model based resampling of Sections 6.2.3 and 6.3.3 of Davidson and Hinckley (1997), Bootstrap Methods an | Bootstrap prediction interval
Consider the much simpler solution than the excelent answer offered by Bill, that following the model based resampling of Sections 6.2.3 and 6.3.3 of Davidson and Hinckley (1997), Bootstrap Methods and Their Application consider X as fixed by design.
Simply add sample(resid(fit.b), size = ... | Bootstrap prediction interval
Consider the much simpler solution than the excelent answer offered by Bill, that following the model based resampling of Sections 6.2.3 and 6.3.3 of Davidson and Hinckley (1997), Bootstrap Methods an |
7,259 | How to use both binary and continuous variables together in clustering? | You are right that k-means clustering should not be done with data of mixed types. Since k-means is essentially a simple search algorithm to find a partition that minimizes the within-cluster squared Euclidean distances between the clustered observations and the cluster centroid, it should only be used with data where... | How to use both binary and continuous variables together in clustering? | You are right that k-means clustering should not be done with data of mixed types. Since k-means is essentially a simple search algorithm to find a partition that minimizes the within-cluster squared | How to use both binary and continuous variables together in clustering?
You are right that k-means clustering should not be done with data of mixed types. Since k-means is essentially a simple search algorithm to find a partition that minimizes the within-cluster squared Euclidean distances between the clustered obser... | How to use both binary and continuous variables together in clustering?
You are right that k-means clustering should not be done with data of mixed types. Since k-means is essentially a simple search algorithm to find a partition that minimizes the within-cluster squared |
7,260 | How to use both binary and continuous variables together in clustering? | Look at this paper by Finch, http://www.jds-online.com/files/JDS-192.pdf. It describes both why applying continuous methods to binary data may inaccurately cluster the data, and more importantly what are some choices in appropriate distance functions. It does not answer how to cluster with k-means, but rather how to ... | How to use both binary and continuous variables together in clustering? | Look at this paper by Finch, http://www.jds-online.com/files/JDS-192.pdf. It describes both why applying continuous methods to binary data may inaccurately cluster the data, and more importantly what | How to use both binary and continuous variables together in clustering?
Look at this paper by Finch, http://www.jds-online.com/files/JDS-192.pdf. It describes both why applying continuous methods to binary data may inaccurately cluster the data, and more importantly what are some choices in appropriate distance functi... | How to use both binary and continuous variables together in clustering?
Look at this paper by Finch, http://www.jds-online.com/files/JDS-192.pdf. It describes both why applying continuous methods to binary data may inaccurately cluster the data, and more importantly what |
7,261 | Internal vs external cross-validation and model selection | Let me add a few points to the nice answers that are already here:
Nested K-fold vs repeated K-fold: nested and repeated k-fold are totally different things, used for different purposes.
As you already know, nested is good if you want to use the inner cv for model selection.
repeated: IMHO you should always repeat ... | Internal vs external cross-validation and model selection | Let me add a few points to the nice answers that are already here:
Nested K-fold vs repeated K-fold: nested and repeated k-fold are totally different things, used for different purposes.
As you alre | Internal vs external cross-validation and model selection
Let me add a few points to the nice answers that are already here:
Nested K-fold vs repeated K-fold: nested and repeated k-fold are totally different things, used for different purposes.
As you already know, nested is good if you want to use the inner cv for m... | Internal vs external cross-validation and model selection
Let me add a few points to the nice answers that are already here:
Nested K-fold vs repeated K-fold: nested and repeated k-fold are totally different things, used for different purposes.
As you alre |
7,262 | Internal vs external cross-validation and model selection | A key reference explaining this is:
@ARTICLE{pic90,
author = {Picard, R. R. and Berk, K. N.},
year = 1990,
title = {Data splitting},
journal = The American Statistician,
volume = 44,
pages = {140-147}
}
See also:
@Article{mic05pre,
author = {Michiels, Stefan and Koscielny, Serge and Hill, Catherine... | Internal vs external cross-validation and model selection | A key reference explaining this is:
@ARTICLE{pic90,
author = {Picard, R. R. and Berk, K. N.},
year = 1990,
title = {Data splitting},
journal = The American Statistician,
volume = 44,
pages | Internal vs external cross-validation and model selection
A key reference explaining this is:
@ARTICLE{pic90,
author = {Picard, R. R. and Berk, K. N.},
year = 1990,
title = {Data splitting},
journal = The American Statistician,
volume = 44,
pages = {140-147}
}
See also:
@Article{mic05pre,
author = ... | Internal vs external cross-validation and model selection
A key reference explaining this is:
@ARTICLE{pic90,
author = {Picard, R. R. and Berk, K. N.},
year = 1990,
title = {Data splitting},
journal = The American Statistician,
volume = 44,
pages |
7,263 | Internal vs external cross-validation and model selection | It really depends on your model building process, but I found this paper helpful
http://www.biomedcentral.com/content/pdf/1471-2105-7-91.pdf
The crux of what is discussed here is the significant liberal bias (estimating model performance to be better than it will actually be) that will occur if you are selecting your m... | Internal vs external cross-validation and model selection | It really depends on your model building process, but I found this paper helpful
http://www.biomedcentral.com/content/pdf/1471-2105-7-91.pdf
The crux of what is discussed here is the significant liber | Internal vs external cross-validation and model selection
It really depends on your model building process, but I found this paper helpful
http://www.biomedcentral.com/content/pdf/1471-2105-7-91.pdf
The crux of what is discussed here is the significant liberal bias (estimating model performance to be better than it wil... | Internal vs external cross-validation and model selection
It really depends on your model building process, but I found this paper helpful
http://www.biomedcentral.com/content/pdf/1471-2105-7-91.pdf
The crux of what is discussed here is the significant liber |
7,264 | Internal vs external cross-validation and model selection | I think your understanding is correct, the estimator for loss obtained by using a single hold-out test set usually has high variance. By performing something like K-folds cross validation you obtain a more accurate idea of the loss, as well as sense of distribution of the loss.
