| xvi |
If you have a good understanding of statistics, either by practice or formal training, but you have never being ... |
If you have a good understanding of statistics, either by practice or formal training, but you have never being... |
Thanks Behrouz B. |
| xvi |
...and may require a couple read troughs
|
...and may require a couple read-throughs
|
Thanks John M. Shea |
| xvi |
For a reference on Python, or how to setup the computation environment needed for this book, go to README.md in Github to understand how to setup a code environment |
For a reference on how to setup the computation environment needed for this book, go to README.md in GitHhub. |
|
| 1 |
...we introduce these concepts and methods, many, which... |
...we introduce these concepts and methods, many of which... |
Thanks Thomas Ogden |
| 2 |
...though this is not a guaranteed of any Bayesian model. |
...though this is not a guarantee of any Bayesian model. |
Thanks Guilherme Costa |
| 7 |
...(conceptually it means it is equally likely are we are... |
...(conceptually it means it is equally likely we are... |
Thanks Behrouz B. |
| 8 |
At line 20.... |
At line 14... |
Thanks Behrouz B. |
| 8 |
...it will depends on the result... |
...it will depend on the result.. |
Thanks Ero Carrera |
| 9 |
Some people make the distinction that a sample is made up by a collection of draws, other... |
Some people make the distinction that a sample is made up by a collection of draws, others... |
Thanks Behrouz B. |
| 9 |
...or simple the posterior. |
...or simply the posterior. |
Thanks Ero Carrera |
| 23 |
An absolute value mean... |
An absolute deviation to the mean... |
Thanks Zhengchen Cai |
| 24 |
One is what could called... |
One is what could be called... |
Thanks Sebastian |
| 26 |
1E8. Rerun Code block |
1E8. Rerun Code Block |
|
| 27 |
Which can can be used to to visualize a Highest Density Interval? |
Which can can be used to visualize a Highest Density Interval? |
|
| 28 |
Build a model that will make these estimation. |
Build a model that will make this estimation. |
|
| 28 |
Determine two prior distribution that satisfy these constraints using Python. |
Determine two prior distributions that satisfy these constraints using Python. |
|
| 31 |
In this chapter we will discuss some of these tasks including**,** checking ... results and model comparison |
In this chapter we will discuss some of these tasks**,** including checking ... results**,** and model comparison |
Thanks Sebastian |
| 42 |
Plotting the ESS for specifics quantiles az.plot_ess(., kind="quantiles"
|
Plotting the ESS for specifics quantiles az.plot_ess(., kind="quantiles") |
Thanks Juan Orduz |
| 49 |
...which means model_0 specified a posterior... |
...which means model_0 specifies a posterior... |
Thanks Sebastian |
| 51 |
Thus increasing the turning steps can help to increase the ESS... |
Thus increasing the tuning steps can help to increase the ESS... |
Thanks Ero Carrera |
| 52 |
where $p_t(\tilde y_i)$ is distribution of the true data-generating process... |
where $p_t(\tilde y_i)$ is the distribution of the true data-generating process... |
Thanks Ero Carrera |
| 52 |
...and it is use in both Bayesians and non-Bayesians contexts. |
...and it is used in both Bayesians and non-Bayesians contexts. |
Thanks Sebastian |
| 53 |
It is important to remember we are are talking about PSIS-LOO-CV... |
It is important to remember we are talking about PSIS-LOO-CV... |
Thanks Ero Carrera |
| 54 |
2. rank: The ranking on the models starting... |
2. rank: The ranking of the models starting... |
Thanks Ero Carrera |
| 54 |
4. p_loo: The list values for the... |
4. p_loo: The list of values for the... |
Thanks Ero Carrera |
| 54 |
...the actual number of parameters in model that has more structure like hierarchical models or can be much higher than the actual.. |
...the actual number of parameters in a model that has more structure like a hierarchical model or can be much higher than the actual... |
Thanks Ero Carrera |
| 58 |
...we can obtain some additional additional information. |
...we can obtain some additional information. |
