I am writing a program that attempts to duplicate the algorithm discussed at the beginning of this article,

<http://www-stat.stanford.edu/~cgates/PERSI/papers/MCMCRev.pdf>

F is a function from char to char. Assume that Pl(f) is a 'plausibility' measure of that function. The algorithm is:

Starting with a preliminary guess at the function, say f, and a then new function f\* --

* Compute Pl(f).
* Change to f\* by making a random transposition of the values f assigns to two symbols.
* Compute Pl(f\*); if this is larger than Pl(f), accept f\*.
* If not, flip a Pl(f)/Pl(f\*) coin; if it comes up heads, accept f\*.
* If the coin toss comes up tails, stay at f.

I am implementing this using the following code. I'm using c# but tried to make it somewhat more simplified for everyone. If there is a better forum for this please let me know. 

```
 var current_f = Initial();    // current accepted function f
 var current_Pl_f = InitialPl();  // current plausibility of accepted function f

 for (int i = 0; i < 10000; i++)
        {
            var candidate_f = Transpose(current_f); // create a candidate function

            var candidate_Pl_f = ComputePl(candidate_f);  // compute its plausibility

            if (candidate_Pl_f > current_Pl_f)            // candidate Pl has improved
            {
                current_f = candidate_f;            // accept the candidate
                current_Pl_f = candidate_Pl_f; 
            }
            else                                    // otherwise flip a coin
            {
                int flip = Flip(); 

                if (flip == 1)                      // heads
                {
                    current_f = candidate_f;        // accept it anyway
                    current_Pl_f = candidate_Pl_f; 
                }
                else if (flip == 0)                 // tails
                {
                    // what to do here ?
                }
            }
        }

```

My question is basically whether this looks like the optimal approach to implementing that algorithm. IT seems like I may be getting stuck in some local maxima / local minima despite implementing this method. 

**EDIT** - Here is the essentially whats behind Transpose() method. I use a dictionary / hash table of type << char, char >> that the candidate function(s) use to look any given char -> char transformation. So the transpose method simply swaps two values in the dictionary that dictates the behavior of the function. 

```
    private Dictionary<char, char> Transpose(Dictionary<char, char> map, params int[] indices)
    {
        foreach (var index in indices)
        {
            char target_val = map.ElementAt(index).Value;   // get the value at the index

            char target_key = map.ElementAt(index).Key;     // get the key at the index

            int _rand = _random.Next(map.Count);   // get a random key (char) to swap with

            char rand_key = map.ElementAt(_rand).Key;

            char source_val = map[rand_key]; // the value that currently is used by the source of the swap

            map[target_key] = source_val; // make the swap

            map[rand_key] = target_val;
        }

        return map; 
    }

```

Keep in mind that a candidate function that uses the underlying dictionary is basically just:

```
public char GetChar(char in, Dictionary<char, char> theMap)
{
     return theMap[char]; 
}

```

And this is the function that computes Pl(f):

```
    public decimal ComputePl(Func<char, char> candidate, string encrypted, decimal[][] _matrix)
    {
        decimal product = default(decimal);

        for (int i = 0; i < encrypted.Length; i++)
        {
            int j = i + 1;

            if (j >= encrypted.Length)
            {
                break;
            }

            char a = candidate(encrypted[i]);
            char b = candidate(encrypted[j]);

            int _a = GetIndex(_alphabet, a); // _alphabet is just a string/char[] of all avl chars 
            int _b = GetIndex(_alphabet, b);

            decimal _freq = _matrix[_a][_b]; 

            if (product == default(decimal))
            {
                product = _freq;
            }
            else
            {
                product = product * _freq;
            }
        }

        return product;
    }

```