# ssEst: Steady State Estimate In BayesMassBal: Bayesian Data Reconciliation of Separation Processes

 ssEst R Documentation

### Description

Allows for the estimation of process steady state of a single stream for a process using flow rate data.

### Usage

ssEst(y, BTE = c(100, 1000, 1), stationary = FALSE)


### Arguments

 y Vector of mass flow rate observations. Must be specified sequentially with y[1] as the initial observation. BTE Numeric vector giving c(Burn-in, Total-iterations, and Every) for MCMC approximation of target distributions. The function BMB produces a total number of samples of (T - B)/E. E specifies that only one of every E draws are saved. E > 1 reduces autocorrelation between obtained samples at the expense of computation time. stationary Logical indicating if stationarity will be imposed when generating posterior draws. See Details.

### Details

The model of the following form is fit to the data:

y_t = μ + α y_{t-1} + ε

Where ε \sim \mathcal{N}(0,σ^2) and t indexes the time step.

A time series is stationary, and predictable, when |α|< 1. Stationarity can be enforced, using the argument setting stationary = TRUE. This setting utilizes the priors p(α) \sim \mathcal{N}(0, 1000) truncated at (-1,1), and p(μ) \sim \mathcal{N}(0, var(y)*100) for inference, producing a posterior distribution for α constrained to be within (-1,1).

When fitting a model where stationarity is not enforced, the Jeffreys prior of p(μ,α)\propto 1 is used.

The Jeffreys prior of p(σ^2)\propto 1/σ^2 is used for all inference of σ^2

A stationary time series will have an expected value of:

\frac{μ}{1-α}

Samples of this expectation are included in the output if stationary = TRUE or if none of the samples of α lie outside of (-1,1).

The output list is a BMB object, passing the output to plot.BayesMassBal allows for observation of the results.

### Value

Returns a list of outputs

 samples List of vectors containing posterior draws of model parameters stationary Logical indicating the setting of the stationary argument provided to the ssEst function y Vector of observations initially passed to the ssEst function. type Character string giving details of the model fit. Primarily included for use with plot.BayesMassBal

### Examples


## Generating Data
y <- rep(NA, times = 21)

y[1] <- 0
mu <- 3
alpha <- 0.3
sig <- 2
for(i in 2:21){
y[i] <- mu + alpha*y[i-1] + rnorm(1)*sig
}

## Generating draws of model parameters

fit <- ssEst(y, BTE = c(100,500,1))



BayesMassBal documentation built on June 18, 2022, 1:08 a.m.