There is usually a tradeoff, the more CV ... | Internal vs external cross-validation and model selection | I think your understanding is correct, the estimator for loss obtained by using a single hold-out test set usually has high variance. By performing something like K-folds cross validation you obtain a | Internal vs external cross-validation and model selection
I think your understanding is correct, the estimator for loss obtained by using a single hold-out test set usually has high variance. By performing something like K-folds cross validation you obtain a more accurate idea of the loss, as well as sense of distribut... | Internal vs external cross-validation and model selection
I think your understanding is correct, the estimator for loss obtained by using a single hold-out test set usually has high variance. By performing something like K-folds cross validation you obtain a |
7,265 | Experimental evidence supporting Tufte-style visualizations? | The literature is vast. Experimental evidence is abundant but incomplete. For an introduction that focuses on the psychological and semiotic investigations, see Alan M. MacEachren, How Maps Work (1995; 2004 in paperback). Jump directly to chapter 9 (near the end) and then work backwards through any preliminary mater... | Experimental evidence supporting Tufte-style visualizations? | The literature is vast. Experimental evidence is abundant but incomplete. For an introduction that focuses on the psychological and semiotic investigations, see Alan M. MacEachren, How Maps Work (19 | Experimental evidence supporting Tufte-style visualizations?
The literature is vast. Experimental evidence is abundant but incomplete. For an introduction that focuses on the psychological and semiotic investigations, see Alan M. MacEachren, How Maps Work (1995; 2004 in paperback). Jump directly to chapter 9 (near t... | Experimental evidence supporting Tufte-style visualizations?
The literature is vast. Experimental evidence is abundant but incomplete. For an introduction that focuses on the psychological and semiotic investigations, see Alan M. MacEachren, How Maps Work (19 |
7,266 | Experimental evidence supporting Tufte-style visualizations? | Here's some;
Cleveland and McGill (1984, JASA) Graphical Perception: Theory, Experimentation, and Application to the Development of Graphical Methods
Cleveland and McGill (1987, JRSSA) Graphical Perception: The Visual Decoding of Quantitative Information on Graphical Displays of Data
Lewandowsky and Spence (1989) Disc... | Experimental evidence supporting Tufte-style visualizations? | Here's some;
Cleveland and McGill (1984, JASA) Graphical Perception: Theory, Experimentation, and Application to the Development of Graphical Methods
Cleveland and McGill (1987, JRSSA) Graphical Perc | Experimental evidence supporting Tufte-style visualizations?
Here's some;
Cleveland and McGill (1984, JASA) Graphical Perception: Theory, Experimentation, and Application to the Development of Graphical Methods
Cleveland and McGill (1987, JRSSA) Graphical Perception: The Visual Decoding of Quantitative Information on ... | Experimental evidence supporting Tufte-style visualizations?
Here's some;
Cleveland and McGill (1984, JASA) Graphical Perception: Theory, Experimentation, and Application to the Development of Graphical Methods
Cleveland and McGill (1987, JRSSA) Graphical Perc |
7,267 | Experimental evidence supporting Tufte-style visualizations? | It's worth remembering that information visualisation isn't some island cut off from all other forms of visual communication. If you want to produce work based on evidence based princples, I'd argue it's best to look where the evidence is strongest.
I've read specific research on data visualisation techniques, and gen... | Experimental evidence supporting Tufte-style visualizations? | It's worth remembering that information visualisation isn't some island cut off from all other forms of visual communication. If you want to produce work based on evidence based princples, I'd argue i | Experimental evidence supporting Tufte-style visualizations?
It's worth remembering that information visualisation isn't some island cut off from all other forms of visual communication. If you want to produce work based on evidence based princples, I'd argue it's best to look where the evidence is strongest.
I've rea... | Experimental evidence supporting Tufte-style visualizations?
It's worth remembering that information visualisation isn't some island cut off from all other forms of visual communication. If you want to produce work based on evidence based princples, I'd argue i |
7,268 | Experimental evidence supporting Tufte-style visualizations? | There was one really good study in the field of cartography (Hegarty et al. (2009): Naïve cartography: How intuitions about display configuration can hurt performance. Published in: Cartographica The International Journal for Geographic Information and Geovisualization 44(3):171-186)
It is especially interesting as the... | Experimental evidence supporting Tufte-style visualizations? | There was one really good study in the field of cartography (Hegarty et al. (2009): Naïve cartography: How intuitions about display configuration can hurt performance. Published in: Cartographica The | Experimental evidence supporting Tufte-style visualizations?
There was one really good study in the field of cartography (Hegarty et al. (2009): Naïve cartography: How intuitions about display configuration can hurt performance. Published in: Cartographica The International Journal for Geographic Information and Geovis... | Experimental evidence supporting Tufte-style visualizations?