Thanks Ero Carrera |
| 58 |
...comparing p_loo to the number of parameters $p$ can provides us with... |
...comparing p_loo to the number of parameters $p$ can provide us with... |
Thanks Ero Carrera |
| 59 |
...which is transformation in 1D where we can... |
...which is a transformation in 1D where we can... |
Thanks Ero Carrera |
| 61 |
When using a logarithmic scoring rule this is equivalently to compute: |
When using a logarithmic scoring rule this is equivalent to computing: |
Thanks Ero Carrera |
| 61 |
$\max_{n} \frac{1}{n} \sum_{i=1}^{n}log\sum_{j=1}^{k} w_j p(y_i \mid y_{-i}, M_j)$ |
$\max_{w} \frac{1}{n} \sum_{i=1}^{n}log\sum_{j=1}^{k} w_j p(y_i \mid y_{-i}, M_j)$ |
Thanks Ikaro Silva |
| 61 |
...the computation of the weights take into account all models together. |
...the computation of the weights takes into account all models together. |
Thanks Ero Carrera |
| 61 |
...the weights computed with az.compare(., method="stacking"), makes a lot of sense. |
...the weights computed with az.compare(., method="stacking") makes a lot of sense. |
Thanks Ero Carrera |
| 62 |
...Reproduce Figure 2.7, but using az.plot_loo(ecdf=True)... |
...Reproduce Figure 2.7, but using az.plot_loo_pit(ecdf=True)... |
Thanks Alihan Zihna |
| 62 |
Use az.load_arviz_data(.) to load them... |
Use az.from_netcdf(.) to load them... |
Thanks Ikaro Silva |
| 64 |
...and prior distribution $\mathcal{N}(201)... |
...and prior distribution $\mathcal{N}(20, 1)... |
|
| 70 |
|
Figure 3.3 updated to include vertical lines of empirical estimate |
|
| 71 |
Take a moment to compare the estimate of the mean with the summary mean shows... |
Take a moment to compare the estimate of the mean with the summary mean shown... |
Thanks Sebastian |
| 73 |
...the thin line is the interquartile range from 25% to 75% of the posterior and the thick line is the 94% Highest Density Interval |
the thick line is the interquartile range and the thin line is the 94% Highest Density Interval |
Thanks Jose Roberto Ayala Solares |
| 73 |
... more compostable modeling and inference. |
... more composable modeling and inference. |
|
| 75 |
... is the intercept only regression model from
|
is the intercept only regression model in Code Block
|
|
| 77 |
...where the coefficients, also referred to as covariates, are represented by the parameter $\beta_i$... |
...where the coefficients, also referred as parameters, are represented with $\beta_i$. |
Thanks Sebastian |
| 78 |
to parse the categorical information into a design matrix mu = pd.get_dummies(penguins["species"]) @ μ. where |
...to parse the categorical information into a design matrix, and then write mu = pd.get_dummies(penguins["species"]) @ μ, where... |
Thanks Sebastian |
| 81 |
...we would expect the mass of this impossible penguin to somewhere between -4213 and -546 grams. |
...we would expect the mass of this impossible penguin to be somewhere between -4151 and -510 grams. |
Thanks Sebastian |
| 83 |
...which takes a set a value... |
...which takes a set of values... |
Thanks Sebastian |
| 86 |
...has dropped a mean of 462 grams ... to a mean value 298 grams... |
...has dropped from a mean of 462 grams ... to a mean value of 298 grams... |
Thanks Sebastian |
| 88 |
...which lower value than estimated... |
...which is a lower value than the estimated... |
Thanks Sebastian |
| 89 |
...which useful for counterfactual analyses. |
...which is useful for counterfactual analyses. |
Thanks Sebastian |
| 91 |
We are still dealing a linear model here... |
We are still dealing with a linear model here... |
Thanks Sebastian |
| 93 |
...we find it reasonable to equally expect a Gentoo penguin... |
...we find it reasonable to equally expect a Chinstrap penguin... |
Thanks Sebastian |
| 97 |
...and Fig. 3.22.A separation... |
...and Fig. 3.22. A separation... |
Thanks Sebastian |
| 98 |
...from Adelie or Chinstrap penguinsthe... |
...from Adelie or Chinstrap penguins the... |
Thanks Sebastian |
| 101 |
Given these choices we can write our model in Code Block 3.30**)**... |
Given these choices we can write our model in Code Block 3.30 |
Thanks Sebastian |
| 101 |
