# Markov Chain parameter estimates `mcmc_analyze` Computes summary histograms and model-data comparisons from and Markov Chain Monte Carlo parameter estimate for a given model ```r mcmc_analyze( model, data, mcmc_out, mode = "emp", initial_condition = NULL, deltaT = NULL, n_steps = NULL, verbose = TRUE ) ``` ## Arguments - `model`: the model equations that we use to compute the result. - `data`: the data used to assess the model - `mcmc_out`: A dataframe: the first column is the accept flag of the mcmc run (TRUE/FALSE), the log likelihood, and the parameter values - `mode`: two choices: emp --> empirical (default) or de --> differential equations. The estimator works differently depending on which is used. - `initial_condition`: The initial condition for the differential equation (DE mode only) - `deltaT`: The length between timesteps (DE mode only) - `n_steps`: The number of time steps we run the model (DE mode only) - `verbose`: TRUE / FALSE indicate if parameter estimates should be printed to console (option, defaults to TRUE) ## Returns Two plots: (1) fitted model results compared to data, and (2) pairwise parameter histograms and scatterplots to test model equifinality. ## Examples ```r ## Example with an empirical model: ## Step 1: Define the model and parameters phos_model <- daphnia ~ c * algae^(1 / theta) phos_param <- tibble::tibble( name = c("c", "theta"), lower_bound = c(0, 1), upper_bound = c(2, 20)) ## Step 2: Determine MCMC settings # Define the number of iterations phos_iter <- 1000 ## Step 3: Compute MCMC estimate phos_mcmc <- mcmc_estimate(model = phos_model, data = phosphorous, parameters = phos_param, iterations = phos_iter) ## Step 4: Analyze results: mcmc_analyze(model = phos_model, data = phosphorous, mcmc_out = phos_mcmc) ## Example with a differential equation: ## Step 1: Define the model, parameters, and data ## Define the tourism model tourism_model <- c(dRdt ~ resources * (1 - resources) - a * visitors, dVdt ~ b * visitors * (resources - visitors)) # Define the parameters that you will use with their bounds tourism_param <- tibble::tibble( name = c("a", "b"), lower_bound = c(10, 0), upper_bound = c(30, 5)) ## Step 2: Determine MCMC settings # Define the initial conditions tourism_init <- c(resources = 0.995, visitors = 0.00167) deltaT <- .1 # timestep length n_steps <- 15 # must be a number greater than 1 # Define the number of iterations tourism_iter <- 1000 ## Step 3: Compute MCMC estimate tourism_out <- mcmc_estimate( model = tourism_model, data = parks, parameters = tourism_param, mode = "de", initial_condition = tourism_init, deltaT = deltaT, n_steps = n_steps, iterations = tourism_iter) ## Step 4: Analyze results mcmc_analyze( model = tourism_model, data = parks, mcmc_out = tourism_out, mode = "de", initial_condition = tourism_init, deltaT = deltaT, n_steps = n_steps ) ``` ## See Also `mcmc_estimate`

mcmc_analyze function