There was one really good study in the field of cartography (Hegarty et al. (2009): Naïve cartography: How intuitions about display configuration can hurt performance. Published in: Cartographica The |
7,269 | Benefits of stratified vs random sampling for generating training data in classification | Stratified sampling aims at splitting a data set so that each split is similar with respect to something.
In a classification setting, it is often chosen to ensure that the train and test sets have approximately the same percentage of samples of each target class as the complete set.
As a result, if the data set has a ... | Benefits of stratified vs random sampling for generating training data in classification | Stratified sampling aims at splitting a data set so that each split is similar with respect to something.
In a classification setting, it is often chosen to ensure that the train and test sets have ap | Benefits of stratified vs random sampling for generating training data in classification
Stratified sampling aims at splitting a data set so that each split is similar with respect to something.
In a classification setting, it is often chosen to ensure that the train and test sets have approximately the same percentage... | Benefits of stratified vs random sampling for generating training data in classification
Stratified sampling aims at splitting a data set so that each split is similar with respect to something.
In a classification setting, it is often chosen to ensure that the train and test sets have ap |
7,270 | Why are Gaussian process models called non-parametric? | I'll preface this by saying that it isn't always clear what one means by "nonparametric" or "semiparametric" etc. In the comments, it seems likely that whuber has some formal definition in mind (maybe something like choosing a model $M_\theta$ from some family $\{M_\theta: \theta \in \Theta\}$ where $\Theta$ is infinit... | Why are Gaussian process models called non-parametric? | I'll preface this by saying that it isn't always clear what one means by "nonparametric" or "semiparametric" etc. In the comments, it seems likely that whuber has some formal definition in mind (maybe | Why are Gaussian process models called non-parametric?
I'll preface this by saying that it isn't always clear what one means by "nonparametric" or "semiparametric" etc. In the comments, it seems likely that whuber has some formal definition in mind (maybe something like choosing a model $M_\theta$ from some family $\{M... | Why are Gaussian process models called non-parametric?
I'll preface this by saying that it isn't always clear what one means by "nonparametric" or "semiparametric" etc. In the comments, it seems likely that whuber has some formal definition in mind (maybe |
7,271 | Why are Gaussian process models called non-parametric? | Generally speaking, the "nonparametric" in Bayesian nonparametrics refers to models with an infinite number of (potential) parameters. There are a lot of really nice tutorials and lectures on the subject on videolectures.net (like this one) which give nice overviews of this class of models.
Specifically, the Gaussian P... | Why are Gaussian process models called non-parametric? | Generally speaking, the "nonparametric" in Bayesian nonparametrics refers to models with an infinite number of (potential) parameters. There are a lot of really nice tutorials and lectures on the subj | Why are Gaussian process models called non-parametric?
Generally speaking, the "nonparametric" in Bayesian nonparametrics refers to models with an infinite number of (potential) parameters. There are a lot of really nice tutorials and lectures on the subject on videolectures.net (like this one) which give nice overview... | Why are Gaussian process models called non-parametric?
Generally speaking, the "nonparametric" in Bayesian nonparametrics refers to models with an infinite number of (potential) parameters. There are a lot of really nice tutorials and lectures on the subj |
7,272 | Why are Gaussian process models called non-parametric? | The parameters that you referred to as hyperparameters are not physically motivated parameters and hence the name. They are used to solely parameterize the kernel function. To give an example, in a Gaussian kernel:
$K(x_i,x_j) = h^2 \exp(\frac{-(x_i - x_j)^2}{\lambda^2})$
the $h$ and $\lambda$ are the hyperparameters b... | Why are Gaussian process models called non-parametric? | The parameters that you referred to as hyperparameters are not physically motivated parameters and hence the name. They are used to solely parameterize the kernel function. To give an example, in a Ga | Why are Gaussian process models called non-parametric?
The parameters that you referred to as hyperparameters are not physically motivated parameters and hence the name. They are used to solely parameterize the kernel function. To give an example, in a Gaussian kernel:
$K(x_i,x_j) = h^2 \exp(\frac{-(x_i - x_j)^2}{\lamb... | Why are Gaussian process models called non-parametric?
The parameters that you referred to as hyperparameters are not physically motivated parameters and hence the name. They are used to solely parameterize the kernel function. To give an example, in a Ga |
7,273 | Are inconsistent estimators ever preferable? | This answer describes a realistic problem where a natural consistent estimator is dominated (outperformed for all possible parameter values for all sample sizes) by an inconsistent estimator. It is motivated by the idea that consistency is best suited for quadratic losses, so using a loss departing strongly from that ... | Are inconsistent estimators ever preferable? | This answer describes a realistic problem where a natural consistent estimator is dominated (outperformed for all possible parameter values for all sample sizes) by an inconsistent estimator. It is m | Are inconsistent estimators ever preferable?
This answer describes a realistic problem where a natural consistent estimator is dominated (outperformed for all possible parameter values for all sample sizes) by an inconsistent estimator. It is motivated by the idea that consistency is best suited for quadratic losses, ... | Are inconsistent estimators ever preferable?
This answer describes a realistic problem where a natural consistent estimator is dominated (outperformed for all possible parameter values for all sample sizes) by an inconsistent estimator. It is m |
7,274 | Are inconsistent estimators ever preferable? | Here is a very real situation where an inconsistent estimators is preferable due to constraints on sampling.
I point to a variation of 'Importance Sampling' in Sampling theory would most likely constitute an inconsistent but improved estimator of the sample mean, where the correct percentage weighting of this class is ... | Are inconsistent estimators ever preferable? | Here is a very real situation where an inconsistent estimators is preferable due to constraints on sampling.
