Parameter identifiability example - Revision history

Elena.kutumova@biouml.org: /* Interpretation of results */

2022-03-18T07:09:29Z

‎Interpretation of results

Elena.kutumova@biouml.org: /* Interpretation of results */

2022-03-18T06:45:47Z

‎Interpretation of results

Elena.kutumova@biouml.org: /* Interpretation of results */

2022-03-18T06:42:05Z

‎Interpretation of results

Elena.kutumova@biouml.org: /* Interpretation of results */

2022-03-18T06:38:20Z

‎Interpretation of results

Elena.kutumova@biouml.org: /* Parameter identifiability (table) */

2022-03-18T03:16:41Z

‎Parameter identifiability (table)

Elena.kutumova@biouml.org: /* Parameter identifiability (table) */

2022-03-18T03:16:25Z

‎Parameter identifiability (table)

Elena.kutumova@biouml.org: /* Parameter identifiability (table) */

2022-03-18T03:16:00Z

‎Parameter identifiability (table)

Elena.kutumova@biouml.org: /* Parameter identifiability (table) */

2022-03-18T03:14:20Z

‎Parameter identifiability (table)

Elena.kutumova@biouml.org: /* Parameter identifiability (optimization) */

2022-03-18T03:02:36Z

‎Parameter identifiability (optimization)

Elena.kutumova@biouml.org: /* Parameter identifiability (optimization) */

2022-03-18T03:01:49Z

‎Parameter identifiability (optimization)

@@ Line 143: / Line 143: @@
 An increase in the ''J9_V10'' value (steps to the right) gave a stable increase in the objective function value. However, the specified threshold was not exceeded because the parameter value reached the upper bound of the search space. Thus, changing the boundaries of the search space in the optimization problem can change the identifiability profile of model parameters.
-It is also worth noting that the step sizes automatically determined by the algorithm, in particular, depend on how close the value of the fitting parameter is to the search boundary. As can be seen from the identifiability profiles above, for parameters ''J5_V6'', ''J8_V9'', and ''J9_V10'', steps to the right are much smaller than steps to the left.
+It is also worth noting that the step sizes automatically determined by the algorithm, in particular, depend on how close the value of the fitting parameter is to the search boundary. As can be seen from the identifiability profiles above, for parameters ''J5_V6'', ''J8_V9'', and ''J9_V10'', steps to the right are much smaller than steps to the left. An increase in the upper search bounds for these parameters leads to finding a new solution to the optimization problem (the value of the objective function is 31.7 versus 42.2). In this case, all parameters become identifiable:
 ==References==

@@ Line 143: / Line 143: @@
 An increase in the ''J9_V10'' value (steps to the right) gave a stable increase in the objective function value. However, the specified threshold was not exceeded because the parameter value reached the upper bound of the search space. Thus, changing the boundaries of the search space in the optimization problem can change the identifiability profile of model parameters.
-It is also worth noting that the step sizes automatically determined by the algorithm, in particular, depend on how close the value of the fitting parameter is to the search boundary.
+It is also worth noting that the step sizes automatically determined by the algorithm, in particular, depend on how close the value of the fitting parameter is to the search boundary. As can be seen from the identifiability profiles above, for parameters ''J5_V6'', ''J8_V9'', and ''J9_V10'', steps to the right are much smaller than steps to the left.
 ==References==

← Older revision		Revision as of 06:42, 18 March 2022
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	An increase in the ''J9_V10'' value (steps to the right) gave a stable increase in the objective function value. However, the specified threshold was not exceeded because the parameter value reached the upper bound of the search space. Thus, changing the boundaries of the search space in the optimization problem can change the identifiability profile of model parameters.		An increase in the ''J9_V10'' value (steps to the right) gave a stable increase in the objective function value. However, the specified threshold was not exceeded because the parameter value reached the upper bound of the search space. Thus, changing the boundaries of the search space in the optimization problem can change the identifiability profile of model parameters.
		+
		+	It is also worth noting that the step sizes automatically determined by the algorithm, in particular, depend on how close the value of the fitting parameter is to the search boundary.

	==References==		==References==

@@ Line 129: / Line 129: @@
 <br>[[File:parameter_identifiability_results.png]]<br><br>
-Identifiability profiles for parameters ''J0_V1'', ''J1_V2'', ''J4_V5'', ''J8_V9'' cross the threshold of a given deviation from the initial objective function value in both directions. Therefore, the analysis defined these variables as identifiable. The identifiability profiles for parameters ''J5_V6'' and ''J9_V10'' cross the threshold in only one direction, so the analysis determined these parameters as partially non-identifiable. However, it should be noted that the resulting ''J5_V6'' value in the optimization problem is almost equal to the upper bound of the given feasible region. Thus, the identifiability analysis tried to take very small steps to the right in the parameter value, but this was not enough to significantly change the objective function value:
+Identifiability profiles for parameters ''J0_V1'', ''J1_V2'', ''J4_V5'', ''J8_V9'' cross the threshold of a given deviation from the initial objective function value in both directions. Therefore, the analysis defined these variables as identifiable. The identifiability profiles for parameters ''J5_V6'' and ''J9_V10'' cross the threshold in only one direction, so the analysis determined these parameters as partially non-identifiable. However, it should be noted that the resulting ''J5_V6'' value in the optimization problem is almost equal to the upper bound of the given search space. Thus, the identifiability analysis tried to take very small steps to the right in the parameter value, but this was not enough to significantly change the objective function value:
 <code>
@@ Line 141: / Line 141: @@
 </code>
-An increase in the ''J9_V10'' value (steps to the right) gave a stable increase in the objective function value. However, the specified threshold was not exceeded because the parameter value reached the upper bound of the feasible region. Thus, changing the boundaries of the feasible region of the optimization problem can change the identifiability profile of the model parameters.
+An increase in the ''J9_V10'' value (steps to the right) gave a stable increase in the objective function value. However, the specified threshold was not exceeded because the parameter value reached the upper bound of the search space. Thus, changing the boundaries of the search space in the optimization problem can change the identifiability profile of model parameters.
 ==References==

@@ Line 101: / Line 101: @@
 <br>[[File:parameter_identifiability_example_02.png]]<br><br>
-Then click on the phrase "<u>Show expert options>></u>":
+Then click on the phrase "<u>Show expert options >></u>":
 <br>[[File:parameter_identifiability_example_03.png]]<br><br>

@@ Line 82: / Line 82: @@
 '''Time column''' = ''time''
-<li>The maximum number of steps performed by the analysis for each test variable in one direction:<br>
+<li>The maximum number of steps performed by the analysis for each fitting parameter in one direction:<br>
 '''Maximum identifiability steps''' = 50

@@ Line 36: / Line 36: @@
 '''Maximum identifiability steps''' = 50
-<li>As the maximal deviation from the initial objective function value, we considered ten percent of the smallest objective function value (found by the optimization and corresponding to the results in the ''optimizationInfo'' table):<br>
+<li>As the maximal deviation from the initial objective function value (allowable threshold), we considered ten percent of the smallest objective function value (found by the optimization and corresponding to the results in the ''optimizationInfo'' table):<br>
 '''Maximal deviation''' = 4.2