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In Bayesian analysis, we seek a balance between prior information in a form of expert knowledge
or belief and evidence from data at hand. Achieving the right balance is one of the difficulties in
Bayesian modeling and inference. In general, we should not allow the prior information to overwhelm
the evidence from the data, especially when we have a large data sample. A famous theoretical
result, the Bernstein–von Mises theorem, states that in large data samples, the posterior distribution is
independent of the prior distribution and, therefore, Bayesian and likelihood-based inferences should
yield essentially the same results. On the other hand, we need a strong enough prior to support weak
evidence that usually comes from insufficient data. It is always good practice to perform sensitivity
analysis to check the dependence of the results on the choice of a prior.

Multiple datasets in memory in Stata 16
You can now load multiple datasets into memory. You type
. use people
and people.dta is loaded into memory. Next, you type
. frame create counties
. frame counties: use counties
and you have two datasets in memory. people.dta is in the frame named default, and counties.dta is in the frame named counties. Your current frame is still default. Most Stata commands use the data in the current frame. For example, if you typed
. list
then people.dta will be listed. If you typed
. frame counties: list
then counties.dta will be listed. Or you could make counties the current frame by typing
. frame change counties
and list will now list the counties data.
Navigating frames is easy and so is linking them. Imagine that both datasets have a variable named countycode that identifies counties in the same way. Type
. frlink m:1 countycode, frame(counties)
and each person in the default frame is linked to a county in the counties frame. This means you can now use the frget command to copy variables from the counties frame to the current frame. Or you can use the frval() function to directly access the values of variables in the counties frame. For instance, if we have each individual’s income in the default frame and median county income in the counties frame, we can generate a new variable containing relative income by typing
. generate rel_income = income / frval(counties, median_income)
This is the beginning. While this example uses only two frames, you can have up to 100 frames in memory at once, and you can have many links among those frames.

Sample-size analysis for confidence intervals in Stata 16
The new ciwidth command performs Precision and Sample Size (PrSS) analysis, which is sample-size analysis for confidence intervals (CIs). This method is used when you are planning a study and you want to optimally allocate resources when CIs are to be used for inference. Said differently, you use this method when you want to estimate the sample size required to achieve the desired precision of a CI in a planned study.
ciwidth produces sample sizes, precision, and more that are required for the
• CI for one mean
• CI for one variance
• CI for two independent means
• CI for two paired means
The control panel interface lets you select the analysis type and input assumptions to obtain desired results.
ciwidth allows results to be displayed in customizable tables and graphs.
ciwidth also provides facilities for you to add your own methods.

Posterior / Likelihood Prior
If the posterior distribution can be derived in a closed form, we may proceed directly to the
inference stage of Bayesian analysis. Unfortunately, except for some special models, the posterior
distribution is rarely available explicitly and needs to be estimated via simulations. MCMC sampling
can be used to simulate potentially very complex posterior models with an arbitrary level of precision.
MCMC methods for simulating Bayesian models are often demanding in terms of specifying an efficient
sampling algorithm and verifying the convergence of the algorithm to the desired posterior distribution.
Inference is the next step of Bayesian analysis. If MCMC sampling is used for approximating the
posterior distribution, the convergence of MCMC must be established before proceeding to inference.
Point and interval estimators are either derived from the theoretical posterior distribution or estimated
from a sample simulated from the posterior distribution. Many Bayesian estimators, such as posterior
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