I point to a variation of 'Importance Sampling' in Sampling theory would most likely consti | Are inconsistent estimators ever preferable?
Here is a very real situation where an inconsistent estimators is preferable due to constraints on sampling.
I point to a variation of 'Importance Sampling' in Sampling theory would most likely constitute an inconsistent but improved estimator of the sample mean, where the c... | Are inconsistent estimators ever preferable?
Here is a very real situation where an inconsistent estimators is preferable due to constraints on sampling.
I point to a variation of 'Importance Sampling' in Sampling theory would most likely consti |
7,275 | Are inconsistent estimators ever preferable? | More specifically, are there examples of an inconsistent estimator
which outperforms a reasonable consistent estimator for all finite n
(with respect to some suitable loss function)?
Yes there are, and probably are more simpler and usual than you think. Moreover complex or unusual loss functions are not needed abo... | Are inconsistent estimators ever preferable? | More specifically, are there examples of an inconsistent estimator
which outperforms a reasonable consistent estimator for all finite n
(with respect to some suitable loss function)?
Yes there ar | Are inconsistent estimators ever preferable?
More specifically, are there examples of an inconsistent estimator
which outperforms a reasonable consistent estimator for all finite n
(with respect to some suitable loss function)?
Yes there are, and probably are more simpler and usual than you think. Moreover complex... | Are inconsistent estimators ever preferable?
More specifically, are there examples of an inconsistent estimator
which outperforms a reasonable consistent estimator for all finite n
(with respect to some suitable loss function)?
Yes there ar |
7,276 | Are inconsistent estimators ever preferable? | I can't comment, so I will add this as an answer. Whuber answer is just showing that one specific inconsistent estimator can be better than another specific consistent estimator. Since the questions was: "are there examples of an inconsistent estimator which outperforms a reasonable consistent estimator for all finite ... | Are inconsistent estimators ever preferable? | I can't comment, so I will add this as an answer. Whuber answer is just showing that one specific inconsistent estimator can be better than another specific consistent estimator. Since the questions w | Are inconsistent estimators ever preferable?
I can't comment, so I will add this as an answer. Whuber answer is just showing that one specific inconsistent estimator can be better than another specific consistent estimator. Since the questions was: "are there examples of an inconsistent estimator which outperforms a re... | Are inconsistent estimators ever preferable?
I can't comment, so I will add this as an answer. Whuber answer is just showing that one specific inconsistent estimator can be better than another specific consistent estimator. Since the questions w |
7,277 | Equivalence between least squares and MLE in Gaussian model | In the model
$ Y = X \beta + \epsilon $
where $\epsilon \sim N(0,\sigma^{2})$, the loglikelihood of $Y|X$ for a sample of $n$ subjects is (up to a additive constant)
$$ \frac{-n}{2} \log(\sigma^{2}) - \frac{1}{2 \sigma^{2}} \sum_{i=1}^{n} (y_{i}-x_{i} \beta)^{2} $$
viewed as a function of only $\beta$, the maximizer... | Equivalence between least squares and MLE in Gaussian model | In the model
$ Y = X \beta + \epsilon $
where $\epsilon \sim N(0,\sigma^{2})$, the loglikelihood of $Y|X$ for a sample of $n$ subjects is (up to a additive constant)
$$ \frac{-n}{2} \log(\sigma^{2}) | Equivalence between least squares and MLE in Gaussian model
In the model
$ Y = X \beta + \epsilon $
where $\epsilon \sim N(0,\sigma^{2})$, the loglikelihood of $Y|X$ for a sample of $n$ subjects is (up to a additive constant)
$$ \frac{-n}{2} \log(\sigma^{2}) - \frac{1}{2 \sigma^{2}} \sum_{i=1}^{n} (y_{i}-x_{i} \beta)... | Equivalence between least squares and MLE in Gaussian model
In the model
$ Y = X \beta + \epsilon $
where $\epsilon \sim N(0,\sigma^{2})$, the loglikelihood of $Y|X$ for a sample of $n$ subjects is (up to a additive constant)
$$ \frac{-n}{2} \log(\sigma^{2}) |
7,278 | Does Cox Regression have an underlying Poisson distribution? | Yes, there is a link between these two regression models. Here is an illustration:
Suppose the baseline hazard is constant over time: $h_{0}(t) = \lambda$. In that case, the survival function is
$S(t) = \exp\left(-\int_{0}^{t} \lambda du\right) = \exp(-\lambda t)$
and the density function is
$f(t) = h(t) S(t) = \lambda... | Does Cox Regression have an underlying Poisson distribution? | Yes, there is a link between these two regression models. Here is an illustration:
Suppose the baseline hazard is constant over time: $h_{0}(t) = \lambda$. In that case, the survival function is
$S(t) | Does Cox Regression have an underlying Poisson distribution?
Yes, there is a link between these two regression models. Here is an illustration:
Suppose the baseline hazard is constant over time: $h_{0}(t) = \lambda$. In that case, the survival function is
$S(t) = \exp\left(-\int_{0}^{t} \lambda du\right) = \exp(-\lambd... | Does Cox Regression have an underlying Poisson distribution?
