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What is Bayesian analysis?
Bayesian analysis is a statistical analysis that answers research questions about unknown parameters
of statistical models by using probability statements. Bayesian analysis rests on the assumption that
all model parameters are random quantities and thus are subjects to prior knowledge. This assumption
is in sharp contrast with the more traditional, also called frequentist, statistical inference where all
parameters are considered unknown but fixed quantities. Bayesian analysis follows a simple rule
of probability, the Bayes rule, which provides a formalism for combining prior information with
evidence from the data at hand. The Bayes rule is used to form the so called posterior distribution of
model parameters. The posterior distribution results from updating the prior knowledge about model
parameters with evidence from the observed data. Bayesian analysis uses the posterior distribution to
form various summaries for the model parameters including point estimates such as posterior means,
medians, percentiles, and interval estimates such as credible intervals. Moreover, all statistical tests
about model parameters can be expressed as probability statements based on the estimated posterior
distribution.

Frequentist hypothesis testing is based on a deterministic decision using a prespecified significance
level of whether to accept or reject the null hypothesis based on the observed data, assuming that
the null hypothesis is actually true. The decision is based on a p-value computed from the observed
data. The interpretation of the p-value is that if we repeat the same experiment and use the same
testing procedure many times, then given our null hypothesis is true, we will observe the result (test
statistic) as extreme or more extreme than the one observed in the sample (100 p-value)% of the
times. The p-value cannot be interpreted as a probability of the null hypothesis, which is a common
misinterpretation. In fact, it answers the question of how likely are our data given that the null
hypothesis is true, and not how likely is the null hypothesis given our data. The latter question can
be answered by Bayesian hypothesis testing, where we can compute the probability of any hypothesis
of interest.

Stata 16 has a new suite of commands for performing meta-analysis. This suite lets you explore and combine the results from different studies. For instance, if you have collected results from 20 studies about the effect of a particular drug on blood pressure, you can summarize these studies and estimate the overall effect using meta-analysis.
The new meta suite is broad, but what sets it apart is its simplicity.
You can type, for instance,
. meta set effectsize stderr
to declare precomputed effect sizes or use meta esize to compute effects from summary data. With this, you can perform random-effects, fixed-effects, or common-effect meta-analysis.
To estimate an overall effect size and its confidence interval, obtain heterogeneity statistics, and more, you simply type
. meta summarize
And visualizing the results is as easy as typing
. meta forestplot
But the meta suite provides much more.
Meta-regression and subgroup analysis allow you to evaluate the heterogeneity of studies. These are available via meta regress and meta forestplot, subgroup() or meta summarize, subgroup().
You can investigate potential publication bias. Check visually for funnel-plot asymmetry using meta funnelplot; formally test for funnel-plot asymmetry using meta bias; and assess publication bias using the trim-and-fill method with meta trimfill.
You can even perform cumulative meta-analysis with meta summarize, cumulative().
All the meta-analysis features are documented in the new Meta-analysis Reference Manual.

Nonlinear DSGE models in Stata 15
In Stata 15, we introduced the dsge command for fitting linear DSGE models, which are time-series models used in economics and finance. These models are an alternative to traditional forecasting models. Both attempt to explain aggregate economic phenomena, but DSGE models do this on the basis of models derived from microeconomic theory.
New in Stata 16, the dsgenl command fits nonlinear DSGE models. Most DSGE models are nonlinear, and this means that you no longer need to linearize them by hand. When you enter equations into dsgenl, it linearizes them for you.
After estimating the parameters of your model with dsgenl, you can obtain the transition and policy matrices; determine the model’s steady state; estimate variables’ variances, covariances, and autocovariances implied by the system of equations; and create and graph impulse–response functions.
This is likely to be the favorite feature of macroeconomists and anyone working in a central bank.
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