This is not a fully uninformative priors... |
This is not a fully uninformative prior... |
Thanks Sebastian |
| 102 |
...fall into bounds that more reasonable... |
...fall into bounds that are more reasonable... |
Thanks Sebastian |
| 126 |
... describes the distribution of for the parameters of the prior itself... |
... describes the distribution for the parameters of the prior itself... |
|
| 130 |
...the estimates of the pizza and salad categories... |
...the estimates of the pizza and sandwich categories... |
Thanks @paw-lu |
| 133 |
(In Code Block 9.1) inside function gen_hierarchical_salad_sales all reference to hierarchical_salad_df
|
should be input_df
|
Thanks Alihan Zihna |
| 156 |
Fig 5.7 y_labels is count_std
|
should be count_normalized
|
Thanks Paulo S. Costa |
| 183 |
...a backshift operator, also called Lag operator) |
...a backshift operator **(**also called Lag operator) |
|
| 189 |
Equation (6.9) $y_t = \alpha + \sum_{i=1}^{p}\phi_i y_{t-period-i} + \sum_{j=1}^{q}\theta_j \epsilon_{t-period-j} + \epsilon_t$
|
$y_t = \alpha + \sum_{i=1}^{p}\phi_i y_{t-period \cdot i} + \sum_{j=1}^{q}\theta_j \epsilon_{t-period \cdot j} + \epsilon_t$ |
Thanks Marcin Elantkowski |
| 191 |
(footnote) The Stan implementation of SARIMA can be found in https://github.com/asael697/**varstan**. |
The Stan implementation of SARIMA can be found in e.g., https://github.com/asael697/**bayesforecast**. |
|
| 197 |
we can apply the Kalman filter to to obtains the posterior |
we can apply the Kalman filter to obtain the posterior |
|
| 227 |
Only the first 2 independent variables are unrelated... |
Only the first 2 independent variables are related... |
Thanks icfly2 |
| 261 |
Some commons elements to all Bayesian analyses, |
Some common elements to all Bayesian analyses, |
Thanks Ero Carrera |
| 262 |
(In Figure 9.1.) Model Compasion
|
Model Comparison
|
Thanks Ben Vincent |
| 262 |
...averaging some of all of them, or even presenting all the models and discussing their strength and... |
...averaging some or all of them, or even presenting all the models and discussing their strengths and... |
Thanks Ero Carrera |
| 262 |
A more detailed version of the Bayesian workflow can be see in a paper... |
A more detailed version of the Bayesian workflow can be seen in a paper... |
Thanks Ero Carrera |
| 262 |
...but should not be confused with driving question... |
...but should not be confused with the driving question... |
Thanks Ero Carrera |
| 264 |
...report regarding the potential financial affects. |
...report regarding the potential financial effects. |
Thanks Ero Carrera |
| 264 |
...risk of making a poor decision far outweights... |
...risk of making a poor decision far outweighs... |
Thanks Ero Carrera |
| 264 |
...in the sub-sections with title start with Applied Example. |
...in the sub-sections with titles starting with Applied Example. |
Thanks Ero Carrera |
| 264 |
Likewise inference is impossible without data. challenging with poor quality data, and the best statisticians... |
Likewise, inference is impossible without data and challenging with poor quality data. The best statisticians... |
Thanks Ero Carrera |
| 264 |
For statistician the equivalent is Sample surveys... |
For statistician the equivalent is sample surveys... |
Thanks Ero Carrera |
| 265 |
foraging for ingredients are growing by themselves. |
foraging for ingredients that are growing by themselves. |
|
| 265 |
When collecting data be sure not only pay attention to what is present, but consider what may not be present. |
When collecting data be sure to not only pay attention to what is present, but consider also what may not be present. |
Thanks Ero Carrera |
| 267 |
We do this using numerous tools, diagnostics, and visualizations that we have seen through out this book. |
We do this using the numerous tools, diagnostics, and visualizations that we have seen throughout this book. |
Thanks Ero Carrera |
| 267 |
The fundamentals of Bayes formula has no opinion... |
The fundamentals of Bayes formula have no opinion... |
Thanks Ero Carrera |
| 267 |
We take a moment to collect our detail... |
We take a moment to collect in detail... |