Yes, there is a link between these two regression models. Here is an illustration:
Suppose the baseline hazard is constant over time: $h_{0}(t) = \lambda$. In that case, the survival function is
$S(t) |
7,279 | Why Beta/Dirichlet Regression are not considered Generalized Linear Models? | Check the original reference:
Ferrari, S., & Cribari-Neto, F. (2004). Beta regression for modelling
rates and proportions. Journal of Applied Statistics, 31(7), 799-815.
as the authors note, the parameters of re-parametrized beta distribution are correlated, so
Note that the parameters $\beta$ and $\phi$ are not o... | Why Beta/Dirichlet Regression are not considered Generalized Linear Models? | Check the original reference:
Ferrari, S., & Cribari-Neto, F. (2004). Beta regression for modelling
rates and proportions. Journal of Applied Statistics, 31(7), 799-815.
as the authors note, the p | Why Beta/Dirichlet Regression are not considered Generalized Linear Models?
Check the original reference:
Ferrari, S., & Cribari-Neto, F. (2004). Beta regression for modelling
rates and proportions. Journal of Applied Statistics, 31(7), 799-815.
as the authors note, the parameters of re-parametrized beta distributi... | Why Beta/Dirichlet Regression are not considered Generalized Linear Models?
Check the original reference:
Ferrari, S., & Cribari-Neto, F. (2004). Beta regression for modelling
rates and proportions. Journal of Applied Statistics, 31(7), 799-815.
as the authors note, the p |
7,280 | Why Beta/Dirichlet Regression are not considered Generalized Linear Models? | The answer by @probabilityislogic is on the right track.
The beta distribution is in the two parameter exponential family. The simple GLM models described by Nelder and Wedderburn (1972) do not include all of the distributions in the two parameter exponential family.
In terms of the article by N&W, the GLM applies to t... | Why Beta/Dirichlet Regression are not considered Generalized Linear Models? | The answer by @probabilityislogic is on the right track.
The beta distribution is in the two parameter exponential family. The simple GLM models described by Nelder and Wedderburn (1972) do not includ | Why Beta/Dirichlet Regression are not considered Generalized Linear Models?
The answer by @probabilityislogic is on the right track.
The beta distribution is in the two parameter exponential family. The simple GLM models described by Nelder and Wedderburn (1972) do not include all of the distributions in the two parame... | Why Beta/Dirichlet Regression are not considered Generalized Linear Models?
The answer by @probabilityislogic is on the right track.
The beta distribution is in the two parameter exponential family. The simple GLM models described by Nelder and Wedderburn (1972) do not includ |
7,281 | Why Beta/Dirichlet Regression are not considered Generalized Linear Models? | I don't think the beta distribution is part of the exponential dispersion family. To get this, you need to have a density
$$f (y;\theta,\tau)=\exp\left (\frac {y\theta - c (\theta)}{\tau} + d (y,\tau)\right)$$
for specified functions $c ()$ and $d () $. The mean is given as $ c'(\theta)$ and the variance is given as $\... | Why Beta/Dirichlet Regression are not considered Generalized Linear Models? | I don't think the beta distribution is part of the exponential dispersion family. To get this, you need to have a density
$$f (y;\theta,\tau)=\exp\left (\frac {y\theta - c (\theta)}{\tau} + d (y,\tau) | Why Beta/Dirichlet Regression are not considered Generalized Linear Models?
I don't think the beta distribution is part of the exponential dispersion family. To get this, you need to have a density
$$f (y;\theta,\tau)=\exp\left (\frac {y\theta - c (\theta)}{\tau} + d (y,\tau)\right)$$
for specified functions $c ()$ and... | Why Beta/Dirichlet Regression are not considered Generalized Linear Models?
I don't think the beta distribution is part of the exponential dispersion family. To get this, you need to have a density
$$f (y;\theta,\tau)=\exp\left (\frac {y\theta - c (\theta)}{\tau} + d (y,\tau) |
7,282 | What are the most useful sources of economics data? | For the US:
FRED: Federal Reserve Economic Data (the best)
Bureau of Labor Statistics
Bureau of Economic Analysis
U.S. Census | What are the most useful sources of economics data? | For the US:
FRED: Federal Reserve Economic Data (the best)
Bureau of Labor Statistics
Bureau of Economic Analysis
U.S. Census | What are the most useful sources of economics data?
For the US:
FRED: Federal Reserve Economic Data (the best)
Bureau of Labor Statistics
Bureau of Economic Analysis
U.S. Census | What are the most useful sources of economics data?
For the US:
FRED: Federal Reserve Economic Data (the best)
Bureau of Labor Statistics
Bureau of Economic Analysis
U.S. Census |
7,283 | What are the most useful sources of economics data? | The World Bank data API is particularly good and I wish that more global and state-level organisations would release this much. Here are a few more to complement @check123:
UK government data project;
US government data project;
Infochimps - massive resource of a wide variety of public and private (commercial) dataso... | What are the most useful sources of economics data? | The World Bank data API is particularly good and I wish that more global and state-level organisations would release this much. Here are a few more to complement @check123:
UK government data projec | What are the most useful sources of economics data?
The World Bank data API is particularly good and I wish that more global and state-level organisations would release this much. Here are a few more to complement @check123:
UK government data project;
US government data project;
Infochimps - massive resource of a wi... | What are the most useful sources of economics data?
The World Bank data API is particularly good and I wish that more global and state-level organisations would release this much. Here are a few more to complement @check123:
UK government data projec |
7,284 | What are the most useful sources of economics data? | In addition to what you've got already, there's http://www.zanran.com/q/ - a search-engine dedicated to numerical data | What are the most useful sources of economics data? | In addition to what you've got already, there's http://www.zanran.com/q/ - a search-engine dedicated to numerical data | What are the most useful sources of economics data?
