<p>The library <a href="https://www.tensorflow.org/probability" rel="nofollow noreferrer">TensorFlow Probability</a> is designed for this purpose. In fact, the first example currently at the web site involves the creation of synthetic data which is then used for a regression example:</p>
<pre><code>import tensorflow as tf
import tensorflow_probability as tfp

# Pretend to load synthetic data set.
features = tfp.distributions.Normal(loc=0., scale=1.).sample(int(100e3))
labels = tfp.distributions.Bernoulli(logits=1.618 * features).sample()

# Specify model.
model = tfp.glm.Bernoulli()

# Fit model given data.
coeffs, linear_response, is_converged, num_iter = tfp.glm.fit(
    model_matrix=features[:, tf.newaxis],
    response=tf.cast(labels, dtype=tf.float32),
    model=model)
# ==&gt; coeffs is approximately [1.618] (We're golden!)
</code></pre>

CC BY-SA 4.0
2022-11-18T19:26:03.457Z
2022-11-18T19:26:03.457Z
Dan Piponi
<p><strong>YES</strong></p>
<p>I’ll give an example in R.</p>
<pre><code>set.seed(2022)

# Set sample size
#
N &lt;- 100

# Declare some regression feature
#
x &lt;- seq(1, 100, 1)

# Define the outcome variable, using a
# random normal error term (this is 
# the Monte Carlo part)
#
y &lt;- 1 - x + rnorm(N)
</code></pre>
<p>Now your have a synthetic data set and can run a regression, for instance.</p>
<p>An example of where this might be useful is if you develop a new hypothesis test for a regression coefficient and want to see how it performs when the null hypothesis is true. Thus, you loop through <span class="math-container">$1000$</span> regression simulations like this and hypothesis test each time, collecting the p-value of each hypothesis test.</p>
<pre><code>set.seed(2022)
N &lt;- 100
R &lt;- 1000
ps &lt;- rep(NA, R)
x &lt;- seq(1, N, 1)
for (i in 1:R){

    y &lt;- 1 + rnorm(N) # zero slope coefficient 
    L &lt;- lm(y ~ x)
    ps[i] &lt;- summary(L)$coef[2, 4] # extract p-value of t-testing slope 

}

plot(
    ps, 
    ecdf(ps)(ps),
    xlab = &quot;p-value&quot;,
    ylab = &quot;quantile&quot;
    )
abline(0, 1)
</code></pre>
<p>If you were the inventor of the t-test used here, you would see that your test gives uniform p-values under the null hypothesis of zero slope (exactly the desired behavior).</p>
<p><a href="https://i.sstatic.net/fEHOj.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/fEHOj.png" alt="enter image description here" /></a></p>

CC BY-SA 4.0
2022-11-18T11:46:32.373Z
2022-11-19T11:44:54.750Z
2022-11-19T11:44:54.750Z
Dave
<p>I am aware that Monte-Carlo Simulation is used for making accurate assumptions by introducing randomness. But can it be used to synthesize or create a dataset? If yes, can someone share an example?</p>

<econometrics><mathematical-economics><data><portfolio-theory>
Can data be created using Monte Carlo Simulation
Marmik Pancholi
# Can data be created using Monte Carlo Simulation

(Asked by: username_0 on 2022-11-18)

I am aware that Monte-Carlo Simulation is used for making accurate assumptions by introducing randomness. But can it be used to synthesize or create a dataset? If yes, can someone share an example?

**Tags:** econometrics, mathematical-economics, data, portfolio-theory

---

## 2 answers

### Answer by username_2 on 2022-11-18. Score: 5 | Accepted answer

YES
I’ll give an example in R.
set.seed(2022)

# Set sample size
#
N <- 100

# Declare some regression feature
#
x <- seq(1, 100, 1)

# Define the outcome variable, using a
# random normal error term (this is 
# the Monte Carlo part)
#
y <- 1 - x + rnorm(N)

Now your have a synthetic data set and can run a regression, for instance.
An example of where this might be useful is if you develop a new hypothesis test for a regression coefficient and want to see how it performs when the null hypothesis is true. Thus, you loop through $1000$ regression simulations like this and hypothesis test each time, collecting the p-value of each hypothesis test.
set.seed(2022)
N <- 100
R <- 1000
ps <- rep(NA, R)
x <- seq(1, N, 1)
for (i in 1:R){

    y <- 1 + rnorm(N) # zero slope coefficient 
    L <- lm(y ~ x)
    ps[i] <- summary(L)$coef[2, 4] # extract p-value of t-testing slope 

}

plot(
    ps, 
    ecdf(ps)(ps),
    xlab = "p-value",
    ylab = "quantile"
    )
abline(0, 1)

If you were the inventor of the t-test used here, you would see that your test gives uniform p-values under the null hypothesis of zero slope (exactly the desired behavior).


---

### Answer by username_1 on 2022-11-18. Score: 3

The library TensorFlow Probability is designed for this purpose. In fact, the first example currently at the web site involves the creation of synthetic data which is then used for a regression example:
import tensorflow as tf
import tensorflow_probability as tfp

# Pretend to load synthetic data set.
features = tfp.distributions.Normal(loc=0., scale=1.).sample(int(100e3))
labels = tfp.distributions.Bernoulli(logits=1.618 * features).sample()

# Specify model.
model = tfp.glm.Bernoulli()

# Fit model given data.
coeffs, linear_response, is_converged, num_iter = tfp.glm.fit(
    model_matrix=features[:, tf.newaxis],
    response=tf.cast(labels, dtype=tf.float32),
    model=model)
# ==> coeffs is approximately [1.618] (We're golden!)


---