Thanks Ero Carrera |
| 267 |
(In Code Block 9.1) df = pd.read_csv("../data/948363589_T_ONTIME_MARKETING.zip",
|
df = pd.read_csv("../data/948363589_T_ONTIME_MARKETING.zip") |
|
| 269 |
...or likelihood distributions are preordained, What is printed in this book... |
...or likelihood distributions are preordained. What is printed in this book... |
Thanks Ero Carrera |
| 276 |
We can also generate a visual check with 9.7which
|
We can also generate a visual check with Code Block 9.7 which
|
|
| 276 |
Thus, there still room for improvement... |
Thus, there is still room for improvement... |
Thanks Ero Carrera |
| 276 |
What is important at this step is we are sufficiently... |
What is important at this step is that we are sufficiently... |
Thanks Ero Carrera |
| 277 |
...maps how wet or dry a person’s clothes is to... |
...maps how wet or dry a person’s clothes are to... |
Thanks Ero Carrera |
| 277 |
...map those outcomes to expected reward... |
...map those outcomes to expected rewards... |
Thanks Ero Carrera |
| 280 |
...the airline, If a flight is between 0 and 10 minutes late, the fee is 1,000 dollars. if the flight is... |
...the airline, if a flight is between 0 and 10 minutes late, the fee is 1,000 dollars. If the flight is... |
Thanks Ero Carrera |
| 280 |
...more time than all the previous one combined. |
...more time than all the previous ones combined. |
Thanks Ero Carrera |
| 281 |
...and legality but is important to note this. |
...and legal considerations but is important to note this. |
Thanks Ero Carrera |
| 282 |
When environments cannot be replicated one outcome is code that was working... |
When environments cannot be replicated one possible outcome is that code that used to work... |
Thanks Ero Carrera |
| 282 |
This can occur because the library may change, or the algorithm itself. |
This can occur because the libraries may change, or the algorithms themselves. |
Thanks Ero Carrera |
| 282 |
workflow should be robust that changing the seed |
workflow should be robust so that changing the seed |
Thanks Ero Carrera |
| 282 |
In short reproducible analyses both helps you and others build confidence in your prior results, and also helps future efforts extend the work. |
In short reproducible analyses both help you and others build confidence in your prior results, and also help future efforts extend the work. |
Thanks Ero Carrera |
| 284 |
which used a shaking needle gauge to highlight. |
highlight the uncertainty in the estimation of which candidate would ultimately win.
|
Thanks ST John |
| 284 |
or the randomness of the plinko drops in Matthew Kay's |
or the randomness of the Plinko drops in Matthew Kay's |
|
| 286 |
... a cross section area of .504 inches (12.8mm) by .057 inches (1.27)... |
... a cross section area of .504 inches (12.8 mm) by .057 inches (1.27 mm)... |
Thanks Juan Orduz |
| 289 |
... In both the plots a value of 0 seems is relatively unlikely ... |
... In both the plots a value of 0 is relatively unlikely ... |
|
| 297 |
|
Equation 10.1 and Code 10.4 updated for readability |
Thanks ST John |
| 299 |
The Zen of Python detai the philosophy behind this idea of pythonic design... |
The Zen of Python details the philosophy behind the idea of pythonic design ... |
|
| 318 |
As you can see, there is a lot of rooms for... |
As you can see, there is a lot of room for... |
|
| 344 |
...will make the skweness independent... |
...will make the skewness independent... |
Thanks Alihan Zihna |
| 371 |
...a simple Python implementation in Code block
|
...simple Python implementation in Code Block
|
|
| 376 |
We can see that all these trajectories when wrong. We call this kind these divergences and we can used as diagnostics of the HMC samplers. |
We can see that all these trajectories went wrong. We call this kind of trajectories divergences and can be used as a diagnostic of HMC samplers |
Thanks Alihan Zihna |
| 380 |
... if you future lab... |
... if your future lab... |
Thanks Alihan Zihna |
| 385 |
...more parameters than can be justified by the data.[2]
|
... more parameters than can be justified by the data. |
|