In addition to what you've got already, there's http://www.zanran.com/q/ - a search-engine dedicated to numerical data | What are the most useful sources of economics data?
In addition to what you've got already, there's http://www.zanran.com/q/ - a search-engine dedicated to numerical data |
7,285 | What are the most useful sources of economics data? | Local/Foreign governments:
Data from Finance Ministry and its bodies
Reserve Bank
Official publication of annual accounts of the country
Academic Sources:
Research papers and journals
Internal archives of universities and institutions
Dedicated policy and welfare research centers
Theory/Text books often have further... | What are the most useful sources of economics data? | Local/Foreign governments:
Data from Finance Ministry and its bodies
Reserve Bank
Official publication of annual accounts of the country
Academic Sources:
Research papers and journals
Internal arch | What are the most useful sources of economics data?
Local/Foreign governments:
Data from Finance Ministry and its bodies
Reserve Bank
Official publication of annual accounts of the country
Academic Sources:
Research papers and journals
Internal archives of universities and institutions
Dedicated policy and welfare r... | What are the most useful sources of economics data?
Local/Foreign governments:
Data from Finance Ministry and its bodies
Reserve Bank
Official publication of annual accounts of the country
Academic Sources:
Research papers and journals
Internal arch |
7,286 | What are the most useful sources of economics data? | The U.S. Census Bureau was one of the first government agencies to put data on the web. I still remember the elation I felt back in 1995 when I found out I could get up to date CPS reports and data online instead of having to go through library shelves. They provide both summary tables and public use microdata.
Similar... | What are the most useful sources of economics data? | The U.S. Census Bureau was one of the first government agencies to put data on the web. I still remember the elation I felt back in 1995 when I found out I could get up to date CPS reports and data on | What are the most useful sources of economics data?
The U.S. Census Bureau was one of the first government agencies to put data on the web. I still remember the elation I felt back in 1995 when I found out I could get up to date CPS reports and data online instead of having to go through library shelves. They provide b... | What are the most useful sources of economics data?
The U.S. Census Bureau was one of the first government agencies to put data on the web. I still remember the elation I felt back in 1995 when I found out I could get up to date CPS reports and data on |
7,287 | What are the most useful sources of economics data? | Rescued from a deleted answer:
If you are interested in the European Union or in some of its member states, you can have a look at Eurostat's databases. | What are the most useful sources of economics data? | Rescued from a deleted answer:
If you are interested in the European Union or in some of its member states, you can have a look at Eurostat's databases. | What are the most useful sources of economics data?
Rescued from a deleted answer:
If you are interested in the European Union or in some of its member states, you can have a look at Eurostat's databases. | What are the most useful sources of economics data?
Rescued from a deleted answer:
If you are interested in the European Union or in some of its member states, you can have a look at Eurostat's databases. |
7,288 | What are the most useful sources of economics data? | Don't forget http://www.icpsr.umich.edu/ | What are the most useful sources of economics data? | Don't forget http://www.icpsr.umich.edu/ | What are the most useful sources of economics data?
Don't forget http://www.icpsr.umich.edu/ | What are the most useful sources of economics data?
Don't forget http://www.icpsr.umich.edu/ |
7,289 | What are the most useful sources of economics data? | For macroeconomic and financial data, Quandl is a great resource, because it effectively acts as a wrapper around many of the excellent sources mentioned here, and many others.
What is more library(Quandl) makes accessing the data in R gratifyingly simple. | What are the most useful sources of economics data? | For macroeconomic and financial data, Quandl is a great resource, because it effectively acts as a wrapper around many of the excellent sources mentioned here, and many others.
What is more library(Qu | What are the most useful sources of economics data?
For macroeconomic and financial data, Quandl is a great resource, because it effectively acts as a wrapper around many of the excellent sources mentioned here, and many others.
What is more library(Quandl) makes accessing the data in R gratifyingly simple. | What are the most useful sources of economics data?
For macroeconomic and financial data, Quandl is a great resource, because it effectively acts as a wrapper around many of the excellent sources mentioned here, and many others.
What is more library(Qu |
7,290 | What are the most useful sources of economics data? | If you're looking for free monthly global economic indicators to download, have a look at the database on the blog www.morethanbrics.com/blog. They publish a monthly database for up to 169 countries since 1995. I like it because you can download the whole excel file for free and it's updated on a monthly basis. It's ba... | What are the most useful sources of economics data? | If you're looking for free monthly global economic indicators to download, have a look at the database on the blog www.morethanbrics.com/blog. They publish a monthly database for up to 169 countries s | What are the most useful sources of economics data?
If you're looking for free monthly global economic indicators to download, have a look at the database on the blog www.morethanbrics.com/blog. They publish a monthly database for up to 169 countries since 1995. I like it because you can download the whole excel file f... | What are the most useful sources of economics data?
If you're looking for free monthly global economic indicators to download, have a look at the database on the blog www.morethanbrics.com/blog. They publish a monthly database for up to 169 countries s |
7,291 | What are the most useful sources of economics data? | There are very related questions in the Economics and quant stacks:
https://economics.stackexchange.com/questions/4679/what-are-some-good-repositories-for-economic-data
https://quant.stackexchange.com/questions/141/what-data-sources-are-available-online
Answers from there: The American Economic Association has a list o... | What are the most useful sources of economics data? | There are very related questions in the Economics and quant stacks:
https://economics.stackexchange.com/questions/4679/what-are-some-good-repositories-for-economic-data
https://quant.stackexchange.com | What are the most useful sources of economics data?
There are very related questions in the Economics and quant stacks:
https://economics.stackexchange.com/questions/4679/what-are-some-good-repositories-for-economic-data
https://quant.stackexchange.com/questions/141/what-data-sources-are-available-online
Answers from t... | What are the most useful sources of economics data?
There are very related questions in the Economics and quant stacks:
https://economics.stackexchange.com/questions/4679/what-are-some-good-repositories-for-economic-data
https://quant.stackexchange.com |
7,292 | What is the difference between Conv1D and Conv2D? | I'd like to explain the difference visually and in detail(comments in code) and in a very easy approach.
Let's first check the Conv2D in TensorFlow.
c1 = [[0, 0, 1, 0, 2], [1, 0, 2, 0, 1], [1, 0, 2, 2, 0], [2, 0, 0, 2, 0], [2, 1, 2, 2, 0]]
c2 = [[2, 1, 2, 1, 1], [2, 1, 2, 0, 1], [0, 2, 1, 0, 1], [1, 2, 2, 2, 2], [0, 1... | What is the difference between Conv1D and Conv2D? | I'd like to explain the difference visually and in detail(comments in code) and in a very easy approach.
Let's first check the Conv2D in TensorFlow.
c1 = [[0, 0, 1, 0, 2], [1, 0, 2, 0, 1], [1, 0, 2, | What is the difference between Conv1D and Conv2D?
I'd like to explain the difference visually and in detail(comments in code) and in a very easy approach.
Let's first check the Conv2D in TensorFlow.
c1 = [[0, 0, 1, 0, 2], [1, 0, 2, 0, 1], [1, 0, 2, 2, 0], [2, 0, 0, 2, 0], [2, 1, 2, 2, 0]]
c2 = [[2, 1, 2, 1, 1], [2, 1,... | What is the difference between Conv1D and Conv2D?
I'd like to explain the difference visually and in detail(comments in code) and in a very easy approach.
Let's first check the Conv2D in TensorFlow.
c1 = [[0, 0, 1, 0, 2], [1, 0, 2, 0, 1], [1, 0, 2, |
7,293 | What is the difference between Conv1D and Conv2D? | Convolution is a mathematical operation where you "summarize" a tensor or a matrix or a vector into a smaller one. If your input matrix is one dimensional then you summarize along that on dimensions, and if a tensor has n dimensions then you could summarize along all n dimensions. Conv1D and Conv2D summarize (convolve)... | What is the difference between Conv1D and Conv2D? | Convolution is a mathematical operation where you "summarize" a tensor or a matrix or a vector into a smaller one. If your input matrix is one dimensional then you summarize along that on dimensions, | What is the difference between Conv1D and Conv2D?
Convolution is a mathematical operation where you "summarize" a tensor or a matrix or a vector into a smaller one. If your input matrix is one dimensional then you summarize along that on dimensions, and if a tensor has n dimensions then you could summarize along all n ... | What is the difference between Conv1D and Conv2D?
Convolution is a mathematical operation where you "summarize" a tensor or a matrix or a vector into a smaller one. If your input matrix is one dimensional then you summarize along that on dimensions, |
7,294 | What is the difference between Conv1D and Conv2D? | I will be using a Pytorch perspective, however, the logic remains the same.
When using Conv1d(), we have to keep in mind that we are most likely going to work with 2-dimensional inputs such as one-hot-encode DNA sequences or black and white pictures.
The only difference between the more conventional Conv2d() and Conv1d... | What is the difference between Conv1D and Conv2D? | I will be using a Pytorch perspective, however, the logic remains the same.
When using Conv1d(), we have to keep in mind that we are most likely going to work with 2-dimensional inputs such as one-hot | What is the difference between Conv1D and Conv2D?
I will be using a Pytorch perspective, however, the logic remains the same.
When using Conv1d(), we have to keep in mind that we are most likely going to work with 2-dimensional inputs such as one-hot-encode DNA sequences or black and white pictures.
The only difference... | What is the difference between Conv1D and Conv2D?
I will be using a Pytorch perspective, however, the logic remains the same.
When using Conv1d(), we have to keep in mind that we are most likely going to work with 2-dimensional inputs such as one-hot |
7,295 | What is the difference between Conv1D and Conv2D? | In summary, In 1D CNN, kernel moves in 1 direction. Input and output data of 1D CNN is 2 dimensional. Mostly used on Time-Series data.
In 2D CNN, kernel moves in 2 directions. Input and output data of 2D CNN is 3 dimensional. Mostly used on Image data.
In 3D CNN, kernel moves in 3 directions. Input and output data of 3... | What is the difference between Conv1D and Conv2D? | In summary, In 1D CNN, kernel moves in 1 direction. Input and output data of 1D CNN is 2 dimensional. Mostly used on Time-Series data.
In 2D CNN, kernel moves in 2 directions. Input and output data of | What is the difference between Conv1D and Conv2D?
In summary, In 1D CNN, kernel moves in 1 direction. Input and output data of 1D CNN is 2 dimensional. Mostly used on Time-Series data.
In 2D CNN, kernel moves in 2 directions. Input and output data of 2D CNN is 3 dimensional. Mostly used on Image data.
In 3D CNN, kernel... | What is the difference between Conv1D and Conv2D?
In summary, In 1D CNN, kernel moves in 1 direction. Input and output data of 1D CNN is 2 dimensional. Mostly used on Time-Series data.
In 2D CNN, kernel moves in 2 directions. Input and output data of |
7,296 | What is the difference between Conv1D and Conv2D? | This 1d convolution is cost saver, it work in the same way but assume a 1 dimension array that makes a multiplication with the elements. If you want to visualize think of a matrix of either row or columns i.e a single dimension when we multiplies we get an array of same shape but of lower or higher values, thus it help... | What is the difference between Conv1D and Conv2D? | This 1d convolution is cost saver, it work in the same way but assume a 1 dimension array that makes a multiplication with the elements. If you want to visualize think of a matrix of either row or col | What is the difference between Conv1D and Conv2D?
This 1d convolution is cost saver, it work in the same way but assume a 1 dimension array that makes a multiplication with the elements. If you want to visualize think of a matrix of either row or columns i.e a single dimension when we multiplies we get an array of same... | What is the difference between Conv1D and Conv2D?
This 1d convolution is cost saver, it work in the same way but assume a 1 dimension array that makes a multiplication with the elements. If you want to visualize think of a matrix of either row or col |
7,297 | Origin of "5$\sigma$" threshold for accepting evidence in particle physics? | History and origin
According to Robert D Cousins$^{1}$ and Tommaso Dorigo$^{2}$, the origin of the $5\sigma$ threshold origin lies in the early particle physics work of the 60s when numerous histograms of scattering experiments were investigated and searched for peaks/bumps that might indicate some newly discovered par... | Origin of "5$\sigma$" threshold for accepting evidence in particle physics? | History and origin
According to Robert D Cousins$^{1}$ and Tommaso Dorigo$^{2}$, the origin of the $5\sigma$ threshold origin lies in the early particle physics work of the 60s when numerous histogram | Origin of "5$\sigma$" threshold for accepting evidence in particle physics?
History and origin
According to Robert D Cousins$^{1}$ and Tommaso Dorigo$^{2}$, the origin of the $5\sigma$ threshold origin lies in the early particle physics work of the 60s when numerous histograms of scattering experiments were investigate... | Origin of "5$\sigma$" threshold for accepting evidence in particle physics?
History and origin
According to Robert D Cousins$^{1}$ and Tommaso Dorigo$^{2}$, the origin of the $5\sigma$ threshold origin lies in the early particle physics work of the 60s when numerous histogram |
7,298 | Origin of "5$\sigma$" threshold for accepting evidence in particle physics? | In most applications of statistics there is that old chestnut about 'all models are wrong, some are useful'. This being the case, we would only expected a model to perform at a given level since we are describing some incredibly complicated process using some simple model.
Physics is very different, so intuition develo... | Origin of "5$\sigma$" threshold for accepting evidence in particle physics? | In most applications of statistics there is that old chestnut about 'all models are wrong, some are useful'. This being the case, we would only expected a model to perform at a given level since we ar | Origin of "5$\sigma$" threshold for accepting evidence in particle physics?
In most applications of statistics there is that old chestnut about 'all models are wrong, some are useful'. This being the case, we would only expected a model to perform at a given level since we are describing some incredibly complicated pro... | Origin of "5$\sigma$" threshold for accepting evidence in particle physics?
In most applications of statistics there is that old chestnut about 'all models are wrong, some are useful'. This being the case, we would only expected a model to perform at a given level since we ar |
7,299 | Origin of "5$\sigma$" threshold for accepting evidence in particle physics? | For a reason entirely different from that of physics, there are other fields with much more strict alphas when they engage in hypothesis testing. Genetic Epidemiology is among them, especially when they use "GWAS" (Genome-Wide Association Study) to look at various genetic markers for disease.
Because a GWAS study is a ... | Origin of "5$\sigma$" threshold for accepting evidence in particle physics? | For a reason entirely different from that of physics, there are other fields with much more strict alphas when they engage in hypothesis testing. Genetic Epidemiology is among them, especially when th | Origin of "5$\sigma$" threshold for accepting evidence in particle physics?
For a reason entirely different from that of physics, there are other fields with much more strict alphas when they engage in hypothesis testing. Genetic Epidemiology is among them, especially when they use "GWAS" (Genome-Wide Association Study... | Origin of "5$\sigma$" threshold for accepting evidence in particle physics?
For a reason entirely different from that of physics, there are other fields with much more strict alphas when they engage in hypothesis testing. Genetic Epidemiology is among them, especially when th |
7,300 | Origin of "5$\sigma$" threshold for accepting evidence in particle physics? | The level is so high to avoid premature announcements of news that later turns out to be spurious. For more discussion on this, see
https://physics.stackexchange.com/questions/8752/standard-deviation-in-particle-physics?rq=1
https://physics.stackexchange.com/questions/31126/how-many-sigma-did-the-discovery-of-the-w-bos... | Origin of "5$\sigma$" threshold for accepting evidence in particle physics? | The level is so high to avoid premature announcements of news that later turns out to be spurious. For more discussion on this, see
https://physics.stackexchange.com/questions/8752/standard-deviation- | Origin of "5$\sigma$" threshold for accepting evidence in particle physics?
The level is so high to avoid premature announcements of news that later turns out to be spurious. For more discussion on this, see
https://physics.stackexchange.com/questions/8752/standard-deviation-in-particle-physics?rq=1
https://physics.sta... | Origin of "5$\sigma$" threshold for accepting evidence in particle physics?
The level is so high to avoid premature announcements of news that later turns out to be spurious. For more discussion on this, see
https://physics.stackexchange.com/questions/8752/standard-deviation- |
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